project_thesis_syed

Design of Linear Ultrasonic Motor (LUM) Using
Finite Element Analysis (FEA)
M. Tech. Dissertation in
Electrical Machinery Design
Department of Electrical Engineering
Submitted By : SYED SAQLAINE G
Reg. No. : 14ETEE034005
Supervisor : Mr. VEERABHADRA
Assistant Professor, Dept. of EE, MSRUAS
August – 2016
FACULTY OF ENGINEERING AND TECHNOLOGY
M. S. RAMAIAH UNIVERSITY OF APPLIED SCIENCES
BENGALURU -560 054

Design of Linear Ultrasonic Motor Using FEA
ii
Faculty of Engineering and Technology
Certificate
This is to certify that the Dissertation titled “Design of Linear
Ultrasonic Motor (LUM) Using Finite Element Analysis (FEA)” is a
bonafide record of the work carried out by Mr. Syed Saqlaine G, Reg. No.
14ETEE034005 in partial fulfilment of requirements for the award of M.
Tech. Degree of M S Ramaiah University of Applied Sciences in the
Department of Electrical Engineering.
August – 2016
Mr. VEERABHADRA
Academic Supervisor
Assistant Professor Dept. of EE MSRUAS
Dr. K. Manickavasagam Prof. H. K. Narahari
Head-Dept. Of EE, MSRUAS Dean-FET, MSRUAS

M.S. Ramaiah University of Applied Sciences – Faculty of Engineering and Technology (FET)
iii
Declaration
“Design of Linear Ultrasonic Motor (LUM) Using Finite Element
Analysis (FEA)”
The dissertation is submitted in partial fulfilment of academic
requirements for the M.Tech. Degree of M. S. Ramaiah University of
Applied Sciences in the Department of Electrical Engineering. This
dissertation is a result of my own investigation. All sections of the text and
results, which have been obtained from other sources, are fully referenced.
I understood that cheating and plagiarism constitute a breach of University
regulations, hence this dissertation has been passed through plagiarism
check and the report has been submitted to the supervisor.
Signature :
Name of the Student : Mr. Syed Saqlaine G
Reg. No. : 14ETEE034005
Date : 23 August 2016

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Acknowledgement
It is my great pleasure to express my sincere thanks and gratitude to my
academic guides, Mr. VEERABHADRA, Assistant professor, Department of Electrical
Engineering Department, MSRUAS, for their valuable suggestions and guidance for the
successful completion of my project.
I would also like to thank Dr. K. Manickavasagam HOD of Electrical Engineering
Department, MSRUAS for his encouragement, guidance and support for successful
completion of my project.
I would also like to thank Mr. ISHWAR MARA from TECHNO CENTRE Engineering,
MSRUAS for his encouragement, guidance and support for successful completion of my
project. He helped me in understanding the software tools.
I would also like to thank Mr. RITENDRA MISHRA from Defence Institute of High
Altitude Research, DRDO, Leh, Ladakh for his encouragement, guidance and support for
successful completion of my project. He helped me in understanding the working
principle of Ultrasonic Motor.
I would like to express my thanks and gratitude to Dr. H K Narahari, Dean of
MSRUAS for giving me the opportunity to study this course and for his continuous
support, advice, guidance and encouragement throughout the completion of the
project. I am thankful to the management of M .S. Ramaiah University of Applied
Sciences for providing all the facilities and resources for the successful completion of the
course.

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Abstract
Recently technology is playing a lead role in many areas, such as robotics,
aerospace, automatic control, military industry, medical and chemical mixing instrument
that needs an exact control for chemical mixing. The electromagnetic motor is restricted
to provide more and more small motor likely to give high torque per weight unit. Hence
the consideration of researcher moved towards a new type of motor i.e. Ultrasonic
Motor.
In this thesis, the Linear Ultrasonic Motor with double sided stator has been
designed. It can be used to reduce the time and cost in the pipetting device. Model
analysis and harmonic analysis, the model analysis is carried out to find out the
frequency at which the motor will operate then with this frequency the velocity is
analysed. ANSYS APDL has been used to for the Finite element analysis.
The operating frequency for the Linear Ultrasonic Motor with double sided stator
is 27.93 KHz analytically and 27.94 KHz by Finite Element Analysis. The velocity was
found to be 127.64 mm/s. There are numerous strategies to enhance execution of
motor, for example, utilizing actuators that are made of multi-layer piezoelectric
earthenware production rather than single-layer piezoelectric pottery since they create
bigger mechanical yield for a given voltage, consequently yielding the higher engine
speed and driving burden.

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Table of Contents
Declaration...........................................................................................................................iii
Acknowledgement................................................................................................................iv
Abstract.................................................................................................................................v
Table of Contents..................................................................................................................vi
List of Tables....................................................................................................................... viii
List of Figures........................................................................................................................ix
Nomenclature........................................................................................................................x
Abbreviation and Acronyms..................................................................................................xi
1. Introduction.......................................................................................................................1
1.1 Introduction .................................................................................................................. 1
1.2 Motivation..................................................................................................................... 2
1.3 Techniques to design a compact LUM.......................................................................... 2
1.4 Organization of the Thesis ............................................................................................ 2
2. Literature Review and Problem Formulation ......................................................................4
2.1 Background Theory....................................................................................................... 4
2.1.1 Piezoelectric ceramic.......................................................................................... 4
2.1.2 Polarization......................................................................................................... 4
2.1.3 Limitations in piezoelectric materials................................................................. 6
2.1.4 Resonance Frequency......................................................................................... 7
2.2 Piezoelectric theory ...................................................................................................... 8
2.2.1 Piezoelectric constants....................................................................................... 8
2.2.2 Vibration modes ............................................................................................... 11
2.3 Applications................................................................................................................. 13
2.3.1 Generators........................................................................................................ 13
2.3.2 Actuators........................................................................................................... 14
2.4 Critical review of literature......................................................................................... 15

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2.5 Problem Formulation:................................................................................................. 20
2.6 Conclusions:......................................................................................................... 20
3. Problem Statement..........................................................................................................21
4. Problem Solving ...............................................................................................................23
4.1 Proposed Block Diagram............................................................................................. 23
4.2 Motor design process ................................................................................................. 23
4.3 Design of Linear Ultrasonic Motor.............................................................................. 24
4.4 Design of the Linear Ultrasonic Motor (LUM) ............................................................ 28
4.5 FEA Approach for LUM................................................................................................ 30
4.6 Conclusion................................................................................................................... 33
5. Results and Discussions....................................................................................................34
5.1 Analytical Calculation and Finite Element Results...................................................... 34
5.1.1 Operating Frequency........................................................................................ 34
5.1.2 Calculation of Velocity...................................................................................... 35
5.1.3 Current Calculation........................................................................................... 36
5.2 Validation of results obtained for LUM ...................................................................... 37
Conclusions and Future Directions .......................................................................................38
6.1 Conclusions ................................................................................................................. 38
6.2 Future Directions ........................................................................................................ 38
References...........................................................................................................................39

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List of Tables
Table 2.1 Elastoelectric matrix for T and E taken as independent variables ............................................. 11
Table 2.2 List of Literature review ............................................................................................................. 17
Table 4.2 Dimension of design .................................................................................................................. 29
Table 4.3 Material Properties of Linear Ultrasonic Motor ........................................................................ 30
Table 5.1 Analytical result of operating frequency ................................................................................... 34
Table 5.1 Operating frquency comparison between single sided and double sided lum.......................... 37
Table 5.2 Velocity comparision betwwen single sided and double sided lum .......................................... 37

ix
List of Figures
Figure. 2.1 Crystal Structure of Piezoelectric Ceramic .................................................................................5
Figure. 2.2 Polarizing a Piezoelectric Ceramic .............................................................................................5
Figure. 2.3 a) hysteresis curve for polarization, b) elongation / contraction of a ceramic element ............6
Figure 2.4 frequency response .....................................................................................................................8
Figure. 2.5 Axes notation .............................................................................................................................8
Figure. 2.5 Longitudinal Vibration Mode .................................................................................................. 12
Figure. 2.6 Transversal Vibration Mode .................................................................................................... 12
Figure. 2.7 The shear vibration mode ........................................................................................................ 13
Figure. 2.8 Piezoelectric ignition system ................................................................................................... 13
Figure. 2.9 a) Traveling wave ultrasonic motor developed b) application in a camera mechanism ........ 14
Figure 2.10 Pipette Device ......................................................................................................................... 15
Figure 4.1 Proposed Diagram of LUM. ...................................................................................................... 23
Figure 4.2 Developemnt process ............................................................................................................... 24
Figure 4.3 Block diagram of LUM .............................................................................................................. 29
Figure 4.4 Designed Model of LUM ........................................................................................................... 31
Figure 5.1 Finite Element Analysis Results ................................................................................................ 35
Figure 5.2 12th
Vibration Mode Shape ...................................................................................................... 35
Figure 5.3 Harmonic Response of the LUM ............................................................................................... 36

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Nomenclature
Symbol Description Units
b Width Mm
c Wave speed m/s
F Frequency 1/s
h Stator thickness Mm
ht Height of the teeth Mm
ha Actuator thickness Mm
I Moment of inertia Mm^4
L Length of beam Mm
La Length of actuator Mm
M Mass per unit length of
beam
Kg/mm
P
T
W
Tt
λ
Mass density
Time
Driving frequency
Thickness of teeth
wavelength
kg/m^3
s
1/s
Mm
mm

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Abbreviation and Acronyms
Acronyms Description
A
AC
D15
D31
D33
Fa
Fp
Fn
Fs
Fr
Fm
FEA
K
LUM
PZT
S
Signal amplitude
Alternating current
Shear modules
Transversal modules
Longitudinal modules
Antireosnance frequency
Parallel resonance frequency
Maximum impedance frequency
Series resonance frequency
Resonance frequency
Minimum impedance frequency
Finite element analysis
Electromechanical coupling factor
Linear Ultrasonic Motor
Lead zirconate titanate
Permittivity

xii
T
Y
Mechanical strain
Mechanical stress

M.S.Ramaiah University of Applied Sciences – Faculty of Engineering and Technology (FET)
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1. Introduction
The conventional electromagnetic motor has been used in the industry for over a
decade, being the widely used motor. Current evolution trends require more and more
small motor likely to give high torque per weight unit. The electromagnetic motor is
restricted in this regard without new discoveries on super conductor’s materials, so the
consideration of scientists moved towards a new type of motor i.e. the ultrasonic motor
1.1 Introduction
The earlier Linear Ultrasonic Motor (LUM) was produced by Nano motion Inc.
and connected in numerous extremes movement drive circumstances.
Linear ultrasonic motors is an alternative to electromagnetic motors, unlike
electromagnetic motors they have several advantages such as simple construction, quit
operation, quick response, good positioning accuracy, self-locking when the power
source is in off state. Additionally they have great execution attributes like, high power
density, expansive output torque, simple controllability and non-electromagnetic
actuation impedance (Shengjun Shi,et al2006). In the recent years the boltclamped
Ultrasonic motor has been the research topic to increase higher output power. Example
like, longitudinal and flexible dual mode bolt fixed langevin type transducer was
projected (Shengjun Shi, Tao Xie, 2008). In which the longitudinal shaking movement
element provides the driving power while flexible vibration movement component
offers the normal stress between the driving tip and the sides. The project and pressure
of an ultrasonic linear motor-powered by double piezoelectric actuator in this number of
piezo crystal was reducing to lower the power consumption (Pruittikorn smithmaitrie,
2012).
LUM are needed with increasing demand for the Nano particles for the micro
application. Therefore the LUM with more compactness and with high driving force
become a significant research topic.

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1.2 Motivation
The advantages of LUM over conventional motor are simple in construction,
silent operation, quick response, good positioning accuracy, self-locking when the power
source is in off state and absences of noise in the audible range. The interaction of rotor-
stator is described by friction law; the instruction to optimize the presentation of the
ultrasonic motor-powered the study of material hardness and effect of surface
roughness is essential. The interest of working on LUM was laid after going through the
uniqueness of this motor. Its characteristics like torque and efficiency can be improved
by varying the motor design
1.3 Techniques to design a compact LUM
The aim of this work is to design and analyse a Bi-directional ultrasonic motor
with two sided rotor. The motor will be compared with design made by Pruittikorn
smithmaitrie.
1) Mathematical calculation: To calculate the operating frequency.
The mathematical calculation will be carried out to calculate the operating
frequency of the designed model, through which we can predict at what frequency the
designed model will operate.
2) To perform the model analysis of design.
By using finite element tool, the model analysis will be carried out to know the
operating frequency of the motor in ANSYS APDL.
3) To perform the harmonic analysis of design.
The harmonic analysis of the motor will be carried out in ANSYS APDL and the
velocity of the motor is calculated from the displacement.
1.4 Organization of the Thesis
The entire work has been divided into six chapters. Each chapter will highlight
the introduction, investigation and conclusions.
Chapter 1: contains the brief introduction, Motivation and Techniques to design
LUM.

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Chapter 2: Brieﬂy describes the general background of piezoelectricity
considering ceramic materials, fundamental relations with some application ﬁelds and in
particular ultrasonic motors. As well as it provides with the literature survey on the LUM.
Chapter 3: Presents the overall structure and descriptions of the technical tasks
to be realized for design of LUM for reduction of force ripple by using FEA.
Chapter 4: Elucidates the design procedure for a LUM. The procedures are
followed during the FEA of a LUM are described. The theoretical determination of
operating frequency, velocity and other parameter are described.
Chapter 5: Gives a comprehensive study of LUM and their design modifications
for double sided displacement. Therefore from design modification the operating
frequency and velocity is simulated and analysed using FEA. The simulation results are
compared with the existing design of LUM.
Chapter 6: Provides a comprehensive summary of the major conclusion derived
from the thesis. Suggestions on possible area of future research work.

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2. Literature Review and Problem Formulation
Miniaturization of systems is required in all systems where weight and size are
important. The major application is the micro motors. They find application in micro
robots, lens in cameras, in biomedical engineering. This chapter aims to discuss the
principle and operations of LUM
2.1 Background Theory
2.1.1 Piezoelectric ceramic
To make piezoelectric porcelain, fine ashes of the element metallic oxides are
varied in specific quantities and formerly fiery towards form an smooth ash. The
precipitate is varied through a carbon-based binder and is shaped into essential
elements having the preferred form (circles, bars). The components are heated for
specific period of time. Then they are cooled, then molded or cut to for the required
design, and conductors are connected to the reasonable appearances.
Most piezoelectric devices are made of oxide piezoelectric:
 Lead zirconate titanate (PZT) is the most usually used piezoelectric ceramic.
 Quartz crystals are also widely used. The crystalline structure of PZT and of
many other useful piezoelectric is the perovskite structure or a derivative of
perovskite. Now, the lead containing perovskites such as PZT is by far the
best performing for actuators, transducers and sensors. Some essential
materials and materials related issues are now described.
2.1.2 Polarization
Old piezoelectric clay are form of perovskite quartzes to each containing a minor,
tetravalent metallic ion, frequently titanium or zirconium, in a frame of bigger, divalent
metallic ions, frequently lead or barium, and O2- ions (Figure. 2.1). Under circumstances
that discuss tetragonal or rhombohedral equilibrium of the quartzes, individually crystal
has a dipole moment .Over a perilous heat, the Curie point, independently perovskite
quartz in the fired clay component shows a straightforward cubic balance with no dipole

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moment (Figure. 2.1). Nonetheless, a temperature under the Curie point, every quartz
has rhombohedral balance and a dipole dislodging.
Figure. 2.1 Crystal Structure of Piezoelectric Ceramic
Adjacent dipoles form areas of limited arrangement called territories. The plan
offers a net displacement of dipole in to the space, then consequently the total
extremity. The track of polarity between neighbouring fields is casual, so that the clay
component needs no whole polarization Figure. 2.2.
Figure. 2.2 Polarizing a Piezoelectric Ceramic
The areas in a clay component are associated by showing the component almost
a solid, straight current electrical field, habitually at warmth somewhat under the Curie
point Figure. 2.2b. Over this polarizing (poling) activity, spaces best intently connected to
the electrical field increase the outlay of regions that stay adjusted by the field, other
than the component increments in to the direction of field. After electrical input is
withdrawn, maximum dipoles are sheltered into the close configuration Figure. 2.2c.
now, the component has a stable polarization, the remnants polarity, and is lastingly
elongated.
Figure.2.3a displays the characteristic of hysteresis curve produced through
applying an electrical field E towards a piezoelectric clay component until extreme

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polarity P is reached, decreasing the field near nil to regulate the remanent polarity,
withdrawing the field towards conquer a undesirable full polarity then negative
remanent polarity, besides withdrawing the field to return the positive remanent
polarity. Moreover, Figure. 2.3b shows the comparative variation in the element of the
clay component (strain S) beside the path of polarity corresponding towards the
variation in the electrical field. The comparative rise / fall in the height similar near the
path of the electrical field is attended through a resultant, but around 50% lesser
,comparative fall/rise in the measurement perpendicular to the electrical field.
Figure. 2.3 a) hysteresis curve for polarization, b) elongation / contraction of a ceramic
element
2.1.3 Limitations in piezoelectric materials
There are various defects of piezoelectric materials, for instance:
•Exhaustion disaster resulting from the irregular stress in the ceramic components
• Detachment of the piezoelectric properties in the area of the Curie temperature point
(>300oC)
•Weakening of the adhesive bond happening underneath the Curie point
• Change in Young's modulus with temperature bringing on an adjustment in the
resounding recurrence and along these lines bringing about bringing down the execution
of the gadget

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• Short life traverse inferable from quick wear and tear
• Large frictional misfortunes because of the mind boggling nature of vibrations together
with other marvels
2.1.4 Resonance Frequency
When piezoelectric clay element is excited by an AC electrical field, it changes
measurements consistently, at the cycling recurrence of the field. The clay element
vibrates most freely at a particular applied frequency, where the conversion of electrical
energy input into mechanical energy is most efficiently this particular frequency is
known as resonance recurrence.
The frequency response of the element is shown inFigure 2.4. When frequency is
amplified, the element reaches a frequency where minimum will be the impedance. Due
to this minimum impedance frequency,(𝑓𝑚), the series resonance frequency will be
approximated , (𝑓𝑠), the frequency at which impedance in an electrical circuit describing
the element is zero, if resistance caused by mechanical losses is ignored. The minimum
impedance frequency also is the resonance frequency, (𝑓𝑟). the composition of the clay
material and the shape and volume of the element determine the resonance frequency
generally, a thicker element has a lower resonance frequency than a thinner element of
the same shape.
As the cycling frequency is further increased, impedance increases to a
maximum. The maximum impedance frequency, (𝑓𝑛), approximates the parallel
resonance frequency, (𝑓𝑝), the frequency at which parallel resistance in the equivalent
electrical circuit is infinite if resistance caused by mechanical losses is ignored. The
maximum impedance frequency also is the antireosnance frequency; (𝑓𝑎) , maximum
response from the element will be at a point between(𝑓𝑚) and (𝑓𝑛).

8
Figure 2.4 frequency response
A elements oscillation will first reaches the impedance frequency of minimum
value (𝑓𝑎 ) , where element will vibrates utmost readily, and converts electrical energy
into mechanical energy efficiently.
2.2 Piezoelectric theory
2.2.1 Piezoelectric constants
Since a piezoelectric artistic is anisotropic, physical components identify with
commonly the method for the connected mechanical or electric power and the bearings
opposite to the connected power.
Figure. 2.5 Axes notation
In this way, every steady typically has two subscripts that demonstrate the headings of
the two related amounts, for example, weight (power on the earthenware
component/surface range of the component) and strain (change long of
component/unique length of component) for versatility. The method for positive
polarization for the most part is to concur with the z-axis of a quadrilateral arrangement

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of z, y, and x axes (see Figure. 2.4). Course z, y, or x is spoken to by the subscript 3, 2, or
1 correspondingly and shear around one of these axes is spoken to by the subscript 4, 5,
or 6, separately. The constants which are used commonly and conditions for deciding
and interconnecting are introduced in the following sections.
i. Piezoelectric charge constant (d)
The piezoelectric charge unfaltering d is the polarization made per unit of
mechanical stress (T) associated with a piezoelectric significant or, rather, is the
machine-driven strain (S) experienced by a piezoelectric material for every unit of
electric field associated (E). The first subscript to d exhibits the course of polarization
delivered in the material when the electric field is zero or on the other hand, is the
strategy for the associated field power. The second subscript is the course of the
associated tension or the influenced strain independently. Since the strain influenced in
a piezoelectric material by an associated electric field is the aftereffect of the value for
the electric field and the quality for d, d is an essential pointer of a material's
appropriateness for strain-subordinate applications (actuators).
ii. Piezoelectric voltage constant (g)
The piezoelectric voltage unfaltering g is the electricfield delivered by a
piezoelectric material for every unit of mechanical anxiety associated or, then again, is
the mechanical strained x perpended by a piezoelectric material for each unit of electric
migration associated. The first subscript to g exhibits the heading of the electric field
created in the material, or the course of the associated electric dislodging (D). The
second subscript is the heading of the associated nervousness or the influenced strain,
correspondingly. Since the upside of the provoked electric field conveyed by a
piezoelectric material in answer to an associated physical weight is the consequence of
the quality for the associated tension and the value for g, g is basic for measuring a
material's appropriateness for distinguishing applications (sensors).

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iii. Permittivity (𝝐)
The permittivity or dielectric steady ε, for a piezoelectric terminated material, is
the dielectric migration per unit electric field. εT is the permittivity at reliable
uneasiness, εS is the permittivity at relentless strain. The first subscript to ε decides the
strategy for the dielectric advancement; the second is the course of the electric field.
iv. Elastic compliance (s)
Adaptable consistence s is the strain made in a piezoelectric material for each
unit of uneasiness significant and, for the 11 and 33 ways, is the equivalent of the
modulus of adaptability (Young's modulus, Y). sD is the comprehension under a constant
electric advancement; sE is the consistence under an enduring electric field. The first
subscript allocates the heading of strain; the second is the direction of uneasiness.
v. Young’s modulus (y)
Young's modulus Y is a presentation of the immovability of a clay material. Y is
determined from the value for the nervousness associated with the huge secluded by
the cost for the resulting strain in the same heading.
vi. Electromechanical coupling factor (k)
The electromechanical coupling variable k is a marker of the ampleness with
which a piezoelectric material changes electrical imperativeness into mechanical
essentialness, or adherents’ mechanical essentialness into electrical imperativeness. The
first subscript to k infers the way along which the terminals are associated; the second
shows the heading along which the mechanical essentialness is associated or set up. k
measures referred to in pottery suppliers' specifications generally are theoretical full
values.
vii. Dielectric dissipation factor (tan δ)
The dielectric dispersal variable (dielectric misfortune element) tan δ, for a clay
material, is the digression of the dielectric cost point. Tan δ is unfaltering by the
proportion of genuine conductance to current susceptance in a parallel circuit,

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measured by utilizing an impedance span. Values for tan δ commonly are resolved at 1
kHz.
viii. Mechanical quality factor (Qm)
In similarity to the electrical quality element Q, the mechanical quality variable
Qm portrays the proportion of the strain in stage with the anxiety to the strain out of
stage with the anxiety in the vibrating body. Qm is the 3dB width of the piezoelectric
reverberation separated to the reverberation recurrence. "Hard" materials have a better
Qm in correlation than "delicate" materials, this is the reason they are more adjusted for
applications requiring a high mechanical quality element, for example, resonators.
Despite what might be expected, for applications that need a given band-width, for
example, filters, the utilization of "delicate" (low Qm) materials is more appropriate.
2.2.2 Vibration modes
In practice, the variation of the electric field will deform a piezoelectric body in
different directions with different intensities. According to the type of the used
piezoelectric effect (the directions of the applied electric field and the extension), three
main groups of vibration modes can be achieved. These modes are the longitudinal
mode (d33), the transversal mode (d31) and the shear mode (d15).
Table 2.1: Elastoelectric matrix for T and E taken as independent variables

12
• Longitudinal mode (33)
In the longitudinal mode, the disFigureurements occur parallel to the connected
electric ﬁeld and the polarization, as shown inFigure. 2.5. This mode is usually used for
small movements and high forces.
Figure. 2.5 Longitudinal Vibration Mode
•Transversal mode (31)
In the transversal mode, the disFigureureurements happen opposite to the
electric pivot as appeared in Figurer. 2.6. This mode is likewise utilized for little
developments and high strengths furthermore have high firmness.
Figure. 2.6 Transversal Vibration Mode
•Shear mode (15)
In the shear mode, the distortions happen about the hub opposite towards the
arrangement enclosing the electrical ﬁeld path and the polarity as appeared in Figure.
2.7. They are chiefly utilized for vast developments and have low firmness.

13
Figure. 2.7 The shear vibration mode
2.3 Applications
2.3.1 Generators
Piezoelectric ceramic production can create voltages sufﬁcient to start over a
cathode crevice, and in this manner it can be utilized as ignitors as a part of fuel lighters,
gas stoves, and welding
Figure. 2.8 Piezoelectric ignition system
Piezoelectric ignition frameworks are little and basic, particular preferences with respect
to option frameworks that contain lasting magnets or high voltage transformers and
capacitors Figure. 2.8 demonstrates the primary get together of a piezoelectric ignition
framework. Typically, two piezoelectric chambers are stacked and worked in parallel, so
that no further high voltage protection is required. On the other hand, the electrical
vitality created through a piezoelectric component can remain putting away. Strategies
used to create multi-layer capacitors have stood utilized towards building multilayer

14
piezoelectric generators. Such generators are exceptional minimized state batteries for
electronic circuits.
2.3.2 Actuators
A piezoelectric actuator changes an electrical movement into a decisively
controlled physical dislodging; to ﬁnely modify exactness machining apparatuses, lenses,
or mirrors. Piezoelectric actuators are additionally used to control water driven valves,
go about as little volume pumps or extraordinary reason motor. A conceivably essential
favourable position of piezoelectric actuators is the nonattendance of electromagnetic
commotion. Besides, if physical uprooting is kept, an actuator will build up a working
power. As a case, the example of an engendering wave sort ultrasonic engine is
appeared for the rotational engine created in Figure. 2.9a) and the use of this engine in a
camera auto-centering instrument is spoken to in Figure. 2.9b). The rotor in contact with
the flexible undulated stator will be driven by method for a voyaging versatile wave
instigated in the stator by a piezoelectric ring fired reinforced onto the stator. The
colossal preferred standpoint of this sort of engine is its low speed and its high torque,
which can be accomplished without riggings by utilizing the little development
amplitudes. Also, the piezoelectric engine begins and stops quick, it is uncaring to solid
attractive ﬁelds and does not create attractive aggravations.
Figure. 2.9 a) Traveling wave ultrasonic motor developed b) application in a camera auto-
focusing mechanism

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 Pipette
One of the example of the piezoelectric actuator is the pipette device, it is a
laboratory tool commonly used in chemistry, biology and medicine to transport a
measured volume of liquid, often as a media dispenser. In this application a piezoelectric
actuator is used where the inverse piezoelectric effect is used. The pipette devices are
used for non-contact dispensing of liquid volumes in the Nano litre to microliter range.
The valve of the device has to open for very short time. For the required specification
the piezoelectric actuator is best suited.
Figure 2.10 Pipette Device
2.4 Critical review of literature
The piezoelectric effect was discovered in 1880 by Pierre and Jacques Curie.
Piezoelectricity is the property of some materials to develop electric charge on their
surface when mechanical stress is exerted on them [Ike96]. The electrical response to
mechanical stimulation is called the direct piezoelectric result and the mechanical
response to electrical stimulation is called the converse piezoelectric effect.
Piezoelectricity is the property of all materials that have non centrosymmetric crystal
structure. It is found in inorganic materials such as quartz (SiO2) or lead zirconate
titanate (PZT), in organic materials and in biological matter (hair, bones). For technical

16
applications of piezoelectric, the focus is on inorganic materials, ceramics and single
crystals. To get the knowledge of previously design LUM, an extensive literature survey
of papers and patents was conducted. The literature survey gives you the idea on the
various techniques used to create LUM. All LUM presented in this survey use the same
techniques of ultrasonic frequency. Many of the existing research focus on the LUM to
get the more velocity for the small motor
 MAXIMILIANF LEISCHER presents the concept of bidirectional piezoelectric
ultrasonic motor which operated with single source. In which the motor can be
driven in both left and right direction, with a maximum speed of 300r/min
(MAximilianf leischer, 1989)
 Siyuan he in their research has focous on single phase standing wave
bidirectional LUM. Whose operational performance was maximum speed of 200
mm/s has been achieved. Further they have focused on the improvement of
speed and on the controlling of LUM (Siyuan, 1998)
 Serra cagatay demonstrated the miniaturized metal tube ultrasonic motor, the
dimension which is 6mm in diameter and 6mm in length, was developed whose
working frequency was 130 kHz. A torque of 0.5 mNm was reached at a
maximum power of 45 mw with a speed of 45 rad/sec. the features such as
simple driving circuit and low cost will make advantages over convention
electromagnetic motor (Serra cagatay, 2003).
 “Design and characteristic analysis of ultrasonic motor considering contact
mechanism”. In this article the highlighted work was on the dynamic mechanism
of the motor in order to improve the analysis and design of the LUM. (Jong seok
rho, 2005)
 Jose m, focous his work on the optimization of LUM by numerical modelling. The
simulation result shows that the rotor displacement is about 1.7mm in the
forward direction and about 1.25mm in the backward direction, and the applied

17
voltage was reduced to 5v from 7v with an operating frequency of 200 kHz (jose
m, 2008)
 Pruittikorn smithmaitrie in their work has focous on the design and performance
testing of an ultrasonic linear motor with dual piezoelectric actuator patches is
studied. This design yields a simpler structure in the smaller number of actuator
and lower stator stiffness compared with conventional design of LUM. The
operating voltage was 54v the frequency of 29.2 kHz, where velocity was 17.59
cm/s. this design has many application that require tiny translation actuator
(Pruittikorn smithmaitrie, 2012).
Table 2.2 List of Literature review
SL.
No
Authors Year
of
Publi
catio
n
Research
Focus
Met
hods
and
Met
hod
ologi
es
used
Research
Findings
Conclusions
drawn by
authors
Limitation
s of Study
Student
Comments
about
Research
Work
1
Pruittiko
rn
smithmai
trie,
panumas
Suybang
dum. 2012
Design and
Performance
Testing of
an
Ultrasonic
Linear
Motor with
Dual
Piezoelectric
Actuators.
COM
SOL.
For the applied
voltage of 30 pp.
the velocity was
16.1 cm/s and
power
consumption was
0.17w.
The new design
has less number
of piezoelectric
material.
The size is
not
compactabl
e for the
MEMS
application.
The size can
be reduced
further so
that it can
be
implemente
d in less
weighted
MAV

18
2
Serra
Cagatay,
Burhanet
tin Koc,
Kenji
Uchino
2003
A 1.6mm,
METAL TUBE
ULTRASONIC
MOTOR.
ATIL
A
FEM
TOOL
The metallic tube
can be used as a
linear actuator
For the
dimension of
(1*6*0.3)mm of
piezo the
obtained torque
was 0.5mNm
The heat
generation
is more for
the
selected
volume.
The heat
generation
can be
reduced by
selecting
different
volume of
material.
3
K.
Spanner,
O.
Vysnevsk
yy, W.
Wischne
wskiy
2006
Design of
miniature
linear
ultrasonic
piezo motor
for precision
mechatronic
systems
ANSY
S
FEM
TOOL
The linear
ultrasonic motor
can be used for
the accurate
precision control
The speed of
100mm/s can be
obtained when
it is excited by
470khz of
frequency
Temperatu
re is high
due to use
of two
sliders.
Temperatur
e can be
reduced by
using only
one slider.
4
A.
Billard,
Y.perriar
d
2006
Modeling
and
optimization
of ultrasonic
linear
motors
ANSY
S.
Linear actuator
can be used for
the rotation
motion
For the input of
7Vwith 200Khz
we can get
1.25mm of
forward
direction and
1.77 mm of
reverse
direction.
Motion of
the motor
is less.
The motion
of motor can
be increased
when
travelling
wave
technique is
used for
excitation .
5
Cheng-
kuci hsu,
jen-yang
ho.
2006
A Flapping
MAV with
PVDF
parylene
composite
skin
.
Matl
ab
Simul
ink.
The movement of
flapping wings
can be done by
using Ultrasonic
actuator.
For the
frequency of
30khz the force
obtained was
0.17W.
The
temperatur
e was high
due to the
friction
losses
By selecting
the different
shapes for
the stator
tip the
temperature
can be
reduced.

19
6
Jose M.
Fernand
ez, yves
perriard.
2008
To
optimization
study of a
new type of
ultrasonic
linear
motor.
Ansy
s
For forward
direction 460khz
is needed and
508khz is needed
for reverse
direction of
motor
the motor
travels 365 µm
for an applied
voltage of 7 V
due to Two
different
frequency
the circuit
is more
complicate
d to control
the motor
The circuit
complexity
can be
reduced by
using of
source for
the
excitation
7
Siyuan
he, paul
r,
chiarot. 2011
A Single
Vibration
Mode
Tubular
Piezoelectric
Ultrasonic
Motor
Ansy
s.
The working
frequencies of
the motors are
27.6Khz and 23.5
kHz.
a single voltage
source can be
used to drive
the motor and
no vibration
mode coupling
is needed
Only
analytical
solution is
carried out
using
analytical
model
analysis can
be carried
out using
computation
al tools
8
Minh H-T
Nguyen,
Kok
Kiong
Tan,
Wenyu
Liang,
Chek
Sing Teo.
2013
Robust
Precision
Positioning
Control on
Linear
Ultrasonic
Motor
Matl
ab/si
muli
nk
To develop
robust MPC
method for
compensation of
friction arising in
linear ultrasonic
motors
A robust MPC
method has
been developed
for
compensation
of friction
arising in linear
ultrasonic
motors.
For more
accurate
results,
analysis
consisting
of more
details with
is
recommen
ded
The
developed
model can
be analyzed
in FEM tool.
9
Hao
Jiang,
Michail
E.
Kiziroglo
u
2015
Energy
harvesting
using
ambient
motion.
Matl
ab.
76% more energy
can be extracted
by the prebias
mechanism
compared to the
unbiased .
A rolling ball
pulse generator
has been
presented in
this paper using
piezoelectric
transduction for
wireless sensing
The source
of
excitation
depends on
the
ambient
motion
only.
Proper
source of
excitation
has to be
designed.

20
10
Joss Paul
P ,
Samuel
Desmon
d Tutu
R,Kevin
Richards
W, Maria
Jerome
V.
2015
Piezoelectric
wireless
power
transfer.
MAT
LAB.
the design of
system which can
harness the
power generated
by the human
movements and
transfer the
power to a device
wirelessly.
Harvesting
energy from
human motions
is an attractive
approach for
obtaining clean
and sustainable
energy.
Mathemati
cal
modelling
has not
been done.
Mathematic
al modelling
and
simulation
can be done
using matlab
and FEM
tool.
2.5 Problem Formulation:
The concept of double sided stator of Linear Ultrasonic Motor is not addressed.
Hence the contribution of this research is to design a geometrically unique double sided
stator of Linear Ultrasonic Motor. This can be used in pipette device to escalate the
production and to reduce the cost.
2.6 Conclusions:
The Linear Ultrasonic Motor made of double sided stator offers more advantages
than the Linear Ultrasonic Motor made of single sided stator. The proposed model of the
Linear Ultrasonic Motor will satisfy many of the requirements, such as compact drive
components, motion drive, low cost with reduced power consumption. The LUM is
analysed using the knowledge of basic piezoelectric actuator and literature has been
reviewed on the inverse piezoelectric effect. Thus complete background theory and
literature survey of inverse piezoelectric actuator is documented in this chapter.

21
3. Problem Statement
This chapter considers the key factors and technical assessment of designing a bi-
directional double sided LUM. The aim, objectives and methodologies employed to
accomplish the idea of thesis are presented.
Title
“Design of Linear Ultrasonic Motor (LUM) Using Finite Element Analysis”
Aim
To design and simulate a linear ultrasonic motor
Objectives
1. To review the literature on Linear Ultrasonic Motor (LUM)
2. To arrive functional and design specifications of the linear ultrasonic motor
3. To model existing LUM and analyze velocity
4. To model modified LUM and analyze velocity
5. To compare magnitude of force and velocity for designed LUM with existing
motor
Methods and Methodology
1. Literature review of Literature on various piezoelectric materials various shape
and on piezoelectric motor will be carried out by referring books, journals,
conference papers and related documents.
2
To arrive functional
and design
specifications of
the linear
ultrasonic motor
Selection of piezo electric material will
be done on the basis of literature
review
Books,
journals etc

22
3
To model existing
LUM and analyze
the velocity
Model the existing and designed LUM
using FEM tool
ANSYS APDL
Assign material and boundary
conditions for the designed motor
Apply mesh to the existing LUM
4 To model modified
LUM and analyze
the velocity
Model the existing and designed LUM
using FEM tool
ANSYS APDL
Assign material and boundary
conditions for the designed motor
Apply mesh to the designed LUM
5 To compare
magnitude of
operating
frequency and
velocity for
designed LUM with
existing motor
Analyze the magnitude of operating
frequency for existing and designed
motors
ANSYS APDL
Analyze the magnitude of velocity for
existing and designed motors

23
4. Problem Solving
This chapter provides operational and theoretical information to analyse the theory
and calculation involved in the design of Linear Ultrasonic Motor (LUM) using Finite
Element Analysis (FEA). The review is focused on operating frequency and velocity in
LUM, performance calculation of LUM, operation and principals involved in the LUM and
modification of design in the LUM.
4.1 Proposed Block Diagram
The proposed LUM has dual piezoelectric actuators be made of a beam stator
with rectangular teeth on either side damping material reinforcements and two
piezoelectric actuators attached with the beam structure near both ends of the beam, as
shown inFigureure 4.1. The two harmonic inputs are Asin (𝜔t) and Acos (𝜔t), the phase
difference of the two harmonic input on the piezoelectric actuators is 90 degree, where
A will be the amplitudes of the input signal and 𝜔 will be the driving frequency and‘t’ is
the time.
Figure 4.1 Proposed Diagram of LUM.
4.2 Motor design process
The Figure 4.2 guides on through the motor design process. The design process
consists of three basic process i.e., pre-processing, processing and post processing. In
pre-processing process the design specifications, dimensions, choosing of the material
properties for the stator, piezoelectric actuator and damping material for the LUM is
done. The processing stage includes applying the boundaries, excitation and meshing to
the model. The post processing stage, analysing the operating frequency and velocity of
the proposed design with existing design will be carried out.

24
Figure 4.2 Developemnt process
4.3 Design of Linear Ultrasonic Motor
The design of Linear Ultrasonic Motor is a kind of traveling wave ultrasonic motor.
This design of the Linear Ultrasonic Motor can turn an incessant structure into wave
medium. In this design two piezoelectric actuator are used for generating the traveling
wave on a flat beam. The design process has been continued in this section.
 Design of LUM
The LUM with dual piezoelectric actuators consists of stators with rectangular
teeth on either side, damping material patches and two actuators. The design of
actuator is equal to the wavelength (𝜆) which can be calculated by using

25
λ =
c
f
− [4.1]
Where,
C wave speed (m/s)
f frequency (1/s)
The actuators are bonded with the stator on the same surface. To drive the rotor
more efficiently, the difference of harmonic excitations will be900
. In order to prevent
the wave reflection, the damping material patches are attached to the stator at both
ends. The direction of the motor can be controlled by changing the phase difference of
the excitation.
The harmonic excitation given at the actuators are
Asin(ωt) − [4.2]
Acos(ωt) − [4.3]
Where,
A Signal amplitude
𝜔 Driving frequency (1/s)
t time (s)
The velocity of the motor can be adjusted by varying the amplitude of voltage on
piezoelectric actuators.
Since we have to deal with the model analysis, one has to understand the
vibration theory of the elastic beam which is applicable to analyse the behaviour of the
stator. The principal equation for the isotropic solid beam is given as
𝑌𝐼
𝜕4 𝑢3
𝜕𝑥4
+ 𝜌𝑏ℎ
𝜕2 𝑢3
𝜕𝑡2
= 0 − [4.4]
Where,
Y Young’s modulus
I Moment of inertia

26
𝑢3 Transverse displacement
𝜌 Mass density
𝑏ℎ Represents the cross-section area
The transverse displacement 𝑢3 is giving by
u3 = Asin(ωt − kx) − [4.5]
Where,
K wave number
A transverse wave amplitude
The movement at the tooth tip is given by
utip = −α
∂𝐮 𝟑
𝛛𝐱
= αAkcos(ωt − kx) − [4.6]
The velocity in the direction of x is expressed as
vx = −αAkωsin(ωt − kx) − [4.7]
The maximum velocity reachable by the motor is represented by equation 4.7.
The motor changes its direction to the applied wave direction. Hence the motors
direction can be changed by reversing the wave direction. The piezoelectric material will
act as capacitor
When it is operated below the resonant frequency, though which the current required
to operate the piezoelectric actuator can be calculated by
i = f ∗ c ∗ v(p − p) − [4.8]
The natural frequency of the beam with stable boundary state can be written as
fi =
1
2πL2
(
(2i+1)π
2
)2√
YI
m
− [4.9]
Where,
L length of the beam
m mass per unit length of the beam
Understanding the concept of the young’s modules, shear modules of modules of
rigidity, bulk modules of the body, and poisons ratio is necessary, in order to define the
properties of the material.

27
Young’s modules (elastic modules (E)), it defines the relationship between the
stress (force per unit area (𝜎)) and strain (proportional deformation (e)) in a material.
This is given as
E =
σ
e
− [4.10]
Shear modules of modules rigidity (G) is defined as the ration of shear stress (𝜏)
and shear strain (𝜑), expressed as
G =
τ
φ
− [4.11]
Bulk modules of the material (K) is the ration of stress (𝜎) and volumetric strain
(𝑒 𝑣), given as
K =
σ
ev
− [4.12]
When pressure is applied on the material two types of deformation will occurs,
1) The deformation in the direction of the applied pressure and
2) The perpendicular direction of the applied pressure.
The deformation which occurs along the direction of applied pressure in known
as lateral strain and deformation which occurs perpendicular to applied pressure is
known as transvers stain. The ratio of transvers strain to the lateral strain is known as
poisson’s ratio, which is expressed as
μ =
eb
el
=
et
el
− [4.13]
The shear modulus can also be calculated by using
G =
E
2(1+μ)
− [4.14]
Where,
G shear modulus
E young’s modulus (elastic modules)

28
𝜇 Poisson’s ratio
4.4 Design of the Linear Ultrasonic Motor (LUM)
Many problems of elasticity can be treated reasonably by two dimensional, or
plane theory of elasticity. There are two general sorts of issues required in this plane
investigation, plane stress and plane strain. These two sorts will be characterized by
setting down specific confinements and presumptions on the anxiety and uprooting
fields. The model is expected to be 2-dimentional plane strain problem. Plane strain can
be defined as states of strain were the strain is normal to x-y plane (𝑒 𝑥, 𝑒 𝑦), and the
shear strain 𝐺𝑥𝑦 and 𝐺 𝑦𝑧 will be presumed to be zero.
The problem of plane strain, it is assumed to be the dimension of the structure in
one direction is very large, compared to dimension of the structure in other direction.
The table 4.1 gives the brief explanation and difference between the plane strain and
plane stress problems.
Table 4.1 Comparison of plane strain and plane stress
Parameter 𝝈 𝒙 𝝈 𝒚 𝝈 𝒛 𝒆 𝒙 𝒆 𝒚 𝒆 𝒛 𝑮 𝒙𝒚 𝑮 𝒙𝒛 𝑮 𝒚𝒛
Plane stress Y Y N Y Y Y Y N N
Plane stain Y Y Y Y Y N Y N N
From the design defined above the Linear Ultrasonic Actuator is modelled to
study the operating frequency, and the velocity of the Actuator. The block diagram of
Linear Ultrasonic Actuator is shown in the Figure 4.3.

29
Figure 4.3 Block diagram of LUM
The dimension of stator, actuator, and teeth are given in the table 4.2, all the
dimension are in mm format only. The dimensions of damping material (silicon rubber)
are silicon rubber width of 6 mm, length of 5 mm, and thickness of 0.5 mm.
To calculate the experimental result, the LUM is modelled and simulated by using
finite element software ANSYS APDL. The designed model boundary condition is too
stipulated at both ends. The 54sin(𝑤𝑡) and 54cos(𝑤𝑡) are the excitation fed to the
actuators.
Table 4.2 Dimension of design
Parameters Values(mm)
Stator width (b) 6
Stator length (L) 85
Stator thickness (h) 1
Height of the teeth (ht) 3
Width of the teeth (b) 6
Thickness of teeth (tt) 1.5
Actuator length (la) 10
Actuator width (b) 6
Actuator thickness (ha) 0.5

30
The operating frequency is obtained by varying the excitation frequency until the
travelling wave is generated. The entire dimensions are assigned according to the
previous description and all material properties are assigned which are described in
table 4.3. To make the calculation part easy, all the material properties have been
converted to mm (millimetre).
Table 4.3 Material Properties of Linear Ultrasonic Motor
parameters Pzt-4
(actuator)
Brass stator Silicon
rubber
Unit
Y11 79000 96000 4.2 N/𝑚𝑚2
Y33 66000 96000 4.2 N/𝑚𝑚2
Density 7.7e-9 8.4e-9 1.51e-9 Kg/𝑚𝑚3
Poisson's ratio 0.33 0.35 0.45 --
Damping
coefficient
0.0013 0.0005 0.05 --
Piezoelectric
constant , e33
1.756e-5 -- -- c/𝑚𝑚2
e31 -4.38e-6 -- -- c/𝑚𝑚2
permittivity 101.8e+3 -- -- F/mm
Share
modules,g11
29.69e+3 -- -- N/𝑚𝑚2
g33 24.8e+3 -- -- N/𝑚𝑚2
4.5 FEA Approach for LUM
This section gives the brief design procedure of the Linear Ultrasonic Motor
(LUM), 2-dimentional Finite element analysis (FEA) is used to verify the analytical
method accuracy. The operating frequency for the various modes of operation and
velocity has been determined. The various types of analysis used to determine the
operating frequency and the velocity has been shown in the following section with brief

31
description. Model analysis is used to demine the operating frequency and harmonic
analysis is used to determine the velocity of the motor.
 Model Analysis
The first analysis used for the examination of Linear Ultrasonic Motor is model
analysis. Since the LUM works on the vibratory nature and it is obvious basic starting
point. It is used to determine the natural frequency and mode shape. The procedure of
model analysis has been continued in this section.
 Procedure
The procedure of model analysis consists of Pre-processing, Processing, and Post-
processing. In which the Pre-processing consist of Assigning of material properties,
Modelling, and Meshing. Where the Processing part consists of Analysis type and option,
loading and solve. And Post-processing consists of reviewing results.
- Before starting the analysis procedure one has to be good in selection of element
type for respected analysis type. For the model analysis the best element type
for the 2-D design is PLANE-83.
- After selection of element type, the material properties are added for the
respected material as discussed in previously
- Then the model is designed for the given dimension, the material properties are
assigned for the respected material. The model designed is shown in Figure 4.4
Figure 4.4 Designed Model of LUM
- After modelling the meshing is done, meshing is a part of procedure which places
an important role if the meshing is not accurate then the results will be
inaccurate. After meshing the total numbers of nodes were 99811 and total
number of element 52150. The Figure 4.5 shows the meshed model of the LUM.

32
Figure 4.5 Meshed model of LUM
- The fixed boundary condition is applied on either side of the motor. Then
analysis type is chosen as model, this comes in processing part.
- From the Analysis Options Block Lanczos method is selected to solve the model
analysis, then the number of modes to extract has to specify, the starting
frequency and ending frequency will be specified.
- Then the solve command is given, it will take few hours/one day depending upon
the mesh quality. The review of model analysis results is done finally.
 Harmonic analysis
It’s a technique where the response for the sinusoidal loads is determined for the
known frequency. Harmonic analysis is done to make sure that a given design
withstands sinusoidal loads at different frequencies.
 Procedure
The procedure of harmonic analysis consists of Pre-processing, Processing, and
Post- processing. In which the Pre-processing consist of Assigning of material properties,
Modelling, and Meshing. Where the Processing part consists of Analysis type and option,
loading and solve. And Post-processing consists of reviewing results.
- Before starting the analysis procedure one has to be good in selection of element
type for respected analysis type. For the harmonic analysis the best element type
for the 2-d design is PLANE-223.
- After selection of element type, the material properties are added for the
respected material, as discussed in previously
- Then the model is designed for the given dimension, the material properties are
assigned for the respected material. The model designed is shown in Figure 4.4

33
- After modelling, meshing is done, meshing is a part of procedure which places an
important role if the meshing is not accurate then the results will be inaccurate.
After meshing the total numbers of nodes were 99811 and total number of
element 52150. The Figure4.5 shows the meshed model of the LUM.
- The fixed boundary condition is applied on either side of the motor, and then the
excitation is applied to the piezoelectric material. Then the harmonic frequency
range with number of sub steps has to be defined.
- Then the solve command is given, it will take few days depending upon the mesh
quality. The review of model analysis results is done finally.
4.6 Conclusion
The analytical calculation of the LUM and the design procedure and analysis
procedure of LUM with double sided stator is explained. The design of LUM is
implemented and analysed using the ANSYS APDL software. Results for LUM are
discussed in the next chapter.

34
5. Results and Discussions
This chapter includes the discussion of Analytical and finite element models of
the Linear Ultrasonic with the single sided stator and double sided stator. This includes
the results of operating frequency and the velocity of the LUM with single sided stator
and double sided stator.
5.1 Analytical Calculation and Finite Element Results.
5.1.1 Operating Frequency
The Analytical calculation is very essential; through this one can cross verify the
results obtained through the Simulation. The LUM basically works on the principle of
vibration; it is very essentially to calculate the frequency at which it will operate. For the
designed LUM the operating frequency can be calculated by using
fi =
1
2πL2 (
(2i+1)π
2
)2√
YI
m
− [5.1]
Where,
L length of the beam (mm)
m mass per unit length of the beam (kg/mm)
Y young’s modulus (N/𝑚𝑚2
)
I moment of inertia of the beam (𝑚𝑚4
)
The ‘I’ is the number of mode, in order to get the Analytical results accurate;
the unit conversion has to be done carefully. The Analytically calculated result at
different modes of operation has been shown in the table 5.1.
Table 5.1 Analytical result of operating frequency
Modes 12 13 14 15
Analytically (kHz) 27.93 32.58 37.58 42.95
The Finite Element results obtained after the model analysis, at different
modes of operation are

35
Figure 5.1 Finite Element Analysis Results
The analytical outcomes are relatively different from the finite element and
experimental results. The intention is that the analytical way has its own drawback due
to the estimate of the geometry derivation. That is, the linear stator is expected to be a
simple beam. Natural frequencies are obtained in the early range of ultrasonic frequency
(just above 20 kHz). The Figure 5.2 illustrates the finite element results of the 12 𝑡ℎ
mode
shape of the LUM at 27942 Hz.
Figure 5.2 12th
Vibration Mode Shape
5.1.2 Calculation of Velocity
Following the Operating Frequency Response of the LUM. The actuators are
excited with two harmonic inputs whose amplitude is 54 V. 54sin(𝑤𝑡) for the left
actuator and 54cos(𝑤𝑡) for the right actuator. And then Harmonic analysis is analysed
for the determination of displacement, through which the velocity can be calculated.
The harmonic response of the LUM is shown in Figure 5.3

36
Figure 5.3 Harmonic Response of the LUM
From the Figure 5.3 it can be seen that the results obtained from the model
analysis matches with the harmonic response of the frequency, where the displacement
can be seen, through which the velocity of the motor can be calculated .
The velocity of the motor can be calculated by using
vx = −αAkωsin(ωt − kx) − [5.2]
Where all the related parameters have been defined earlier, the velocity which
we got from the calculation is 161.66 𝑚𝑚
𝑠⁄ . However the analytical calculated velocity
is without the motor contact condition.
5.1.3 Current Calculation
The piezoelectric material behaviour as a dielectric material, such as capacitor in
which the opposite polarity charges are separated by a distance and all the polarity will
be present near the surface. Hence the piezoelectric material acts as a capacitor under
resonance frequency. Through which the current of the operating piezoelectric material
can be calculated by using
i = f ∗ c ∗ v − [5.3]
Where,
F operating frequency (1/s)
C piezo actuator capacitance (farad (As/v))
V peak to peak applied voltage (v)

37
Hence the current consume during the operation of the actuator is 3.16 𝑒−3
Amps.
5.2 Validation of results obtained for LUM
The operating frequencies are calculated for different modes of operation.
Through the obtained operating frequency the displacement is known and by using
equation 4.7 the velocity is calculated. The operating frequency for the single sided and
double sided LUM are represented in Table 5.1 and velocity for single sided and double
sided LUM are represented in Table 5.2.
 Results of operating frequency
The operating frequency of a LUM is computed for different modes of operation
is calculated and tabulated in Table 5.1. The calculation method has been explained in
chapter 4.
Table 5.1 operating frquency comparison between single sided and double sided LUM
Operating
frequency
modes
Analytical
(single sided
LUM) (kHz)
FEA(single sided
LUM) (kHz)
Analytical
(double
sided LUM)
( kHz)
FEA (double
sided LUM) (
kHz)
12th
23.41 22.186 27.93 27.94
13th
27.30 23.772 32.58 31.76
14th
31.50 24.842 37.58 32.54
15th
35.99 24.479 42.95 32.55
 Results of Velocity
The velocities for the single sided and double sided stator of LUM are computed
and are tabulated in Table 5.2. The calculated velocity for the Single sided and double
sided LUM is for the frequency obtained at the 12th
mode of operation.
Table 5.2 velocity comparision betwwen single sided and double sided lum
Parameter FEA(single sided
LUM)
FEA (double
sided LUM)
VELOCITY (mm/s) 127.14 127.64

38
Conclusions and Future Directions
The conclusion is clarified from the detailed technical specialized determinations,
hypothetical and numerically comes about identified with the outline. The proposed
LUM with double sided stator structure to obtained displacement from both sides. Also,
a conceivable expansion to the center segment of the task has been highlighted the
suggestion of future headings of the undertaking.
6.1 Conclusions
The main objective of the thesis is to design a actuator with reduce number of
piezoelectric actuators, with double sided stator so that it can be used more efficiently
in the pipetting device. The model was designed and analysed in the ANSYS APDL.
The operating frequency of the LUM with double sided stator was 27.73 KHz,
where both analytical and finite element results have shown great comparison. The
velocity for the LUM with double sided stator with the operating frequency of 27. 73 kHz
is 127.67 mm/s.
6.2 Future Directions
The following are the techniques proposed for the future work of the project.
• The performance of motors can further be improved by utilizing actuators which
are prepared of multilayer piezoelectric earthenware production rather than
single-layer piezoelectric pottery since they create bigger mechanical yield at
particular voltage
• Size of the LUM can be reduced to make it more compact for MEMS applications.

39
References
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Piezoelectric Pulse Generator for Wireless Sensing via FM Transmission. Internet
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dissertation, École Polytechnique Fédérale de Lausanne).
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ultrasonic motor. Ultrasonics, Ferroelectrics, and Frequency Control, IEEE
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Hsu, C.K., Ho, J.Y., Feng, G.H., Shih, H.M. and Yang, L.J., A FLAPPING MAV (MICRO AERIAL
VEHICLE) WITH PVDF-PARYLENE COMPOSITE SKIN.
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Schmidt, V.H., 1992, October. Piezoelectric energy conversion in windmills. In IEEE
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Smithmaitrie, P., Suybangdum, P., Laoratanakul, P. and Muensit, N., 2012. Design
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Shah, R., Khandelwal, R., Vishnukumar, A. and Sudha, R., Piezoelectric Power
Generatio Under Quasistatic And Dynamic Conditions.

40
T. Hemsel and J. Wallaschek, “Ultrasonic motors for linear position task in automobile,’’
in Proc. 30th Int. Symp. Automotive Technol. Automation, 1997, pp. 631-637.
Smits, J.G. and Choi, W.S., 1991. The constituent equations of piezoelectric
heterogeneous bimorphs. Ultrasonics, Ferroelectrics, and Frequency
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Jiang, H., Kiziroglou, M.E., Yates, D.C. and Yeatman, E.M., 2015. A Motion-Powered
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