development of a linear ultrasonic motor with segmented ... · development of a linear ultrasonic...

Development of a Linear Ultrasonic Motor with

Segmented Electrodes

by

Jacky Ka Ki Lau

A thesis submitted in conformity with the requirements for the degree

of Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering

University of Toronto

© Copyright by Jacky Ka Ki Lau 2012

ii

Development of a Linear Ultrasonic Motor with Segmented Electrodes

Jacky Ka Ki Lau

Master of Applied Science

Graduate Department of Mechanical and Industrial Engineering


2012

ABSTRACT

A novel segmented electrodes linear ultrasonic motor (USM) was developed. Using a planar

vibration mode concept to achieve elliptical motion at the USM drive-tip, an attempt to

decouple the components of the drive-tip trajectory was made. The proposed design allows

greater control of the drive-tip trajectory without altering the excitation voltage.

Finite element analyses were conducted on the proposed design to estimate the performance

of the USM. The maximum thrust force and speed are estimated to be 46N and 0.5370m/s,

respectively.

During experimental investigation, the maximum thrust force and speed observed were 36N

and 0.223m/s, respectively, at a preload of 70N. Furthermore, the smallest step achievable

was 9nm with an 18µs impulse. Nevertheless, the proposed design allowed the speed of the

USM to vary while keeping the thrust force relatively constant and allowed the USM to

achieve high resolution without a major sacrifice of thrust force.

iii

Acknowledgements

I would like to thank everyone who helped me in to the completion of my thesis and my

Master’s program. Special mention goes to the following people and organizations:

My supervisor, Professor Ridha Ben Mrad, for his guidance and support throughout my

project. He provided an excellent environment to conduct research and provided good

advices and encouragement during my research.

Professor James K. Mills, Professor Beno Benhabib, and Professor Goldie Nejat for their

advices on the project through the CANRIMT UofT Node.

Dr. Eswar Prasad and Dr. Sailu Namana of Sensor Technology Ltd. for their technical

knowledge on piezoceramic.

Members of MMDL, especially Alaeddin, Hirmand, Irman, James, Khalil, Mike, Sadegh,

Sergey, Tae and Vainatey for their help, advices, friendship and making my studies

enjoyable.

Members of the CANRIMT UofT Node.

My girlfriend and soul mate Aki for her support and understanding.

Lastly, CANRIMT, NSERC and OGS for providing funding and financial support.

iv

Table of Contents

Chapter 1 Introduction ......................................................................................................... 1 1.1 Background ................................................................................................................ 1

1.2 Literature Review on Piezoceramic Motor Technologies .......................................... 1 1.2.1 Piezoceramics and the Piezoelectric Effect ........................................................ 2 1.2.2 Quasi-Static Piezomotors .................................................................................... 3 1.2.3 Ultrasonic Motors (USMs) ................................................................................. 7 1.2.4 Summary ........................................................................................................... 15

1.3 Objectives and Motivation ....................................................................................... 16 1.4 Thesis Outline .......................................................................................................... 16

Chapter 2 RmMT Actuator Arrangement Concepts .......................................................... 18 Chapter 3 Motor Design .................................................................................................... 22

3.1 Background .............................................................................................................. 22 3.2 Assessment of Available USM Design and Development of the Novel Segmented

Electrodes Motor Design ..................................................................................................... 24 3.2.1 Confirmation of the E(3,1) Vibration Mode ..................................................... 24

3.2.2 Piezoceramic Material Selection ....................................................................... 29 3.2.3 Analysis of Initial USM Concepts .................................................................... 30 3.2.4 Simple Dynamic Model Development .............................................................. 33

3.2.5 Geometrical Optimization To Characterize Performance of USM Based on the

E(3,1) Concept ................................................................................................................. 36

3.2.6 New Segmented Electrodes Concept ................................................................ 38 Chapter 4 Experimental Assessment of Prototype ............................................................ 48

4.1 Motor Integration ..................................................................................................... 48

4.2 Static Analysis .......................................................................................................... 49

4.3 Experimental Setup for Speed, Force, and Resolution Testing ................................ 51 4.4 Assessment of Motor Performance Using One Amplifier ....................................... 54 4.5 Assessment of Motor Performance Using Two Amplifiers ..................................... 58

Chapter 5 Discussion and Conclusions ............................................................................. 62 5.1 Summary .................................................................................................................. 62

5.2 Recommendations and Future Research .................................................................. 63 References ............................................................................................................................... 64

Appendix A : Geometric Optimization Supplementary Data ............................................ 68 Appendix B : Segmented Electrodes Concept Supplementary Data ................................. 69 Appendix C : Segmented Electrodes Concept 2D FE Dynamic Analysis ......................... 71 Appendix D : Differential Electrode Voltage Concept ...................................................... 76 Appendix E : Impendence Analysis Supplementary Data ................................................ 81

Appendix F : Supplementary Data .................................................................................... 84 Appendix G : Piezoceramic and USM Drawings .............................................................. 86

v

List of Figures

Figure 1.1: (a) No electrical field present; (b) With electrical field present. ............................ 2 Figure 1.2: PiezoLEGS® motors working principle [4]. .......................................................... 5

Figure 1.3: PiezoLEGS® motors working principle [4]. .......................................................... 5 Figure 1.4: Inchworm® motors working principle [4]. ............................................................ 6 Figure 1.5: SIDM motor working principle [4]. ....................................................................... 7 Figure 1.6: Sample standing-wave USM working principle [4]. .............................................. 8 Figure 1.7: Longitudinal and Bending Hybrid Motor using BLTs [21]. .................................. 9

Figure 1.8: Piezoceramic Hollow Cylinder working principle [4]. ........................................ 10 Figure 1.9: Standing-wave Rotary USM [24]. ........................................................................ 10 Figure 1.10: Actuator model and drive-tip motion path [26]. ................................................. 11 Figure 1.11: Nanomotion motor and its working principle [28]. ............................................ 12

Figure 1.12: Physik Instrumente motor and its working principle [20]. ................................. 13 Figure 1.13: Linear motor driven by BLTs [27]. .................................................................... 14

Figure 1.14: Rotary traveling-wave USM working principle [4]. .......................................... 15 Figure 2.1: RmMT concept drawing. ...................................................................................... 18

Figure 2.2: Linear Actuator Concepts for RmMT. ................................................................. 19 Figure 2.3: Concept #1 of curvilinear/annular actuator driving the vertical columns. ........... 20 Figure 2.4: Concept #2 of curvilinear/annular actuator driving the vertical columns. ........... 20

Figure 2.5: Linear actuator in (a) linear and (b) curvilinear application. ............................... 21 Figure 3.1: Piezo-plate and coordinate system used. .............................................................. 24

Figure 3.2: Coordinate system used with equations (3.3) and (3.4). ...................................... 25 Figure 3.3: Superposition of natural vibration and the stress-strain effect. ............................ 26 Figure 3.4: E(3,1) vibration mode at (a) 60.193 kHz and (b) 67.772 kHz. ............................ 27

Figure 3.5: y-displacement distribution (a) 60.193 kHz and (b) 67.772 kHz. ........................ 27

Figure 3.6: Drive-tip displacement results from harmonic analysis. ...................................... 27 Figure 3.7: Asymmetrical excitation mode shape vibration sequence. .................................. 28 Figure 3.8: Drive-tip trajectory at 67.772 kHz. ...................................................................... 29

Figure 3.8: Actuator concept #1. ............................................................................................. 30 Figure 3.9: Actuator with just a divider, concept #2. .............................................................. 31

Figure 3.10: Actuator with flat bar on top and bottom, concept #3. ....................................... 32 Figure 3.11: y-displacement distribution of an actuator with a flat bar on top and bottom. ... 32

Figure 3.12: Actuator with frame around, concept #4. ........................................................... 33 Figure 3.13: Dynamic model diagram [26]. ............................................................................ 33 Figure 3.14: Performance of a 60 x 30 mm piezoceramic with varying thickness. ................ 37 Figure 3.15: Performance of 9 mm thick piezoceramic with varying length and width while

keeping the product of length and width at 16200. ................................................................. 38

Figure 3.16: FEA model of piezo-plate with drive-tip. .......................................................... 40 Figure 3.17: Electrode diagram. .............................................................................................. 41

Figure 3.18: Drive-tip trajectory at active electrode length of (a) 20mm, (b) 30mm, (c)

40mm, (d) 50mm. ................................................................................................................... 42 Figure 3.19: Estimated USM performance vs. electrode length based on the dynamic model.

................................................................................................................................................. 43 Figure 3.20: Top view of the segmented electrode concept. The arrows indicate the

polarization direction of the piezoceramic. ............................................................................. 44

vi

Figure 3.21: Piezo-plate type USM with proposed segmented electrodes. ............................ 45

Figure 3.22: FEA model of the piezo-plate with drive-tip and simplified support structure and

slider. ....................................................................................................................................... 45 Figure 3.23: Slider displacement estimated from FE dynamic analysis with a 30 mm active

electrode length. ...................................................................................................................... 47 Figure 3.24: Slider displacement estimated from FE dynamic analysis with a 40 mm active

electrode length. ...................................................................................................................... 47 Figure 4.1: 60 x 30 x 9 mm DL50 piezoceramic with segmented electrodes. ........................ 48 Figure 4.2: 60 x 30 x 9 mm piezoceramic with wires attached to the 14 electrodes. ............. 49

Figure 4.3: 60 x 30 x 9 mm piezoceramic with wires attached to the ground electrode. ....... 49 Figure 4.4: Overall USM structure. ........................................................................................ 50 Figure 4.5: Impendence analysis with 11 electrodes activated and a 50N preload. ............... 51 Figure 4.6: Original USM setup. ............................................................................................. 52

Figure 4.7: Final USM setup used. ......................................................................................... 52 Figure 4.8: Experimental setup workspace. ............................................................................ 53

Figure 4.9: Experimental setup block diagram. ...................................................................... 53 Figure 4.10: Maximum force testing setup. ............................................................................ 54

Figure 4.11: Amplifier output current versus number of active electrodes. ........................... 55 Figure 4.12: Maximum achievable speed result versus active electrode length. .................... 56 Figure 4.13: Maximum achievable force result versus active electrode length. ..................... 56

Figure 4.14: Displacement response with one active electrode and 18 µs impulse. ............... 57 Figure 4.15: Smallest achievable step result versus active electrode length. ......................... 58

Figure 4.16: Maximum achievable speed results with two amplifiers in parallel. ................. 59 Figure 4.17: Maximum achievable force results with two amplifiers in parallel. .................. 59 Figure 4.18: Total amplifier output current at 200 Vp versus number of active electrodes. ... 60

Figure 4.19: Maximum performance at 70 N preload with two amplifiers in parallel. .......... 61

vii

List of Tables

Table 1.1: Summary of Performance Characteristics of Selected Linear Piezomotors .......... 15 Table 1.2: Actuators Performance Requirement. .................................................................... 16

Table 3.1: FEA data of piezoceramic with varying thickness. ............................................... 37 Table 3.2: Electrodes dimension. ............................................................................................ 44

Chapter 1 Introduction

1.1 Background

Ultra accuracy actuators and positioners are needed in various fields of science and

engineering including automation of various biomedical laboratory protocols and in the

production of biochips, metrology research, and MEMs/NEMs and semi-conductor

manufacturing. The demand for actuators that can achieve nanometers accuracy yet having

an extended range of travel in the 10s and 100s of millimeters is continuously increasing [1],

[2]. Traditional DC brush motor cannot achieve the high accuracy requirement due to the

nature of its working principle. When a DC motor is attached to a screw actuator assembly,

only accuracy in the micrometer range can be achieved [3]. Piezoceramic actuators, on the

other hand, can achieve submicron accuracy. However, their thrust forces are much lower

compared to a DC screw actuator [1], [2].

1.2 Literature Review on Piezoceramic Motor Technologies

Piezoceramic actuators are transducers that transform electrical energy into mechanical

energy using the inverse piezoelectric effect [3]. They are superior in the mm-size range to

conventional electromagnetic (EM) motors since their efficiency is insensitive to size [5].

Some of the advantages of piezoceramic actuators are: quick response, immunity to external

magnetic fields, high holding force, high accuracy, and simple structure [1], [4]-[7].

Based on the working principle of the piezoceramic actuators, they can be classified into two

categories: quasi-static motors and ultrasonic motors (USMs). A quasi-static motor operates

at a frequency well below its resonant frequency and achieves motion by applying a DC

voltage across the piezoceramic. USM, on the other hand, drive its piezoceramic at its

resonant frequency, which is above the audible frequency, using an AC voltage.

In subsection 1.2.1, the basics of piezocreamics and the piezoelectric effect are discussed. In

subsection 1.2.2, a survey on quasi-static motors is conducted followed by a survey on USM

which is presented subsection 1.2.3.

1.2.1 Piezoceramics and the Piezoelectric Effect

The piezoelectric effect is a phenomenon that exists in piezoceramic material in which the

strain-stress characteristic is coupled with the electrical characteristic of the piezoceramic [1],

[2]. When an electrical field is applied to the piezoceramic, it will either expand or contract

depending on the polarity of the electrical field and the polarization direction of the

piezoceramic. Figure 1.1 (a) and (b) below shows a piezoceramic without the presence of an

electrical field and with the presence of an electrical field, respectively. The direction of the

arrow shows the polarization direction of the piezoceramic. The electrical field is applied

through electrodes on top and at the bottom of the piezoceramic.

Figure 1.1: (a) No electrical field present; (b) With electrical field present.

The relationship between the electric parameters and the mechanical parameters can be

represented by the constitutive equations of piezoelectricity and can be written in two forms:

{ } [ ]{ } [ ] { } (1.1)

{ } [ ]{ } [ ]{ } (1.2)

and

{ } [ ]{ } [ ] { } (1.3)

{ } [ ]{ } [ ]{ } (1.4)

(+)

(-)

(b) (a)

where,

{ } is the stress vector

{ } is the strain vector

{ } is the electric displacement vector

{ } is the electric field vector

[ ] is the compliance matrix at constant electric field

[ ] is the stiffness matrix at constant electric field

[ ] is the piezoelectric matrix relating strain to electric field

[ ] is the piezoelectric matrix relating stress to electric field

[ ] is the dielectric matrix at constant stress

[ ] is the dielectric matrix at constant strain

Equation (1.1) and (1.2) are widely used by manufacturers to present piezoelectricity

information and relationship. However, an equivalent form of the piezoelectricity

relationships is also shown using equation (1.3) and (1.4). These latter forms are used for

instance in implementing piezoelectric materials into FEA software such as ANSYS. In order

to transform the manufacturers’ data into the form of equation (1.3) and (1.4), the following

equations are used:

[ ] [ ] (1.5)

[ ] [ ] [ ] [ ] [ ] (1.6)

[ ] [ ] [ ] [ ] [ ] (1.7)

1.2.2 Quasi-Static Piezomotors

Quasi-static piezomotors directly actuate a slider or the moving object using the inverse

piezoelectric effect. Unlike an USM which uses an AC current to create waves in a solid

medium, a DC current is used to create a strain in the piezoelectric material. Key features of

this type of motors are their simplicity in operation and the fact that they operate well below

the resonant frequency [4].

1.2.2.1 Stepping Type Quasi-Static Piezomotors

Piezomotors using the stepping principle can offer higher resolution and force than USM.

They usually consist of several piezoceramic actuators integrated within a frame and generate

motion through a succession of coordinated clamp-unclamp and expand-contract cycles.

Each extension cycle provides only a few µm of movement, but these motors are typically

running at 100s to 1000s of cycles per second to achieve a macroscopic motion. However,

the main disadvantage is their low travel speed as compared to USM.

Piezomotors using the stepping principle includes the Inchworm® motors [8] by Burleigh

Instruments, Inc. (now EXFO Burleigh Product Group Inc.), the PiezoWalk® motors [9] by

Physik Instrumente, the PiezoLEGS® motors [10] by PiezoMotor AB and a Piezoworm

Stage [11] by S. Salisbury et al.

Figure 1.2 and Figure 1.3 shows the working principle of [10]. Each leg is made of a

piezoceramic with two electrodes. When the piezoceramic is energized with one electrode

acting as the active electrode and the other one acting as the ground electrode, a bimorph is

created. Two set of legs are used to create an engage-disengage pattern to generate motion.

Backward movement can be achieved by flipping the polarity of the electrodes [4].

Both [9] and [10] use the walking concept described above while [8] and [11] use the clamp-

unclamp concept to achieve locomotion as shown in Figure 1.4. The piezoworm stage in [11]

added a unique complementary clamp concept [12] to the inchworm concept to allow the use

of only two amplifiers instead of three and the potential of running at a higher frequency than

[8].

Recently, improvements on the performance of [8] were made according to [13]. Compared

to [8] which only have a speed of 1.5 mm/s and a thrust force of 10 – 15 N, the new HMR

EM2 motor was able to reach a speed of 25 mm/s and a thrust force of 120 N. The major

advancement was due to the use of pseudoelastic NiTi and MEMS microstructure at the

clamping surface [14]. The clamping surface modifications led to the coefficient of friction to

reach a value of 1.2.

Figure 1.2: PiezoLEGS® motors working principle [4].

Figure 1.3: PiezoLEGS® motors working principle [4].

Figure 1.4: Inchworm® motors working principle [4].

1.2.2.2 Inertial Type Quasi-Static Piezomotors

Piezomotors using the inertial principle consist of a moving part clamped to a metal shaft

which is attached to a piezoelectric actuator. When the piezoceramic expands or contracts

with low acceleration, the moving part moves with the motion of the metal shaft due to

friction. When the piezoceramic expands or contracts with high acceleration, the inertia of

the moving part prevents it from moving and it slides on the metal shaft.

The SIDM motor in Figure 1.5 by Konica Minolta Ltd. [15] is an example of a piezomotor

that uses the inertial principle. Konica Minolta Ltd. is using the technology in the anti-shake

mechanism for cameras. The main disadvantage of this type of motor is the high wear rate

due to sliding friction.

Figure 1.5: SIDM motor working principle [4].

1.2.3 Ultrasonic Motors (USMs)

The first USM was invented by V.V. Lavrinenko of USSR in 1965 and was granted an USSR

patent [16]. USM are excited at one of the piezoceramic’s natural frequencies using an AC

current to generate either a standing-wave or a traveling wave. This allows the motor to have

a smooth friction contact leading to a continuous motion of the moving part [4]. The

operating frequency of an USM is above the audible range.

1.2.3.1 Standing-Wave Type USM

Linear USMs are usually standing-wave motors that rely on the superposition of two

vibration modes to achieve bidirectional motion [4]. The two vibration modes are required

for the drive-tip of the motor to achieve an elliptical motion. Linear motion at the slider is

achieved by pressing the drive-tip against the slider using a preload. The two vibration modes

are most easily achieved by using two actuators as described in Figure 1.6.

Figure 1.6: Sample standing-wave USM working principle [4].

However, achieving elliptical motion is also possible using one actuator. The HR Series

USM [17] by Nanomotion Ltd. was the first commercially available USM that uses the single

actuator principle described in [18]. The PILine® series USM [19] by Physik Instrumente

also uses a single actuator to achieve motion but it uses a difference vibration mode than

[17]. [19] uses a rectangular piezoceramic plate along with two exciter electrodes on the front

surface and a common drain electrode on the back surface to generate elliptical motion at the

drive-tip [20] to generate a 3rd

x-expansion 1st y-expansion E(3,1) vibration mode instead of

the 1st longitudinal 2

nd bending mode (1L2B) vibration mode used in [17]. It was claimed in

[20] that the E(3,1) vibration mode allowed a higher-powered system because of it higher

resonant frequency. Due to the significance of [17] and [19] to this thesis, more details on

them are presented in subsections 1.2.3.1.2 and 1.2.3.1.3, respectively.

Thanks to their light weight and high speed characteristics, there are many other standing-

wave linear motors that are under development. Other linear USMs that use the standing-

wave principle include a high power motor [21] by Yun et al. which is reported to achieve a

maximum thrust force of 92N and a speed of 470mm/s. This linear USM, on the other hand,

uses the bolt-clamped Langevin transducer (BLT) concept to achieve the 1L2B mode for

elliptical motion at the drive-tips as shown in Figure 1.7. The motor consist of two sets of

piezoceramics: one set is responsible for the longitudinal vibration and one set is responsible

for the bending or flexural vibration. Motion is achieved by activating them in a sequential

manner.

Figure 1.7: Longitudinal and Bending Hybrid Motor using BLTs [21].

Rotary USM that uses the standing-wave principle are also available such as an ultra-small

USM developed by Seiko Instruments Inc. [22] that uses the standing-wave principle.

Another rotary motor that uses the standing-wave principle is a piezoceramic hollow cylinder

[23]. Similar in principle to [19], [23] uses the E(3,1) vibration mode in a cylindrical

configuration as shown in Figure 1.8. The inner surface of the cylinder is a common drain

electrode while the outer surface is covered by two groups of exciter electrodes. Lastly,

Hitachi Maxel proposed a standing-wave USM [24] that uses the BLT concept to generate

rotary motion with the help of a torsional coupler. Shown in Figure 1.9, the torsional coupler

transforms the linear motion of the BLT into circular motion which pushes a propeller.

A special single-element standing-wave USM also exists. The π-shape motor by J.R. Friend

[25] uses only one set of piezoceramic with one active-common electrode pair. The

bidirectional ability of the USM depends on the activation frequency.

Figure 1.8: Piezoceramic Hollow Cylinder working principle [4].

Figure 1.9: Standing-wave Rotary USM [24].

1.2.3.1.1 The standing-wave USM working principle

Before analyzing the Nanomotion USM and the Physik Instrumente USM, it is essential to

understanding the working principle of the standing-wave USM. The underlying concept of a

standing-wave USM is a preload force pushing an actuator that produces an elliptical motion

at the drive-tip against a slider. Depending on the phase angle and the amplitude of the

components of the elliptical motion, the path can be completely circular or a long ellipse as

shown in Figure 1.10. Two vibration modes are required to create the elliptical standing-

wave and the frequency of the two vibration modes must be the same or else the phase will

become inconsistent [26].

The friction force transferred from the drive-tip to the slider depends on the normal force

between them. The normal force varies depending on the phase of the drive-tip. If the phase

angle is positive, the friction force is at its peak when the drive-tip moves from left to right

according to Figure 1.10 and at its minimum when the drive-tip moves from right to left.

Although the drive-tip cannot make contact with the slider without relative motion due to the

large inertia of the slider, the drive-tip can accelerate or decelerate the slider and contribute to

the overall motion.

Figure 1.10: Actuator model and drive-tip motion path [26].

1.2.3.1.2 The Nanomotion Motor

The Nanomotion HR Series USM is a single actuator USM that uses geometric coupling of

two eigenmodes of a piezoceramic plate to produce elliptical motion [28]. The geometric

coupling allows the USM to use only one amplifier and eliminate the need for frequency

coupling of the two modes [20].

A ceramic tip is used as the drive-tip for the actuator. By exciting two of the four electrodes

on the rectangular piezoceramic plate (the two labelled with arrows in Figure 1.11) at its

resonant frequency of about 39.6 kHz, elliptical motion is created at the drive-tip through the

1L2B vibration mode [26]. According to [20], since the 1L2B vibration mode for the

geometry occurs at about 40 kHz when the size of the piezoceramic is about

mm, it is very difficult to scale up the size of the piezoceramic to achieve a force higher than

the current 4 N thrust force because the resonant frequency will decrease as the size pf the

piezoceramic increases.

Figure 1.11: Nanomotion motor and its working principle [28].

1.2.3.1.3 The Physik Instrumente Motor

The Physik Instrumente PILine® Series USM is another single actuator USM that uses

geometric coupling of two eigenmodes. The difference between this and the USM in the

previous subsection is the geometry of the piezoceramic plate and the vibration mode used

[28]. Instead of using a piezoceramic plate with a low aspect ratio, a ratio of about 6:3:1 for

X:Y:Z, respectively, is used [20]. As shown in Figure 1.12, by dividing the top surface into

two equal size electrodes and covering the back surface with a single common ground

electrodes, elliptical motion at the drive-tip can be achieved when exciting one of the top

electrodes at the E(3,1) resonant frequency. The E(3,1) is described in subsection 3.2.1 of

this thesis as well as in [20]. The drive-tip is located at the middle of the long side. Both the

design of this motor and the motor in the previous subsection is very simple in terms of ease

of manufacturing. However, the efficiency of the motor in this subsection is relatively higher

[28].

Figure 1.12: Physik Instrumente motor and its working principle [20].

1.2.3.2 Traveling Wave-Type USM

Traveling-wave USMs are usually used in rotary applications because a continuous path or

an infinitely long path for the wave is required. However, linear traveling-wave motors are

possible as shown in Figure 1.13. This motor uses two BLTs with one as the vibrator and one

as the absorber to generate a traveling wave along the transmission rod. The problem with

this motor is its low efficiency because the entire transmission rod must be excited with only

a small portion of it contributing to the output.

Figure 1.13: Linear motor driven by BLTs [27].

The most prominent traveling-wave motor is the rotary motor invented by Sashida [29].

Traveling-wave USMs achieve elliptical motion by combining two standing waves that are

offset by 90° in space and in time. This can be shown mathematically with the formulas

below.

Equation (1.8) is the equation of a standing wave and equation (1.9) is the equation of a

traveling wave.

( ) ( ) ( ) (1.8)

( ) ( ) (1.9)

By using the trigonometric relation of equation (1.10), equation (1.9) can be rewritten as

equation (1.11) which is the summation of two standing waves offset by 90° in space and in

time.

( ) ( ) ( ) ( ) ( ) (1.10)

( ) ( ) ( ) ( ⁄ ) ( ⁄ ) (1.11)

Shown in Figure 1.14, the rotor of a traveling-wave USM surfs on top of the traveling-wave

and uses the tangential friction force at the wave peak to achieve motion. While in [30], a

rotary motor with piezoelectric element along the circumference of the motor is proposed,

[31] and [32] proposed a rotary motor with BLTs attached to the circular stator to generate a

traveling wave. This configuration was claimed to be more efficient because it uses the d33

mode of the piezoceramic instead of the lower efficiency d13 mode.

One of the disadvantages of traveling-wave USMs versus standing-wave USM is they have a

low theoretical efficiency. Since two vibration sources are needed to generate two standing

waves for a traveling wave, the theoretical maximum efficiency can only be 50%.

Nevertheless, rotary USMs similar in concept to Sashida’s motor mentioned above are

widely used in Canon’s interchangeable lens for their EOS series camera [33].

Figure 1.14: Rotary traveling-wave USM working principle [4].

1.2.4 Summary

The characteristics of some of the piezomotors discussed are summarized in Table 1.1.

Table 1.1: Summary of Performance Characteristics of Selected Linear Piezomotors

Linear

Motor

Max Speed

[mm/s]

Stroke

[mm]

Thrust

Force

[N]

Holding

Force

[N]

Size [mm] Weight

[g]

Principle of

Operation

Co

mm

erci

al

Piezo LEGS

Linear 20N 20 55 20 22 22 x 10.8 x 21 40 Stepping

PiezoWalk®

N-216.2 1 20 600 800 95 x 80 x 72 1250 Stepping

PILine®

U-164 500 - 4 - 120 x 40 x 9 - Standing-wave

HR8 250 - 30-36 28 42 x 47 x 24 170 Standing-wave

HMR EM2 25 25 120 120 Ø17.8 x 101.6 - Inchworm

Res

earc

h

Salisbury et

al. 2009 8.5 - 6 - 45 x 27 x 43 - Inchworm

Y.X. Liu et

al. 2010 1160 - 20 - ~99 x ~116 - Standing-wave

W.S. Kim et

al. 2008 450 - 75 - Ø20 x 247 - Standing-wave

C.H. Yun et

al. 2001 470 - 92 - Ø40 x 92 - Standing-wave

1.3 Objectives and Motivation

The main objective of this thesis is to select or develop an actuator for the Reconfigurable

meso-Milling Machine Tool (RmMT) being developed by the Canadian Network for

Research and Innovation in Machining Technology (CANRIMT) University of Toronto

Node. The RmMT requires linear and curvilinear actuators with the specification outlined in

Table 1.2.

Table 1.2: Actuators Performance Requirement.

Speed [mm/s] 100

Accuracy [µm] 0.1

Stiffness [N/µm] 100

Force/Holding [N] 80

Furthermore, an actuator with the given performance requirements can also be used in

various fields of automation including biomedical laboratory, production of biochips,

MEMS/NEMS manufacturing, etc. Due to the accuracy and holding force requirements, a

piezoceramic motor is deemed to be the most suitable solution for the application. But, from

the literature review listed in the previous subsection, no commercially available

piezoceramic motor can meet the requirements. As a result, the goal of this thesis is to

develop a high speed, high force, and high accuracy piezoceramic motor characterized by the

following:

The motor should have a minimum travel of 150 mm and allow operation in both

linear and curvilinear applications.

The motor should be easily controllable and allow easy integration with the RmMT.

Another objective for the project is to develop a motor with the ability of decoupling the

force and the speed output. This objective is discussed further in Chapter 3.

1.4 Thesis Outline

This thesis is a combination of the material from two conference papers, [34] and [35], as

well as progress reports throughout the project and results from experimental investigations.

Chapter 2 describes a linear motor setup concept and two curvilinear motor setup concepts

for the RmMT with the presentation of the proposed integration method at the end of the

chapter.

Several USM optimization concepts as well as the proposed motor concepts with FE analysis

results are present in Chapter 3. Some of the results in Chapter 3 are presented in the form of

a summary. Full result can be found in the appendices. Chapter 4 presents the results from

the experimental investigation of the proposed motor and Chapter 5 concludes the thesis with

a summary and recommendations for future research.

Chapter 2 RmMT Actuator Arrangement Concepts

The Reconfigurable meso-Milling Machine Tool (RmMT) [36] is a project being developed

at the University of Toronto. The machine uses parallel mechanism to support a tool centre in

the middle. A concept drawing of the machine is shown in Figure 2.1 and arrows are used to

show the actuator requirement of the machine. The purposed dimensions of the machine are

250 mm in diameter, 100 mm in height, and the height of each vertical column is 80 mm.

The RmMT require 3 curvilinear actuators and 3 linear actuators with performance listed in

Table 1.2.

Figure 2.1: RmMT concept drawing.

Figure 2.2 describes two possible concepts for the linear motors arrangement. Using similar

working principles as [17] and [19], the approach is to integrate multiple motors together

then redesign and optimize the assembly to achieve the required performance. The contact

area will be increased by increasing the number of drive-tips and the size of the drive-tips. A

high friction interface will also be used.

Figure 2.2 (a) describes a concept with a rectangular rail while Figure 2.2 (b) describes a

concept with a triangular rail. In both concepts, the motors and the rail guide will be fixed to

a structure while the rail or the slider moves up and down when it is driven by the drive-tips.

Bearings will be used at the slider-guide interface to ensure smooth sliding. In order to

Ø250mm

translate the elliptical motion at the drive-tips into linear motion, preload will be applied at

the motors to press the drive-tips against the slider. The triangular rail in Figure 2.2 (b)

allows the slider to be more structurally stable than a rectangular rail while still providing the

same amount of area for actuation as well as a flat surface for the rail guide.

Figure 2.2: Linear Actuator Concepts for RmMT.

The curvilinear/annular motors needed for the RmMT present additional challenges besides

accuracy, speed and thrust force. It is desired to have a curvilinear/annular motor that is free

to rotate 360° along the circumference of the RmMT. However, having a moving motor will

increase the complexity of the design and decrease the stability of the structure. As a result,

two concepts with fixed motors pushing a curved slider are presented.

Figure 2.3 and Figure 2.4 describe two possible configuration concepts for the

curvilinear/annular motors. In both concepts, linear motors are used to actuate the slider. In

Figure 2.3, three stationary motors are equally spaced along the circular ring. Each motor

will actuate a curved slider: an arc segment of 60° inside the circular rails. The slider will run

smoothly inside the circular rails using bearings and springs will be used to provide the

required preload. Vertical columns with vertical motors will be attached to each slider.

Figure 2.4 describes another concept in which multiple motors are placed along the entire

circumference of the circular ring to generate the required thrust force. The motors will be

fixed to the structure while the vertical columns are attached to the moving rings. Each

vertical column will have its own moving ring in which they will be stacked concentrically

on top of each other. Each ring will have its own set of motors.

Figure 2.3: Concept #1 of curvilinear/annular actuator driving the vertical columns.

Figure 2.4: Concept #2 of curvilinear/annular actuator driving the vertical columns.

As mentioned, however, it is desired that the curvilinear/annular motors to have 360° motion

on a common rail. Therefore, the concepts mentioned above were not pursued and a concept

of using linear motors for both linear motion and curvilinear motion was pursued instead. In

the new concept, each curvilinear/annular motor will run on a fixed common circular rail.

The motor for the vertical column will be mounted on top of the curvilinear motors as

described in Figure 2.5. Linear motors will be used for both linear and curvilinear

applications to increase the modularity of the design. The mounting base of the linear motor

and the curvilinear motor will have a linear guide and a curvilinear guide, respectively.

Figure 2.5: Linear actuator in (a) linear and (b) curvilinear application.

Chapter 3 Motor Design

3.1 Background

The speed of a piezoceramic motor is directly related to its operating principle which dictates

its step size per stroke, and its operating frequency. The step size of a quasi-static motor is

limited to the amount of extension in its extension-contraction actuator, which is usually a

piezo-stack. A typical piezo-stack only has an extension displacement in the 0.1% range of

its original length. At a typical operational frequency of around 1 kHz, a quasi-static

piezomotor only has a travel speed of around 10 mm/s but can achieve a thrust force up to

100s of Newtons. On the other hand, an USM operating at its resonant frequency can have a

travel speed in the 100s mm/s range but with a typical thrust force in the 10s of Newton. As a

result, a USM is preferred over a quasi-static motor when designing a piezoceramic motor for

a high speed application and quasi-static motor is preferred for high force application.

However, improving the travel speed of a quasi-static motor is difficult then improving the

thrust force of a USM because of their operating principle.

In order for an USM to generate a higher thrust force, the amount of friction force between

the drive-tip and the slider needs to increase or remain high during both high speed and low

speed operation. The basic friction laws are listed in equations (3.1) and (3.2). Equation (3.1)

is used when there is no sliding between the two surfaces and equation (3.2) is used when

sliding exists.

(3.1)

(3.2)

where,

is the static friction force

is the dynamic friction force

is the normal force

is the static coefficient of friction

is the dynamic coefficient of friction

Increasing the friction between the drive-tip and the slider can be done by increasing the

coefficient of friction between the two surfaces such as by using a high friction interface

similar to the one in [14] or by increasing the amount of normal force at the contact surface.

There are a few methods to increase the amount of normal force at the contact surface. The

simplest method is perhaps by increasing the amount of preload applied to the actuator.

However, this method only works until the amount of preload is too high and prohibits the

drive-tip to detach from the slider on the return stroke. Another method is to excite the

actuator at a higher power to increase the expansion and contraction of the piezoceramic.

This method can lead to satisfactory results but can also potentially overstress the

piezoceramic and cause permanent damage. Lastly, the amount of the normal force can be

increased by designing an actuator with a geometry that will lead to amplification in the

vertical displacement of the drive-tip when operating at a resonant frequency.

On top of the speed and the thrust force requirements, there is the accuracy requirement of

the piezocearmic motor. The accuracy depends on the resolution of the feedback system and

the ability to reach the desired accuracy depends on the smallest step achievable by the

motor. The accuracy of a quasi-static motor, in the case of an inchworm motor, is very high

and ultra-high accuracy is easily achievable because the extension and contraction of the

piezo-stack used in the inchworm motor, for instance, is directly related to the applied

voltage. A USM, on the other hand, is different since the motion requires the generation of an

elliptical motion at the drive-tip, thus its accuracy is limited by the size of the ellipse.

Furthermore, the commercially available USMs in [17] and [19] run into problems in high

force and low speed operation because both speed and force are coupled and the only control

parameter is the operating voltage. As a result, the USM is not likely to perform effectively

in such an operating condition, commonly known as the dead zone of the USM, which leads

to a limited accuracy when speed is low.

Despite the mentioned disadvantages of USM, a USM is pursued for the project. The new

USM to be developed needs to achieve high speed and high force while improving the

achievable accuracy by eliminating or reducing the dead zone problem that characterizes the

currently commercially available USMs.

3.2 Assessment of Available USM Design and Development of the Novel

Segmented Electrodes Motor Design

The new USM will operate in both linear and curvilinear modes for the RmMT application

by using the E(3,1) vibration mode concept. This vibration mode corresponds to the

standing-wave principle which is characterized by high efficiency and simplicity in design

and its potential for scaling for a high force application.

3.2.1 Confirmation of the E(3,1) Vibration Mode

In order to develop a USM using the E(3,1) vibration mode, the concept need to be modeled,

confirmed, and fully understood first. This is pursued in this subsection and the achieved

results are compared to published information in [20]. The E(3,1) vibration mode is a two

dimensional standing-wave mode in which the x-component is in the third vibration mode

and the y-component is in the first vibration mode. This vibration mode only occurs when the

dimensions of a solid are such that an X:Y ratio of around 2:1 exists and the thickness in the

z-direction is relatively small in order for the geometry to be a considered a plate as shown in

Figure 3.1.

Figure 3.1: Piezo-plate and coordinate system used.

According to [20], the mode shape of a symmetrically excited piezo-plate can be described

by equations (3.3) and (3.4) with the origin at the centre of the piezo-plate as shown in Figure

3.2.

( ) (

) ( (

) ) ( ) (3.3)

( ) ( (

)) (

) ( ) (3.4)

Piezoceramic x

y

z

where,

is the displacement in the x-direction for a point in the piezo-plate

is the displacement in the y-direction for a point in the piezo-plate

are constants that depend on the geometry

is the length of the piezo-plate in the x-direction

is the height of the piezo-plate in the y-direction

Figure 3.2: Coordinate system used with equations (3.3) and (3.4).

As a result, the largest y-displacement happens at and ⁄ . When the piezo-

plate is excited asymmetrically, the standing-wave is shifted causing the point with the

largest y-displacement to also have an x-displacement. By putting a drive-tip at this location,

the piezo-plate can be used to provide motion for an actuator.

The displacement at the drive-tip location is the superposition of the natural vibration of the

E(3,1) mode and the strain-stress effect in the piezoceramic. When the piezo element at the

active electrode is excited and it expands, the stress created results in a strain in the x- and y-

directions. At the first and third half-wave along the x-direction, the natural vibration

prevents the element from expanding in the y-direction causing all the strain to be in the x-

direction. This strain eventually reaches the elements at the middle half-wave which is not

constrained from expanding in the y-direction. This, along with the natural vibration,

produces further displacement at the drive-tip as shown in Figure 3.3.

x

y

z

Figure 3.3: Superposition of natural vibration and the stress-strain effect.

ANSYS FEA was conducted on a piezoceramic plate with dimensions mm. The

dimensions were chosen to reflect the dimensions in [20]. A common drain electrode that

covers the entire back surface and two 30 x 30 mm excitation electrodes were placed on the

front surface of the piezoceramic plate. The common electrode was set to have a voltage of 0

V and both excitation electrodes were set to have a voltage up to of 200 Vp. It should be

noted that the magnitude of the voltage is not important because the ANSYS analysis is only

concerned with the sign of the voltage during a modal analysis.

From the FEA, it was found that this geometry has two E(3,1) vibration modes. One of the

vibration modes is at 60.193 kHz and the second one is at 67.722 kHz as shown in Figure

3.4. These two resonant frequencies confirmed the results presented in [20]. The small

discrepancy between the frequencies was due to missing data from [20] such as material

properties, damping factors, etc. which was substituted by properties of common

piezoceramic.

The E(3,1) vibration mode at 67.772 kHz is the one of interest because the largest vertical

displacement occurs at the centre of the top edge compared to one-quarter and third-quarter

of the way along the top edge at 60.193 kHz. Figure 3.5 shows the y-displacement

distribution of the two E(3,1) vibration modes.

The actuator was then excited asymmetrically by exciting only one of the two top electrodes

at 200 Vp. Similar results as [20] were once again found from the FEA. When the

piezoceramic is excited asymmetrically, a linear motion at the drive-tip location can be

observed in Figure 3.7.

(a) (b)

Figure 3.4: E(3,1) vibration mode at (a) 60.193 kHz and (b) 67.772 kHz.

(a) (b)

Figure 3.5: y-displacement distribution (a) 60.193 kHz and (b) 67.772 kHz.

From the harmonic analysis results in Figure 3.6, the two E(3,1) modes can be clearly

observed as the two peaks in x- and y-displacement of the drive-tip. The peak with the higher

frequency correspond to the desired E(3,1) vibration mode because both of its x- and y-

displacement are at their maximum.

Figure 3.6: Drive-tip displacement results from harmonic analysis.

1.E-09

1.E-08

1.E-07

1.E-06

55000 57500 60000 62500 65000 67500 70000

Dis

pla

cem

en

t [m

]

Frequency [Hz]

UX

UY

Figure 3.7: Asymmetrical excitation mode shape vibration sequence.

From a dynamic analysis, it was found that the drive-tip trajectory, shown in Figure 3.8, had

an x-displacement of 0.39 µm and a y-displacement of about 0.51 µm, in line with the

manufacturer’s data. As a result, this analysis confirmed that the E(3,1) concept is a viable

option for the development of the new USM.

Figure 3.8: Drive-tip trajectory at 67.772 kHz.

3.2.2 Piezoceramic Material Selection

Different piezoceramics come with different material properties and selecting the right

piezoceramic for the USM to be developed can greatly enhance its performance. Lead

Zirconate Titanate (PZT) is the most common piezoceramic material used in USM. PZT is

usually divided into two groups: soft PZT and hard PZT [34]. Soft PZT has high domain

mobility resulting in a ferroelectrically soft behavior meaning it is easy to polarize and leads

to a large displacement under an electrical field. On the other hand, hard PZT is stable even

when subjected to high electrical and mechanical stresses making hard PZT ideal for high-

power applications.

Another advantage of hard PZT is its high mechanical quality factor because of the limited

domain mobility. The benefit is a reduction of internal friction when the PZT is excited under

an electrical field and an overall increase in efficiency. However, the drawbacks are reduced

electro-mechanical coupling factors.

Equation (3.5) shows the coupling factors for a typical PZT-4 and equation (3.6) for a typical

PZT-5 [38].

[ ] [

]

(3.5)

[ ] [

]

(3.6)

PZT-4 is a hard PZT and PZT-5 is a soft PZT. By comparison, the soft PZT has a

significantly higher coupling factor than the hard PZT which results in a higher displacement

when subject to the same electrical field. One thing to note is that the quality factor for soft

PZT is typically in the 10s and 100s while it is in the 1000s for hard PZT.

Nevertheless, soft PZT will be used in the proposed USM being developed because

efficiency is not a design objective in the development of the first version of the motor while

high performance in terms of high speed and high force are desired.

3.2.3 Analysis of Initial USM Concepts

The key of the USM performance lies within the design of the piezoceramic and the structure

surrounding it. By keeping the E(3,1) vibration mode in mind, some new designs were

proposed. The new designs were a modification of the one presented in [20] and focused on

increasing the y-displacement at the drive-tip. The initial approach was to divide the

rectangular piezoceramic into two piezoceramics each with its own excitation and ground

electrode as shown in Figure 3.9.

Figure 3.9: Actuator concept #1.

By dividing the piezoceramic into two smaller piezoceramics, the two smaller piezoceramics

can now be excited and controlled individually. With this flexibility, the two piezoceramics

can be excited with a phase lag between them in an attempt to increase the maximum y-

displacement and thus increase the amount of thrust force the actuator produces. The drive-

tip remained at the middle of the top edge. A frame is used to keep the two piezoceramics in

place.

Preliminary analysis results showed that the y-displacement of the above actuator was not

increased but decreased due to the constraints imposed by the frame. As a result, three

simpler versions of the actuator were modeled to understand the effect the frame has on the

motion generated. The first design modeled was an actuator with two piezoceramics with a

divider glued in between as shown in Figure 3.10. This actuator exhibited similar

characteristic as [20] but with a lower y-displacement when excited at its E(3,1) resonant

frequency. As a result, there was no improvement.

The next geometry modeled was two piezoceramics connected by a flat bar on top and

bottom as shown in Figure 3.11. Modal analysis of the model shows the piezoceramics freely

expand into the gap between the two piezoceramics. Also, the removal of the divider allowed

the centre of the structure to expand freely upward and downward; creating a slightly higher

y-displacement than the previous model as well as the model in [20]. Figure 3.12 shows the

y-displacement distribution of the actuator at its E(3,1) resonant frequency.

However, further analysis of concept #3 showed that although the displacement of the drive-

tip in the y-direction was greater than [20], the stiffness of the structure was greatly reduced

because of the gap in between the piezoceramics. As a result, the overall performance was

not improved.

Figure 3.10: Actuator with just a divider, concept #2.

Figure 3.11: Actuator with flat bar on top and bottom, concept #3.

Lastly, the actuator was modeled with a frame around the piezoceramics. The gap between

the two piezoceramics remained open to allow free expansion into the centre as shown in

Figure 3.13. This model exhibited similar characteristics as the model above but with a

slightly lower y-displacement due to the added constraints. As a result, the overall

performance was also not improved.

Based on the above analysis and the inability so far to enhance the performance of the USM

through simple modifications of the design in [20], further study into the problem was

conducted.

Figure 3.12: y-displacement distribution of an actuator with a flat bar on top and

bottom.

Figure 3.13: Actuator with frame around, concept #4.

3.2.4 Simple Dynamic Model Development

The performance of an USM cannot be fully estimated directly from the x- and y-

displacement of the drive-tip. Numerical solving methods along with a dynamic model are

required to assess the performance. The drive-tip trajectory and the performance can be

estimated using a simplified dynamic model that relates the motion of the slider to the drive-

tip [26]. This is pursued in this subsection by developing a model for the interface. A

diagram of the model is shown in Figure 3.14. This dynamic model is used subsequently to

assess the performance of the USM.

Figure 3.14: Dynamic model diagram [26].

Slider with mass, m

Piezoceramic

Drive

-tip

where,

is speed of the drive-tip

is speed of the slider

is acceleration due to gravity

is the friction force acting on the slider

is the preload force applied to the piezoceramic

The motion of the drive-tip can be represented by equations (3.7) and (3.8) where the x and y

directions are as defined previously.

( ) (3.7)

( ) (3.8)

where,

is x-displacement of the drive-tip

is y-displacement of the drive-tip

is maximum x-displacement of the drive-tip

is maximum y-displacement of the drive-tip

is the operating frequency

is the time

is the phase difference between the x-displacement and y-displacement

Therefore, the velocity of the drive-tip can be written as equation (3.9) and (3.10) below.

( ) (3.9)

( ) (3.10)

where,

is speed of the drive-tip in the x-direction

is the speed of the drive-tip in the y-direction

The amount of force transmitted from the drive-tip to the slider depends on the amount of

friction, , which acts on the slider in two ways: contributes to the motion when the speed of

the drive tip is greater than that of the slider or opposes the motion when the speed of the

drive tip is less than that of the slider.

In summary:

( ) (3.11)

( ) (3.12)

where,

is speed of the slider

is the friction force acting on the slider

If it is assumed that there is no friction between the slider and its bearing, the equation of

motion of the slider can be written as equation (3.13).

( ) (3.13)

where,

is mass of the slider

is acceleration of the slider

If we assume there are no slippage between the drive-tip and the slider, the friction force, ,

is the product of the friction coefficient between the drive-tip and the slider, , and the

normal force, .

(3.14)

The normal force is the sum of the preload force, , and the dynamic force, . The dynamic

force is the product of the piezoceramic stiffness, , and the y-displacement of the drive-tip,

. The normal force cannot be negative.

(3.15)

In [26], it was assumed that the drive tip always made contact with the slider and the normal

is always acting on the slider. However, this may not be the case because the restoring rate of

the slider material is slower than the movement of the drive-tip moving downward. As a

result, if we assume that the normal force only acts on the slider when the drive-tip is moving

upward or when , the equation of motion can be written as equation (3.16).

( ) [ ( ) ] (3.16)

where,

is the mass of the slider

is the acceleration of the slider.

Substituting equations (3.14) and (3.15) into (3.16) and rearranging results in equation (3.17).

( ) [ ( ) ( ) ] ⁄ (3.17)

where,

is the acceleration due to gravity

The gravity term only enters into play when the USM is operating in a vertical configuration.

Equation (3.17) can be solved numerically using an ODE solver within MATLAB.

3.2.5 Geometrical Optimization To Characterize Performance of USM Based on the

E(3,1) Concept

The geometry of the piezoceramic in [20] is mm and FE analysis using PZT-4

data showed an x- and y- displacements of the drive-tip of 0.39 µm and 0.51 µm,

respectively. To improve the motor’s performances, geometrical optimization was conducted

by varying the dimensions of the piezoceramic used in the motor. This optimization and

analysis is intended to provide an insight into the new design of the USM.

When the thickness of the piezoceramic was increased to 10 mm from 9 mm, both the x- and

y-displacement decreased while the stiffness of the structure increased. The speed and force

output of the motor can be determined from a dynamic analysis discussed in subsection 3.2.4.

On the other hand, when the thickness of the piezoceramic was decreased, both the x- and y-

displacements increased. The FEA results corresponding to varying the thickness of the

piezoceramic are shown in Table 3.1.

When the displacement data presented in Table 3.1 are inserted into the dynamic model of

subsection 3.2.4 with [26], [39] with , it was found that thicknesses of 8

mm and 9 mm lead to very similar performance as shown in Figure 3.15. To keep the amount

of change from the benchmark model to a minimum, the thickness of 9 mm is used for

subsequent dimensional analysis.

Table 3.1: FEA data of piezoceramic with varying thickness.

Dimension E(3,1) Freq.

[Hz] UX [m] UY [m] Phase [°]

L W T

60 30 7 60223 1.69707e-6 5.02568e-6 -6.62

60 30 8 60059 1.43382e-6 4.44306e-6 3.45

60 30 9 59884 1.22658e-6 3.91805e-6 3.04

60 30 10 59697 1.00953e-6 3.45112e-6 2.44

60 30 11 59443 1.08948e-6 2.94051e-6 0.32

Figure 3.15: Performance of a 60 x 30 mm piezoceramic with varying thickness.

For the length and width dimensional analysis, the area of the top surface of the piezoceramic

was kept as constant as possible. Since the thickness is set at 9 mm, the length and width

were varied but the product of the two values was kept as close to 16200 as possible while

keeping the length and the width as integers. As the aspect ratio of the piezoceramic, the ratio

between the length and the width, increases from the 2:1 benchmark value, the performance

improved slightly than worsened as the aspect increases to 5:2. On the other hand, when the

aspect ratio decreases from the 2:1 benchmark value, the performance never improved. A

summary of the performance based on varying the length and the width is shown in Figure

3.16.

From the results, a length and width of 62 and 29 mm, respectively, or an aspect ratio of 2.14

leads to achieving the maximum force, while a length and width of 64 and 28 mm,

respectively, or an aspect ratio of 2.29 leads to achieving the maximum speed. However, this

optimization provided only an improvement on the performance based on varying the

5

7

9

11

13

15

17

19

21

23

25

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

7 7.5 8 8.5 9 9.5 10 10.5 11

Esti

mat

ed

Max

imu

m T

hru

st F

orc

e [

N]

Esti

mat

ed

Max

imu

m S

pe

ed

[m

/s]

Thickness [mm]

Speed

Force

dimensions of the piezoceramic whereas the requirement of decoupling the force and speed

output was not solved. Therefore, although the performance of the motor can be controlled to

favor the speed output or the force output by varying the dimensions of the piezoceramic,

changing the dimensions during operation is not feasible with current technology. So a new

concept to decouple the speed and force output of the motor is still required and is pursued

next.

Figure 3.16: Performance of 9 mm thick piezoceramic with varying length and width

while keeping the product of length and width at 16200.

3.2.6 New Segmented Electrodes Concept

As mentioned before, by keeping the ratio of length (L) to width (W) of a piezo-plate near 2

and a thickness (T) near 0.15 × L, the superposition of two vibration modes occurs at one

resonant frequency – making the motor useful in attaining bidirectional motion. One

drawback of the design is the coupling of the speed and force output of the motor. The speed

and force output are directly related to the x- and y-displacement of the drive-tip. Therefore,

in order to decouple the speed and force output, greater control of the drive-tip trajectory is

needed. It was observed previously that the trajectory of the drive-tip can be controlled by

varying the dimensions of the piezoceramic. However, this is currently not feasible in

continuous operation.

5

7

9

11

13

15

17

19

21

23

25

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

1 1.5 2 2.5 3

Esti

mat

ed

Max

imu

m T

hru

st F

orc

e [

N]

Esti

mat

ed

Max

imu

m S

pe

ed

[m

/s]

Aspect Ratio [X:Y]

Speed

Force

The drive-tip in the E(3,1) vibration mode depends on the natural planar expansion and

contraction as well as the stress-strain effect of the element in the piezoceramic. So far, only

the natural vibration portion of the E(3,1) vibration mode was considered for improving the

motor performance through varying the dimensions of the piezoceramic. The stress-strain

effect was not considered in the analysis.

The stress-strain effect’s contribution to the trajectory of the drive-tip depends on the amount

of stress in the x-direction that is translated into strain in the y-direction. If the amount of

stress that is translated to strain can be controlled, then the trajectory of the drive-tip may

become controllable. The amount of stress on the piezoceramic depends on the preload

applied and the electrical field applied. Adjusting the preload is difficult during operation but

changing the electrical field during operation can be done.

A piezoceramic is typically modelled as a capacitor. Therefore, the electrical field across the

piezoceramic depends on the voltage applied to the electrode as well as the area of the

electrodes as shown in equation (3.18). Equation (3.18) represents the general parallel-plate

capacitor model.

(3.18)

where,

is electrical field

is the permittivity

is the area of the parallel plates (or electrodes)

is the distance between the parallel plates (or electrodes)

is the voltage between the parallel plates (or electrodes)

While increasing the applied voltage to the electrodes leads to more deformation of the

piezoceramic, an electrode size-to-performance analysis was not previously conducted. As a

result, varying the electrode size is pursued in order to assess its impact on the deformation

of the piezoceramic and the impact of such a deformation on the motion of the drive-tip. This

is pursued next through FE analysis.

It was mentioned in subsection 3.2.2 that PZT-5 will be used for the new USM. As a result,

BM500 piezoceramic [40] data from equation (3.19) to (3.22) is used for the analysis.

[ ]

[ ]

(3.19)

[ ] [

]

(3.20)

[

] (3.21)

(3.22)

A piezo-plate with dimensions L = 60 mm, W = 30 mm, T = 9 mm was modeled in FE

software, as shown in Figure 3.17. The analysis is pursued to study the effect of varying the

electrode size on the drive-tip trajectory. The active electrode covered the entire length in the

y-direction whereas the length in the x-direction was varied as shown in Figure 3.18. The

active electrode was placed on the top surface while the entire back surface was covered with

a single ground electrode.

The electrode length along the x-direction was varied from 12.5 mm to 57.5 mm at 2.5 mm

increments. First, a modal analysis was conducted at each length followed by a harmonic

analysis based on the results of the modal analysis. The modal analysis was used to find the

E(3,1) resonant frequency of the structure and the harmonic analysis was used to find the x-

and y-displacements of the drive-tip at the E(3,1) frequency.

Figure 3.17: FEA model of piezo-plate with drive-tip.

Figure 3.18: Electrode diagram.

From the harmonic analysis using a 200 Vp excitation voltage, the maximum x-displacement

of the drive-tip was found to be 5.35 µm when the electrode length is 22.5 mm and the

maximum y-displacement of the drive-tip was found to be 10.81 µm when the electrode

length is 57.5 mm. The drive-tip trajectory is shown in Figure 3.19. It can be observed that as

the length of the active electrode increases, the trajectory of the drive-tip becomes more

vertical. This result will be used subsequently as the basis for the design of the new USM

concept. A more vertical drive-tip corresponds to a high force output but a lower speed. The

FEA drive-tip displacement data can be found in Appendix B.

The displacement data is analyzed using the dynamic model presented in subsection 3.2.4

with [26], [39] and . The motor performance versus electrode length graph

is shown in Figure 3.20. The tabulated data can be found in Appendix B. From the analysis,

it was found that the maximum speed is achieved when the electrode length is 22.5 mm and

the maximum force is achieved when the electrode length is 57.5 mm. It should be noted that

when the maximum achievable force is at its maximum, the associated maximum achievable

speed is at its minimum. From the analysis, it can be concluded that by introducing a

mechanism that allows the electrode length to be varied, the speed and force characteristics

of the motor can be varied in real-time.

Electrode Length

Active

Electrode

x

y

Figure 3.19: Drive-tip trajectory at active electrode length of (a) 20mm, (b) 30mm, (c)

40mm, (d) 50mm.

-6.E-06

0.E+00

6.E-06

-4.E-06 0.E+00 4.E-06

UY

[m

]

UX [m]

(a)

-6.E-06

0.E+00

6.E-06

-4.E-06 0.E+00 4.E-06

UY

[m

]

UX [m]

(b)

-6.E-06

0.E+00

6.E-06

-4.E-06 0.E+00 4.E-06

UY

[m

]

UX [m]

(c)

-6.E-06

0.E+00

6.E-06

-4.E-06 0.E+00 4.E-06

UY

[m

]

UX [m]

(d)

Figure 3.20: Estimated USM performance vs. electrode length based on the dynamic

model.

To achieve a varying electrode length, a segmented electrode design is introduced as shown

in Figure 3.21 but not limited to three electrodes. When movement to the right of the page is

desired, the arm labelled “A” is activated and when movement to the left of the page is

desired, the arm labelled “B” is activated with the switch connecting to “B”. This effectively

changes the active electrode area. When more electrodes are incorporated, the effective

active electrode area can be adjusted by activating each electrode in a sequential manner.

To take advantage of the performance profile from different electrode lengths as in Figure

3.20, Figure 3.22 shows a USM with segmented electrodes of various lengths covering the

front surface. The electrode segments near the two ends are finer to benefit from the steeper

slope in the speed curve. The same is true for the electrodes near the middle. The length of

each electrode is shown in Table 3.2. When high speed is desired, about one-third of the front

surface is activated corresponding to the peak of the speed curve. When a lower speed or

higher accuracy is desired, more electrodes are activated. The advantage of activating

electrodes in a sequential manner instead of only controlling the voltage input to control the

drive-tip trajectory is that the new concept provides a new degree of freedom (DOF).

5

10

15

20

25

30

35

40

45

50

0.0

0.1

0.2

0.3

0.4

0.5

0.6

10 20 30 40 50 60

Esti

mat

ed

Max

imu

m T

hru

st F

orc

e [

N]

Esti

mat

ed

Max

imu

m S

pe

ed

[m

/s]

Active Electrode Lengtt [mm]

Est. Max. Speed Curve Fit

Est. Max. Force Curve Fit

Therefore, instead of losing the force by reducing the input voltage to achieve a lower speed,

the segmented electrode design allows the force to be maintained while the speed is reduced.

Lastly, an aluminium oxide pusher is attached to the middle of the top edge to act as the

drive-tip.

Figure 3.21: Top view of the segmented electrode concept. The arrows indicate the

polarization direction of the piezoceramic.

Table 3.2: Electrodes dimension.

Electrode # Electrode Length [mm] Total Electrode Length when

Activated in Sequence [mm]

1 3 3

2 3 6

3 3 9

4 3 12

5 8 20

6 5 25

7 5 30

8 5 35

9 5 40

10 8 48

11 3 51

12 3 54

13 3 57

14 3 60

A 2D FE dynamic analysis was conducted in an attempt to reduce the computational time of

the analysis. However, the result from the 2D analysis is not consistent with the 3D analysis

and therefore was not used. Details on the 2D dynamic analysis can be found in Appendix C.

↓ ↓ ↓ ↓

GND

A B

Figure 3.22: Piezo-plate type USM with proposed segmented electrodes.

Figure 3.23 shows a FE model of the piezo-plate with a simplified support structure and a

slider. The piezoceramic is supported at six support points identified as the points with the

least displacement during vibration. This would allow the E(3,1) vibration to be carried out

with minimal interference. When preloading and a support structure is added into the FE

model, the loading condition is changed from the previous scenarios presented causing the

resonant frequencies to shift and the performance is altered.

Figure 3.23: FEA model of the piezo-plate with drive-tip and simplified support

structure and slider.

Because of the applied preload and the added support structure, the exact resonant

frequencies cannot be easily determined by using modal analysis as the software does not

allow the application of a preload. As a result, a frequency sweep using FE dynamic analysis

at 500 Hz intervals was conducted near the free-space resonant frequency obtained

previously to arrive at an estimated resonant frequency. The actual value of the resonant

Slider

Side Supports Bottom Support

frequency is not critical for the purpose of the current FE analysis since the purpose here is to

demonstrate that the motor can indeed produce a thrust force and to estimate the magnitude

of the thrust force generated.

For the FE dynamic analysis, a 10N preload was applied to the bottom support to push the

drive-tip against the slider. BM500 piezoceramic [40] was used as the material, with a

damping ratio of and [26], [39], for the contact surface between the

drive-tip and the slider. To estimate the thrust force of the motor, a horizontal force opposite

to the motion of the drive-tip is added to the slider. The force is increased in increments until

the motor can no longer move the slider in the positive direction. At this point, the applied

force to the slider is assumed to be the maximum thrust force of the motor.

Due to the computational heavy nature of the FE dynamic analysis, only active electrode

lengths of 30 mm and 40 mm were simulated. Figure 3.24 shows the slider displacement

from the dynamic analysis when the active electrode length is 30 mm and Figure 3.25 shows

the slider displacement when the active electrode length is 40 mm. It should be noted here

that the performance of the USM is very sensitive to the operating frequency. A 1.4 kHz shift

in the operating frequency can alter the performance drastically as demonstrated in the

performance at 56.5kHz compared to 57.9kHz when the active electrode length is 30 mm. A

frequency of 57.9 kHz was found to give the best performance for a 30 mm active electrode

length and 57.5 kHz was found to give the best performance for a 40 mm active electrode

length.

Based on the result in Figure 3.24, it can be concluded that the USM has a thrust force in the

range of 40 – 45 N when the active electrode length is 30 mm and a thrust force greater than

90 N when the active electrode length is 40 mm. This is actually greater than the values

predicted from the dynamic model analysis in the previous section. It should be noted that

although the thrust force is greater than 45 N when the active electrode length is 40 mm, the

initial motion of the slider was in the direction of the applied load before moving in the

positive direction. It is believed that when the active electrode length is 40 mm, it takes a

longer time for the motor to reach steady state due to the larger active electrode size.

Figure 3.24: Slider displacement estimated from FE dynamic analysis with a 30 mm

active electrode length.

Figure 3.25: Slider displacement estimated from FE dynamic analysis with a 40 mm

active electrode length.

A differential electrode voltage concept was also pursued as part of this thesis. However, the

concept did not yield satisfactory results so only a limited amount of analyses were

conducted. Details on this differential electrode voltage concept can be found in Appendix C.

-20

-10

0

10

20

30

40

0 100 200 300 400 500 600

Slid

er

Dis

pla

cem

en

t (µ

m)

Time (µs)

25N Load - 57.9 kHz

30N Load - 57.9 kHz

35N Load - 57.9 kHz

40N Load - 57.9 kHz

45N Load - 57.9 kHz

25N Load - 56.5 kHz

-20

-15

-10

-5

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Slid

er

Dis

pla

cem

en

t (µ

m)

Time (µs)

25N Load - 57.5 kHz

30N Load - 57.5 kHz

35N Load - 57.5 kHz

40N Load - 57.5 kHz

45N Load - 57.5 kHz

Chapter 4 Experimental Assessment of Prototype

4.1 Motor Integration

Based on the design and analysis presented in Chapter 3, a piezoceramic with 14 electrode

segments was manufactured to experimentally verify the segmented electrode USM design.

The dimensions of the piezoceramic are mm. More details on the dimensions of

the piezoceramic and the length of each electrode can be found in Appendix G.

The piezoceramic, is shown in Figure 4.1, was manufactured using DL50 [42] instead of

BM500 [40]. The piezoelectric data of the DL50 is given by equation (4.1) to (4.3) which

exhibits very similar properties as the BM500.

Figure 4.1: 60 x 30 x 9 mm DL50 piezoceramic with segmented electrodes.

[ ]

[ ]

(4.1)

[ ] [

]

(4.2)

[

] (4.3)

An aluminium oxide drive-tip is attached to the middle of the long edge of the piezoceramic

with epoxy. Wires are attached to each of the 14 electrodes on the top surface and the ground

electrode on the bottom surface as shown in Figure 4.2 and Figure 4.3.

Figure 4.2: 60 x 30 x 9 mm piezoceramic with wires attached to the 14 electrodes.

Figure 4.3: 60 x 30 x 9 mm piezoceramic with wires attached to the ground electrode.

4.2 Static Analysis

A network impendence analyzer, Advantest R3754A, was used to find the resonant

frequencies of the motor. The piezoceramics were inserted into the USM structure as shown

in Figure 4.4 and a preload of 50 N was applied to simulate the loading condition of the USM

under normal operation conditions. A thin-film force sensor was used to measure the preload

force applied to the piezoceramic. From the FEA results presented in Chapter 3, the

mechanical resonant frequency for the desired E(3,1) mode was found to be in the 50 kHz to

60 kHz range, therefore, frequency sweeps from 40 kHz to 70 kHz were conducted

experimentally. Since changing the active electrode area changes the resonant frequency, a

frequency sweep was conducted for every change in active electrode area. In Figure 4.5, the

results from the frequency sweep when the active electrode length is 51 mm are shown. The

first resonant frequency was observed to be near 50.0 kHz and the second resonant frequency

was observed to be near 53.6 kHz. It is believed that the 53.6 kHz – the higher of the two

resonant frequencies, is the resonant frequency associated with the desired E(3,1) vibration

mode according to the results from Figure 3.6. Following the 50 N preload analysis,

impendence analysis was repeated for 30 N and 70 N preloads to assess the effect of different

preloading conditions on the resonant frequency. The results from the analysis are

summarized in Appendix E. From the data, it can be seen that the E(3,1) resonant frequency

gradually decreases as more electrodes are activated and the resonant frequency increase as

the amount of preload increases.

Figure 4.4: Overall USM structure.

Figure 4.5: Impendence analysis with 11 electrodes activated and a 50N preload.

4.3 Experimental Setup for Speed, Force, and Resolution Testing

Initially, the setup shown in Figure 4.6 which is also detailed in Appendix G was used to

house the two piezoceramics and to assess the performance of the USM. But the testing was

later switched to a simpler setup used in [11] due to alignment issues with the original setup.

The final setup is shown in Figure 4.7 and drawings of it can also be found in Appendix G.

Only one piezoceramic was used in the final motor design. A linear encoder from [44] was

used to measure the linear displacement of the slider. The encoder has a resolution of 1.22

nm. A differential signal connection circuit was used to take advance of the differential

signal output of the encoder to provide maximum protection against noise from the

environment. As mentioned previously, a thin-film force sensor is used to measure the

amount of preload applied to the piezoceramic.

The full experimental setup can be seen in Figure 4.8 and Figure 4.9 shows a simplified

block diagram of the setup. A PXI controller [45] was used to control the USM and to record

performance data through LabVIEW. A switch matrix is used to connect the output from the

amplifier to the respective electrodes on the piezoceramic. The data acquisition breakout box

was kept as far away from the high-voltage high-frequency amplifier as possible to reduce

EM interference to the encoder signals.

-180

0

180

40

45

50

55

60

65

70

75

80

85

90

40000 45000 50000 55000 60000 65000 70000

Ph

ase

(°)

Mag

nit

ud

e (

dB

)

Frequency (Hz)

Magnitude

Phase

Figure 4.6: Original USM setup.

Figure 4.7: Final USM setup used.

Figure 4.8: Experimental setup workspace.

Figure 4.9: Experimental setup block diagram.

NI LabVIEW PXI

Controller

Function

Generator

USM

Piezo

Switch

Matrix

Digital Input Encoder

PXI

Controller

Alternate FGEN

and amplifier

USM and slider

stage

DAQ breakout

4.4 Assessment of Motor Performance Using One Amplifier

The maximum force test was conducted using a simple pulley and weight setup as shown in

Figure 4.10. An appropriate amount of mass was attached as the weight during the test. The

test started at a preload force of 30N. However, at 30 N preload, the USM wasn’t able to

move the slider under any load and the drive-tip slips against the slider’s aluminium oxide

strip continuously and which prevented a good friction contact from being established. As a

result, the preload was raised to 50 N to continue the test.

At 50 N preload and an applied voltage of 200 Vp, the maximum amount of force or weight

the USM can lift was 17 N when the active electrode length is 30 mm. When more electrodes

are activated, the thrust force decreased instead of an increase as predicted in Chapter 3. The

test was repeated at 70 N preload and an applied voltage of 200 Vp. The maximum thrust

force at this preload condition is 25 N and as in the 50 N preload test, the thrust force also

decreased as more electrodes are activated. When the preload force was further increased to

100 N, the USM was unable to overcome the preload force and no motion was observed.

Figure 4.10: Maximum force testing setup.

The reason behind the discrepancy between the experimental results and the predicted results

was believed to be a problem with the amplifier that saturates at high voltage values since it

is unable to provide sufficient current fast enough to drive the motor. Therefore, the applied

voltage to the motor was reduced to 100 Vp and later to 50 Vp but the same decrease in thrust

force occurred.

Weight

Pulley

USM

Stage

Workbench

The amount of current going into the motor at 70 N preload was measured and is shown in

Figure 4.11. As can be seen, the output current of the amplifier saturated after the active

electrode length was increased above 20 mm. As more electrodes are activated, the effective

active electrodes area increases and more current are required to activate the piezoceramic at

its resonant frequency in the 50 kHz range. Since the amplifier cannot provide sufficient

power fast enough to drive the motor once the active electrode area is greater than one-third

of the top surface, the piezoceramic in the motor cannot be fully charged to provide its

maximum stroke and thrust.

Figure 4.11: Amplifier output current versus number of active electrodes.

The maximum speed test was measured by applying no load to the USM slider. The

resolution of the encoder was set to 40 nm with a maximum speed reading of 250 mm/s. This

number is a reduction by a factor of 8 from the value in the encoder datasheet because the

maximum data frequency the PXI controller can accept is 1.566 MHz, 8 times less than the

maximum quadrature output frequency of the encoder.

The maximum speed achieved was 143 mm/s at an active electrode length of 12 mm when

the preload force is 70 N. The maximum speed of the USM remained relative constant at the

100 mm/s range until an active electrode length of 35 mm then drops to zero. This is not

consistent with the predictions of Chapter 3 and is believed to also be due to amplifier

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Cu

rre

nt

[mA

]

Active Electrode Length [mm]

200 V Applied Voltage



Saturation

saturation. Nevertheless, the experimental speed results followed the same trend as the

theoretical prediction.

The performance data are summarized in Figure 4.12 and Figure 4.13 and the tabulated data

can be found in Appendix F. It should be noted that in addition to the maximum speed, an

average speed was also recorded in the tabulated data. The average speed is related to the

time it took the slider to complete its 60.7 mm travel.

Figure 4.12: Maximum achievable speed result versus active electrode length.

Figure 4.13: Maximum achievable force result versus active electrode length.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60

Max

imu

m S

pe

ed

[m

/s]


70 N Preload - 200 V Applied Voltage70 N Preload - 100 V Applied Voltage70 N Preload - 50 V Applied Voltage50 N Preload - 200 V Applied VoltageTheoretical Max. Speed

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

Max

imu

m F

orc

e [

N]


70 N Preload - 200 V Applied Voltage70 N Preload - 100 V Applied Voltage70 N Preload - 50 V Applied Voltage50 N Preload - 200 V Applied VoltageTheoretical Max. Force

Lastly, the smallest possible step achieved by the USM in open-loop operation was found to

be 9 nm when only one electrode was activated with an impulse of about 18 µs (1 period at

near 55 kHz) and no load. This is much better than the result reported in [20]. Figure 4.14

shows the displacement response with one active electrode. 18 µs is the smallest signal

achievable due to the operating frequency near 55 kHz. Any signal smaller than 18 µs will

either lead to an operating frequency greater than 55 kHz or is an incomplete AC sine wave.

When four electrodes were activated: corresponding to the experimental maximum speed

result, the smallest possible step achieved was 527 nm. Figure 4.15 shows the smallest step

result at different active electrode lengths. Overall, the smallest possible step at all active

electrode length is sub-micron.

Figure 4.14: Displacement response with one active electrode and 18 µs impulse.

0.0E+00

2.0E-09

4.0E-09

6.0E-09

8.0E-09

1.0E-08

1.2E-08

1.4E-08

1.6E-08

0 100 200 300 400 500

Slid

er

Dis

pla

cem

en

t [m

]

Time [µs]

9nm

Figure 4.15: Smallest achievable step result versus active electrode length.

4.5 Assessment of Motor Performance Using Two Amplifiers

It was concluded in subsection 4.4 that the amplifier saturates after the activation of the fifth

electrode. Therefore, an extra amplifier is connected to the first amplifier in parallel to

provide more power to the piezoceramic. Improvement of the performance can be seen in

Figure 4.16 and Figure 4.17 (compared to Figure 4.12 and Figure 4.13, respectively). The

maximum speed achieved was increased to 223 mm/s at an active electrode length of 25 mm

with a 70 N preload and the maximum force achieved was 36 N at an active electrode length

of 20 mm with 70 N preload. However, discrepancies still exist between the theoretical

estimates and the experimental results. In terms of speed, the USM could only achieve half of

the theoretical maximum value. As for the force output, the USM was able to achieve a much

higher force than expected for a small active electrode length but the maximum force drops

as the active electrode increases. This is different from what was predicted from Chapter 3.

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

0 10 20 30 40 50 60

Smal

lest

Ste

p A

chie

ved

[m

]


Figure 4.16: Maximum achievable speed results with two amplifiers in parallel.

Figure 4.17: Maximum achievable force results with two amplifiers in parallel.

The total amplifier current output data shown in Figure 4.18 shows a similar amplifier

saturation behaviour as the one shown in Figure 4.11. The saturation is seen to occur above

an active electrode length of 40 mm. As a result, it is believed that the discrepancy is also

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 10 20 30 40 50 60

Max

imu

m S

pe

ed

[m

/s]


70 N Preload - 200 V Applied Voltage



Theoretical Max. Speed

0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60

Max

imu

m F

orc

e [

N]


70 N Preload - 200 V Applied Voltage50 N Preload - 200 V Applied Voltage30 N Preload - 200 V Applied VoltageTheoretical Max. Force

caused by amplifier saturation. From this pattern, it can be hypothesized that three amplifiers

or a more powerful amplifier that can provide up to 200 mA at 200 Vp are required to satisfy

the power demand of the USM.

However, unlike previous results shown in subsection 4.4 where the maximum thrust force at

a 70 N preload dropped to close to 0 N, the thrust force in this section remained near 20 N

even when the length of the active electrode is above 50 mm. As can be seen in Figure 4.19,

which is showing only the 70 N preload results, the maximum speed output of the USM can

be varied between 150 mm/s and 220 mm/s while the maximum thrust force remained at or

above 30 N. This would allow a much greater control of the speed output without a large

reduction in the thrust force. This is clearly, a key objective of the motor.

Figure 4.18: Total amplifier output current at 200 Vp versus number of active

electrodes.

0

20

40

60

80

100

120

140

160

0 10 20 30 40 50 60

Cu

rre

nt

[mA

]


Saturation

Figure 4.19: Maximum performance at 70 N preload with two amplifiers in parallel.

0

5

10

15

20

25

30

35

40

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 10 20 30 40 50 60

Max

imu

m F

orc

e [

N]

Max

imu

m S

pe

ed

[m

/s]


Speed

Force

Chapter 5 Discussion and Conclusions

5.1 Summary

A novel segmented electrodes USM was developed to satisfy the performance requirement of

the RmMT project. Using a planar vibration mode concept that allows the USM to have a

simple structure, an attempt to decouple the components of the drive-tip trajectory was made.

FE modal analysis was first conducted on the design to narrow the piezoceramic’s desired

resonant frequency. Then harmonic and dynamic analysis followed to determine the

characteristics of the drive-tip trajectory and the performance of USM as a whole. An ODE

dynamic model was also developed to estimate the performance of the USM since FE

dynamic analysis is too computationally heavy. From the result of the FE analysis, the

proposed USM using the segmented electrodes concept exceeded the performance of [20]

and allowed semi-decoupling of the speed and force output. The estimated maximum output

force of the USM was estimated to be 46 N and the maximum output speed was estimated to

be 0.5370 m/s when a different set of electrodes were activated.

The USM was incorporated into a 1D stage for performance testing. Aluminum was used as

the frame for the USM. From the experimental investigations, the maximum output force

recorded was 36 N and the maximum speed achieved was 0.223 m/s at a preload of 70 N.

However, as more electrodes were activated, both the speed and force output decreased

instead of increased as predicted from the FE and ODE dynamic model analysis.

When the high-voltage high-frequency amplifier’s output current was recorded, it was

observed that the amplifier saturates after the activation of the fifth electrode when one

amplifier was used and saturation occur after the activation of the ninth electrode when two

amplifiers were used. As a result, it is believed that the discrepancy between the USM

performance from FE analysis and experimental investigation was largely due to amplifier

saturation. Furthermore, the smallest step achievable in open-loop operation was 9 nm with

an 18 µs impulse, much better than currently commercially available USMs. Nevertheless,

the segmented electrodes design allowed the speed of the USM to vary while keeping the

thrust force relatively constant and allowed the USM to achieve high resolution without a

major sacrifice of thrust force.

5.2 Recommendations and Future Research

As the full potential of the USM were never tested due to equipment limitations, the first

recommendation is to test the USM with a more powerful amplifier. The new amplifier must

be able to provide enough power to activate the entire volume of the piezoceramic. Such

amplifier will be very costly but the true potential of the segmented electrode design cannot

be understood without it. An alternative solution to the problem is to scale the piezoceramic

down into a smaller size. This will reduce the power requirements. However, the problem

with scaling the piezoceramic is the limitation in electrode patterning. The smallest feature

possible is 0.25 mm according to the manufacturer.

Secondly, it is recommended that the support structure and the 1D stage be redesigned for a

better and easier application of preload and a smooth travel. Currently, the preload is applied

through a HEX screw and a more precise load cell cannot be used to measure the preload due

to space limitations. Also, the smoothness of the travel throughout the 60.7 mm of the 1D

stage is not uniform due to fabrication defect of the Aluminum Oxide friction strip. This

caused unexpected slippage between the drive-tip and the slider and led to inconsistent force

and speed output throughout the length of the travel.

Thirdly, a closed-loop controller for the USM needs to be developed. Operating the USM in

closed-loop will allow the USM to achieve great accuracy on top of good resolution. It is

believed that the objective of 0.1 µm can be easily achieved since the smallest resolution

achieved with no load is one magnitude smaller. Because the speed of the USM can be

controlled while keeping the drive voltage constant by varying the number of activated

electrodes, there are no deadzone voltages to worry about. However, the added challenge is

the changing of frequency when different electrodes are activated.

Finally, only sequential activation of electrodes was studied in this project. The activation of

different combination of electrodes can further improve the performance of the USM. With

further testing and development, it is believed that the segmented electrode concept has

potential for commercialization as a high accuracy USM.

References

[1] C.S. Zhao, Ultrasonic Motors: Technologies and Applications, New York: Springer,

2011

[2] Uchino, K., Piezoelectric Actuators and Ultrasonic Motors, Boston, MA : Kluwer

Academic Publishers, 1997

[3] “DL Series Linear Actuator”, Del-Tron Precision, Inc. Catalogue, 2012

[4] K. Spanner, “Survey of the Various Operating Principles of Ultrasonic

Piezomotors”, Physik Instrumente, 2006

[5] K. Uchino, “Piezoelectric ultrasonic motors: overview”, Smart Mater. Struct. 7

(1998) 273-285

[6] Sashida, T., Kenjo, T., An Introduction to Ultrasonic Motors, New York, NY:

Oxford University Press, 1993

[7] Bekiroglu, E., “Ultrasonic motors: Their models, drives, controls and applications”,

J. Electrocream (2008) 20:277-286

[8] W.G. May, “Piezoelectric Electromechanical Translation Apparatus”, U.S. Patent

3,902,084, Aug. 26, 1975

[9] “PiezoWalk® Actuators”, Physik Intrumente, Available at:

http://www.physikinstrumente.com/en/products/linear_actuator/piezowalk_selection

.php

[10] “PiezoLEGS®”, PiezoMotor AB, Available at:

http://www.piezomotor.se/?menu=products&page=legs1

[11] S. Salisbury, R. Ben Mrad, D.F. Waechter, S. Eswar Prasad, “Design, Modeling,

and Closed-Loop Control of a Complementary Clamp Piezoworm Stage”,

IEEE/ASME Trans. On Mechatronics, vol. 14. no. 6, pp. 724-732, December 2009

[12] S. Salisbury, D.F. Waechter, R. Ben Mrad, S.E. Prasad, R.G. Blacow, B. Yan,

“Design considerations for complementary inchworm actuators”, IEEE/ASME

Trans. On Mechatronics, vol. 11. no. 3, pp. 265-272, June 2006

[13] G. Powers, Q. Xu, J. Fasick, J. Smith, “Nanometer Resolution Actuator with Multi-

Millimeter Range and Power-Off-Hold”, Proceeding of SPIE Industrial and

commercial applications of smart structures technology. Conference, San Diego

CA, 4-6 March 2003

[14] S. Chatterjee, G.P. Carman, High friction interface with pseudoelastic NiTi, Applied

Physic Letters 91, 024104 (2007)

[15] “Imaging Field”, Konica Minolta, Available at:

http://www.konicaminolta.com/about/research/core_technology/picture/antiblur.htm

l

[16] V. Lavrinenko, M. Nekrasov, USSR Patent № 217509, 1965

[17] “HR Series Motors”, Nanomotion Ltd., Available at:

http://www.nanomotion.com/index.aspx?id=2574

[18] V. Vishnevsky, L. Gultajeva, I. Kartashev, V. Lavrinenko, “Piezoelectric Motor”,

USSR Patent № 851560

[19] “Ceramic Linear Motors, Actuators & Controllers”, Physik Intrumente, Available

at:

http://www.physikinstrumente.com/en/products/linear_actuator/ultrasonic_motor_se

lection.php

[20] O. Vyshnevskyy, S. Kovalev, W. Wischnewskiy, “A Novel, Single-Mode

Piezoceramic Plate Actuator for Ultrasonic Linear Motors”, IEEE Trans. Ultrason.

Ferroelectr. Freq. Control, vol. 52, no. 11, pp. 2047-2053, November 2005

[21] C.H. Yun, T. Ishii, K. Nakamura, S. Ueha, K. Akashi, “A High Power Ultrasonic

Linear Motor Using a Longitudinal and Bending Hybrid Bolt-Clamped Langevin

Type Transducer”, Jpn. J. Appl. Phys., vol. 40, no. 5B, May 2001, pp. 3773-3776

[22] “Ultrasonic micromotor”, Seiko Instruments Inc., Available at:

http://www.sii.co.jp/info/eg/micro-usm1.html

[23] O. Vyshnevskyy, S. Kovalev, W. Wischnewskiy, “New Type of Standing Wave

Ultraonic Rotary Piezo Motors with Cylindrical Actuators”, Physik Instrumente (PI)

GmbH & Co. KG, Karlsruhe, Germany

[24] A. Kumada, “A Piezoelectric Ultrasonic Motor”, Jpn. J. Appl. Phys. 24 (1985)

Supplement 24-2 pp. 739

[25] J.R. Friends, J. Satonobu, K. Nakamura, S. Ueha, D.S. Stutts, “A Single-Element

Tuning Fork Piezoelectric Linear Actuator,” IEEE Trans. Ultrason. Ferroelectr.

Freq. Control, vol. 50, no. 2, pp. 179-186, November 2003

[26] M.G. Bauer “Design of a Linear High Precision Ultrasonic Piezoelectric Motor”,

Ph.D. Thesis, Mechanical Engineering, North Carolina State University, Raleigh,

2001

[27] M. Kuribayashi, S. Ueha, E. Mori, “Excitation conditions of flexural traveling

waves for a reversible ultrasonic linear motor”, J. Acoust. Soc. Am. vol. 77, issue 4,

pp. 1431-1435 (April 1985)

[28] T. Hemsel, M. Mracek, J. Twiefel, P. Vasiljev, “Piezoelectric linear motor concepts

based on coupling of longitudinal vibrations”, Ultrasonic 44 (2006) 591-596

[29] T. Sashida, “Motor Device Utilizing Ultrasonic Oscillation”, U.S. Patent 4,562,374,

Dec. 31, 1985

[30] W.S. Chen, S.J. Shi, Y.X. Liu, P. Li, “A New Travelling Wave Ultrasonic Motor

Using Thick Ring Stator with Nested PZT Excitation”, IEEE Trans. Ultrason.

Ferroelectr. Freq. Control, vol. 57, no. 5, pp. 1160-1168, May 2010

[31] A. Iula, A. Corbo, M. Pappalardo, “FE analysis and experimental evaluation of the

performance of a travelling wave rotary motor driven by high power ultrasonic

transducers”, Sensor and Actuator A, 160 (2010) 94-100

[32] Y. Wang, J.M. Jin, W.Q. Huang, “A Novel Rotary Ultrasonic Motor Using an In-

plane Traveling Wave”, Journal of the Korean Physical Science, vol. 57, no. 4,

October 2010, pp. 882-885

[33] “Ultrasonic Motor (USM)”, Canon Inc., available at:

http://www.canon.com/technology/canon_tech/explanation/usm.html

[34] J. Lau, S.I. Gubarenko, R. Ben-Mrad, “Design Concepts of Motors For a

Reconfigurable Meso-Milling Machine Tool,” Proceedings of the 23rd

CANCAM,

Vancouver, BC, 2011

[35] J. Lau, S.I. Gubarenko, R. Ben-Mrad, “A Novel Plate-Type Linear Ultrasonic Motor

with Segmented Electrodes,” Proceedings of the 1st VMPT, Montreal, QC, 2012

[36] H. Azulay, C. Hawryluck, J. K. Mills and B. Benhabib, “CONFIGURATION

DESIGN OF A MESO-MILLING MACHINE”, Proceeding of CANCAM 2011,

Vancouver, BC, Canada

[37] “Piezoceramic Materials”, Piezoceramic Materials Catalogue, Physik Instrumente

[38] “Piezo Material Data”, eFunda Inc., available at:

http://www.efunda.com/materials/piezo/material_data/matdata_index.cfm

[39] S.L. Sharp, “Design of a Linear Ultrasonic Piezoelectric Motor”, M.Sc. Thesis,

Mechanical Engineering, Brigham Young University, 2006

[40] Sensor Technology Limited, Collingwood, Ontario, Canada

[41] F. Côté, P. Masson, N. Mrad, V. Cotoni, “Dynamic and static modelling of

piezoelectric composite structure using a thermal analogy with MSC/NASTRAN”,

Composite Structure 65 (2004) 471-484

[42] DeL Piezo Specialties, LLC, West Palm Beach, FL, USA

[43] “FlexiForce® Sensors”, Tekscan, Inc., South Boston, MA, USA

[44] MicroE Systems, GSI Group, Bedford, MA, USA

[45] National Instrument Corporation, Austin, TX, USA

Appendix A : Geometric Optimization Supplementary Data

Table A.1: Performance data of piezoceramic USM with varying thicknesses

Dimension Estimated Maximum

L W T Speed [m/s] Force

[N]

60 30 7 0.0991 17.0

60 30 8 0.1590 36.0

60 30 9 0.1356 35.5

60 30 10 0.1112 34.0

60 30 11 0.1195 30.0

Table A.2: FE analysis showing classical USM performance data with varying length

and width

Dimension E(3,1)

Freq.

[Hz]

UX [m] UY [m] Phase

[°]

Stiffness

[MN/m]

Estimated Maximum

L W T Speed

[m/s]

Force

[N]

72 25 9 67367 2.83970E-06 2.23114E-06 -0.89 319 0.1856 12

69 26 9 64650 2.76468E-06 2.23049E-06 -2.88 316 0.1734 11

67 27 9 62913 3.36396E-06 2.83387E-06 -2.13 312 0.2054 15

64 28 9 61581 3.13731E-06 4.03212E-06 1 309 0.3567 35.5

62 29 9 60468 2.35945E-06 4.38525E-06 0.32 306 0.2634 37.5

60 30 9 59884 1.22658E-06 3.91805E-06 3.04 303 0.1356 35.5

58 31 9 59844 5.03208E-07 2.95447E-06 9.96 302 0.0556 30.5

56 32 9 60128 N/A

53 34 9 61070 1.39090E-07 1.61557E-06 32.57 292 0.0215 17.5

50 36 9 62335 5.41289E-08 1.36756E-06 49.31 288 0.0101 15

49 37 9 62633 2.36358E-08 1.30157E-06 119.43 284 0.0028 11

Appendix B : Segmented Electrodes Concept Supplementary Data

Table B.1: FE analysis data of a 60 x 30 x 9 mm piezoceramic USM with varying

electrode length

Electrode Length E(3,1) Freq. [Hz] UX [m] UY [m] Phase [°]

12.5 56896 2.87258E-06 4.21919E-06 -0.68

15.0 56127 3.88674E-06 5.04765E-06 0.17

17.5 55606 4.22682E-06 5.52109E-06 1.82

20.0 54823 5.28544E-06 6.83959E-06 1.04

22.5 54404 5.35381E-06 7.53443E-06 0.97

25.0 53916 5.13774E-06 8.30410E-06 1.30

27.5 53653 4.84703E-06 8.70057E-06 1.58

30.0 53276 4.05653E-06 9.38170E-06 2.25

32.5 53170 3.63093E-06 9.73448E-06 2.52

35.0 53023 3.09530E-06 1.01928E-05 2.47

37.5 53001 2.90417E-06 1.03370E-05 1.93

40.0 52940 2.61067E-06 1.03560E-05 1.90

42.5 52926 2.47606E-06 1.03442E-05 1.84

45.0 52876 2.40288E-06 1.02280E-05 2.31

47.5 52856 2.26917E-06 1.02300E-05 2.70

50.0 52802 1.96548E-06 1.02596E-05 3.95

52.5 52769 1.41237E-06 1.04137E-05 4.91

55.0 52683 5.33129E-07 1.06772E-05 6.49

57.5 52634 1.03469E-07 1.08155E-05 8.31

Table B.2: Performance estimate of a 60 x 30 x 9 mm piezoceramic USM with varying

active electrode length

Electrode Length Estimated Maximum

Speed [m/s] Force [N]

12.5 0.1586 9.5

15.0 0.4028 18.5

17.5 0.4339 21

20.0 0.5350 25.5

22.5 0.5370 28

25.0 0.5115 31

27.5 0.4802 32.5

30.0 0.3990 35.5

32.5 0.3564 37

35.0 0.3030 38.5

37.5 0.2842 39

40.0 0.2552 39

42.5 0.2419 39

45.0 0.2345 38.5

47.5 0.2214 38.5

50.0 0.1916 40.5

52.5 0.1376 41.5

55.0 0.0518 44

57.5 0.0100 46

Appendix C : Segmented Electrodes Concept 2D FE Dynamic Analysis

FE dynamic analysis is computation heavy especially if the model is 3-dimensional (3D), as

a result, dynamic analysis using a 2-dimensional (2D) model and thermal analogy as

described in [41] are used which exponentially decreases the computational time. However,

before the 2D alternative is pursued, the validity of the 2D analysis in the context of the

current USM needs to be verified.

According to [41], the thermoelastic constitutive equations, equation (C.1), have a similar

form as the piezoelectric constitutive equations, equation (1.3).

{ } [ ]{ } [ ]{ } (C.1)

where,

{ } and { } is the stress and strain vector, respectively

{ } is the electric field vector

[ ] is the stiffness matrix at constant electric field

is the temperature change

Therefore, the relationship between piezoelectric strain and thermal strain is described by

equation (C.2) below.

[ ] { } { } (C.2)

where,

[ ] is the piezoelectric matrix relating strain to electric field

{ } is the thermal expansion constant vector

Since only the expansion and contraction in the x- and y-direction is relevant in a 2D

analysis, only the and constants need to be converted into thermal constants: and

. The electric vector field, { }, depends on the charge and the thickness of the

piezoceramic. As the value of and are equal, the conversion takes the form of

equation (C.3).

(C.3)

where is the voltage difference between the active and the ground electrode in a 3D

model, is the thickness of the piezoceramic between the two electrodes and is the

temperature of the active elements in the 2D model.

If the and variables are assumed to have a 1:1 ratio meaning an applied voltage of 1

unit is equivalent to raising the temperature by 1 unit, the thermal constant for the 2D

analysis can be obtained by the following equation:

⁄ (C.4)

To validate the 2D thermal model, analysis was conducted on a mm piezoceramic

with a thickness of 9 mm. The result is compared to a reference 3D model with dimension of

mm.

When both models underwent symmetric excitation meaning the entire top surface is covered

with one active electrode, both model yielded very similar results with the resonant

frequency result from the 2D model shifted slightly higher as shown in Figure C.1.

When both models underwent asymmetric excitation with only half of the top surface

activated, however, the 2D thermal model does not match closely with the 3D piezoelectric

model. Based on the symmetric excitation 3D model result shown in Figure , there are two

resonant frequencies: around 49.3 kHz and 52.6 kHz, and one anti-resonant frequency around

49.7 kHz for drive-tip displacement between 45 kHz and 65 kHz. The corresponding

resonances can also be seen when the 3D model was excited asymmetrically as shown with

the dotted line in Figure C.1 and Figure C.3. Other resonances also exist due to asymmetric

excitation.

Figure C.1: Drive-tip y-displacement of a symmetrically excited 60 x 30x 9 mm

piezoceramic.

On the other hand, the corresponding resonances for the 2D model can only be seen in the

drive-tip y-displacement result for asymmetric excitation as shown by the solid line in Figure

C.3. The corresponding 2D model resonances are lacking in the drive-tip x-displacement

result in Figure C.2. It should also be noted that the resonant frequency corresponding to the

desired E(3,1) mode for the USM is the peak x- and y-displacement near 53.3 kHz but the

peak displacement for the 2D model occurs near 54.6 kHz for x-displacement and 53.0 kHz

for y-displacement. This indicates that a definite estimate of the E(3,1) mode does not exist

for the 2D model. Further study shows the phase angle result between the 2D model and the

3D model is very dissimilar as shown in Figure C.4. Consequently, it can be concluded that a

2D thermal model alternative cannot be used to replace the 3D piezoelectric model for the

application pursed in this thesis.

1.00E-07

1.00E-06

1.00E-05

1.00E-04

45000 50000 55000 60000 65000

Dis

pla

cem

en

t (m

)

Frequency (Hz)

2D - Thermal Model

3D - Piezoelectric Model

Figure C.2: Drive-tip x-displacement of an asymmetrically excited 60 x 30x 9 mm

piezoceramic.

Figure C.3: Drive-tip y-displacement of an asymmetrically excited 60 x 30x 9 mm

piezoceramic.

1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

45000 50000 55000 60000 65000

Dis

pla

cem

en

t (m

)

Frequency (Hz)

2D - Thermal Model


1.00E-08

1.00E-07

1.00E-06

1.00E-05

1.00E-04

45000 50000 55000 60000 65000

Dis

pla

cem

en

t (m

)

Frequency (Hz)

2D - Thermal Model


Figure C.4: Drive-tip phase angle of an asymmetrically excited 60 x 30x 9 mm

piezoceramic.

-180

-130

-80

-30

20

70

120

170

45000 50000 55000 60000 65000

Ph

ase

(°)

Frequency (Hz)

2D - Thermal Model


Appendix D : Differential Electrode Voltage Concept

The method in subsection 3.2.6 uses the dimensions of the active electrode to control the

amount of stress induced in the piezoceramic. However, the changes in active electrode area

are finite, thus, the control of drive-tip trajectory is limited. Full control of the drive-tip

trajectory can potentially be achieved if the amount of stress can be controlled without any

limitation.

The piezoceramic in [20] has two excitation electrodes and one ground electrode. Only one

of the excitation electrodes is activated at any given time hence the elements at the middle of

the piezoceramic is only subjected to stress on one side. Yet, exciting both electrodes to

apply stress on both sides of the middle elements was not pursued. Therefore, a differential

electrode voltage concept, by applying arm “A” and arm “B” as shown in Figure D.1 with

different voltages simultaneously, is proposed in this project. By applying a second voltage at

the same frequency to the other excitation electrode, the drive-tip trajectory is potentially

more controllable. Since the application of a voltage can be easily controlled with a very high

resolution, the drive-tip trajectory can also be potentially controllable with a very high

resolution too.

Figure D.1: Top view of differential electrode voltage concept. The arrows shows the

polarization direction of the piezoceramic.

↓ ↓ ↓ ↓

GND

A B

FE Harmonic and ODE Dynamic Analysis

The solid model of subsection 3.2.6 is also used to perform the modal and harmonic analysis

in this subsection. However, instead of covering only a portion of the top surface with an

active electrode, the entire top surface is covered with two electrodes of equal size while

different voltages are applied. A schematic of the motor is shown in Figure D.2. It is

expected that the greater the voltage difference between the two electrodes, the more

horizontal the trajectory will be.

Figure C.2: Differential Electrode Voltage Concept Electrode diagram.

Harmonic analysis was conducted on the concept shown in Figure . The resonant frequency

was assumed to be within the range of 50 kHz to 60 kHz based on the results in Chapter 3.

This greatly reduced the frequency sweep of the harmonic analysis.

During the harmonic analysis, the applied voltage to the left electrode was kept at 200 Vp

while the applied voltage to the right electrode was varied. Figure D.3 shows the harmonic

analysis results when the applied voltage to the left electrode and right electrode are 200 Vp

and 100 Vp, respectively. From the harmonic analysis, it was observed that the way the

resonant frequency appears is different from the case of the segmented electrode model

presented in Chapter 3. Instead of one resonant frequency with x- and y- displacements peak,

the two peaks occur at different frequencies. In addition, the phase angle at the two peaks is

near -90° instead of the 0° found with the segmented design concept, therefore, it can be

concluded that the E(3,1) vibration is not present in the differential electrode voltage concept.

Nevertheless, the result from the harmonic analysis were recorded and analyzed in the

dynamic analysis model.

The results from the harmonic analysis are shown Figure D.4, Figure D.5, Table D.1 and

Table D.2. Based on the results, the performance of the concept was deemed unsatisfactory

and further FE dynamic analysis on the model was not conducted.

x

y Elect.

A

Elect.

B

Figure D.3: Harmonic analysis results for the differential electrode voltage concept with

200 Vp applied to the left electrode and 100 Vp applied to the right electrode.

Figure D.4: Performance estimate of a 60 x 30 x 9 mm piezoceramic with differential

electrode voltage at its y-displacement peak.

-180

-150

-120

-90

-60

-30

0

30

60

90

120

150

180

1.E-08

1.E-07

1.E-06

1.E-05

50000 52000 54000 56000 58000 60000

Ph

ase

(°)

Dis

pla

cem

en

t (m

)

Frequency (Hz)

UXUYPhase

20

25

30

35

40

45

50

55

60

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 50 100 150 200

Esti

mat

ed

Th

rust

Fo

rce

[N

]

Esti

mat

ed

Max

imu

m S

pe

ed

[m

/s]

Left Electrode Voltage [V]


Est. Max. Force (Numerical) Curve Fit

Figure D.5: Performance estimate of a 60 x 30 x 9 mm piezoceramic USM with

differential electrode voltage at its x-displacement peak.

Table D.1: FE analysis data of a 60 x 30 x 9 mm piezoceramic USM with differential

electrode voltage at y-displacement peak.

Applied

Voltage E(3,1)

Freq. [Hz] UX [m] UY [m]

Phase

[°]

Estimated Maximum

Left Right Force

[N] Speed [m/s]

200 190 52860 4.44869E-08 1.18650E-05 -83.3 52 0.00617

200 180 52860 8.89739E-08 1.15608E-05 -83.3 50.5 0.01215

200 160 52860 1.77948E-07 1.09523E-05 -83.3 48 0.02410

200 140 52860 2.66922E-07 1.03438E-05 -83.3 45.5 0.03606

200 120 52860 3.55895E-07 9.73537E-06 -83.3 42.5 0.04801

200 100 52860 4.44869E-07 9.12691E-06 -83.3 40 0.05997

200 80 52860 5.33843E-07 8.51845E-06 -83.3 37.5 0.07192

200 60 52860 6.22817E-07 7.90999E-06 -83.3 34.5 0.08387

200 40 52860 7.11791E-07 7.30153E-06 -83.3 32 0.09582

200 20 52860 8.00765E-07 6.69307E-06 -83.3 29.5 0.10778

200 0 52860 8.89739E-07 6.08461E-06 -83.3 26 0.11967

2

2.5

3

3.5

4

4.5

5

5.5

6

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 50 100 150 200

Esti

mat

ed

Th

rust

Fo

rce

[N

]

Esti

mat

ed

Max

imu

m S

pe

ed

[m

/s]

Left Electrode Voltage [V]


Est. Max. Force (Numerical) Curve Fit

Table D.2: FE analysis data of a 60 x 30 x 9 mm piezoceramic USM with differential

electrode voltage at x-displacement peak.

Applied

Voltage E(3,1)

Freq. [Hz] UX [m] UY [m]

Phase

[°]

Estimated Maximum

Left Right Force

[N] Speed [m/s]

200 190 54580 4.80653E-07 1.00751E-06 -87.04 5 0.0702

200 180 54580 9.61307E-07 9.81672E-07 -87.04 5 0.1405

200 160 54580 1.92261E-06 9.30005E-07 -87.04 4.75 0.2810

200 140 54580 2.88392E-06 8.78338E-07 -87.04 4.5 0.4216

200 120 54580 3.84523E-06 8.26671E-07 -87.04 4.25 0.5621

200 100 54580 4.80653E-06 7.75004E-07 -87.04 4 0.7027

200 80 54580 5.76784E-06 7.23337E-07 -87.04 4 0.8430

200 60 54580 6.72915E-06 6.71670E-07 -87.04 3.75 0.9835

200 40 54580 7.69046E-06 6.20003E-07 -87.04 3.5 1.1241

200 20 54580 8.65176E-06 5.68336E-07 -87.04 3.25 1.2648

200 0 54580 9.61307E-06 5.16669E-07 -87.04 3 1.4051

Appendix E : Impendence Analysis Supplementary Data

Table E.1: Impendence analysis results subject to 30N preload

Active

Electrode(s)

Piezoceramic #1 Piezoceramic #2

E(3,1) Resonant

Frequency (kHz) Phase (°)

E(3,1) Resonant


E1-4 55.125 -5.36 55.150 -6.19

E1-5 53.850 4.01 53.825 -1.23

E1-6 53.100 5.89 53.250 2.80

E1-7 53.075 6.30 53.175 2.94

E1-8 53.000 11.48 52.950 5.98

E1-9 52.975 14.22 52.950 10.02

E1-10 52.975 14.25 52.950 9.56

E1-11 52.925 10.54 52.925 9.27

E1-12 52.900 12.49 52.925 10.78

E1-13 52.900 15.65 52.925 13.11

E1-14 52.750 12.97 52.800 12.98

E2-14 52.900 15.32 52.925 14.35

E3-14 52.925 15.22 52.925 12.77

E4-14 52.925 10.13 52.925 11.81

E5-14 52.950 12.47 52.950 7.12

E6-14 52.950 14.52 52.950 9.63

E7-14 53.000 13.99 52.925 11.39

E8-14 53.000 14.00 52.925 10.21

E9-14 53.250 6.01 53.225 8.94

E10-14 53.750 0.62 53.725 2.26

E11-14 55.125 -5.24 55.075 -7.34


Active

Electrode(s)


E(3,1) Resonant


E(3,1) Resonant


E1-4 56.250 -4.52 56.250 -5.50

E1-5 54.900 3.72 54.825 -2.19

E1-6 54.150 6.48 54.225 2.26

E1-7 54.150 6.25 54.225 2.49

E1-8 54.000 10.41 53.925 6.17

E1-9 54.000 14.53 53.925 9.89

E1-10 54.000 15.10 53.925 9.14

E1-11 53.925 10.86 53.925 9.22

E1-12 53.925 12.59 53.925 11.17

E1-13 53.925 15.35 53.925 15.27

E1-14 53.850 13.13 53.850 11.77

E2-14 53.925 15.62 53.925 15.97

E3-14 53.925 15.60 53.925 12.19

E4-14 53.950 10.99 53.925 11.21

E5-14 53.950 12.64 53.950 6.93

E6-14 53.950 14.88 53.950 9.86

E7-14 54.000 14.08 53.925 11.31

E8-14 54.000 14.08 53.925 11.25

E9-14 54.225 6.39 54.225 8.56

E10-14 54.750 0.68 54.750 2.13

E11-14 56.100 -6.24 56.100 -7.41


Active

Electrode(s)


E(3,1) Resonant


E(3,1) Resonant


E1-4 57.650 -4.34 57.150 -5.80

E1-5 55.900 3.26 56.000 0.13

E1-6 55.000 7.15 55.225 3.15

E1-7 55.000 7.67 55.150 2.98

E1-8 54.900 10.42 54.950 7.12

E1-9 54.900 15.18 54.950 10.03

E1-10 54.900 15.66 54.925 9.84

E1-11 54.875 10.23 54.925 9.62

E1-12 54.875 11.45 54.925 10.78

E1-13 54.875 14.92 54.925 14.96

E1-14 54.550 12.74 54.600 11.58

E2-14 54.875 15.38 54.900 16.06

E3-14 54.875 15.69 54.900 11.44

E4-14 54.900 10.62 54.925 11.23

E5-14 54.925 11.99 54.925 10.65

E6-14 54.925 15.04 54.925 9.81

E7-14 55.000 14.66 54.975 11.24

E8-14 55.000 14.72 54.975 11.26

E9-14 55.175 6.33 55.050 9.00

E10-14 55.650 1.00 55.650 3.57

E11-14 57.400 -4.31 57.200 -6.54

Appendix F : Supplementary Data

Table F.1: Performance Data at 200 Vp applied voltage

Active

Electrode(s)

50 N preload – 200 Vp applied voltage 70 N preload - 200 Vp applied voltage

Max. Force

[N]

Max. Speed

[mm/s]

Avg. Speed

[mm/s]

Max. Force

[N]

Max. Speed

[mm/s]

Avg. Speed

[mm/s]

E14 1 8.764 5.226 N/A N/A N/A

E13-14 1 13.837 9.627 N/A N/A N/A

E12-14 2 99.548 68.356 N/A N/A N/A

E11-14 7 85.588 62.577 20 142.660 69.994

E10-14 13 128.028 99.690 21 119.287 74.894

E9-14 15 136.037 105.199 25 114.173 65.543

E8-14 17 94.996 58.647 22 104.789 55.211

E7-14 15 115.229 81.267 20 98.081 32.304

E6-14 15 105.892 79.421 19 29.640 3.380

E5-14 10 91.977 67.106 15 21.300 2.047

E4-14 5 51.354 36.877 11 17.020 1.280

E3-14 4 41.198 28.306 8 8.304 1.023

E2-14 2 32.002 18.706 4 5.105 0.886

Table F.2: Performance Data at 70 N preload

Active

Electrode(s)

70 N preload – 100 Vp applied voltage 70 N preload - 50 Vp applied voltage

Max. Force

[N]

Max. Speed

[mm/s]

Avg. Speed

[mm/s]

Max. Force

[N]

Max. Speed

[mm/s]

Avg. Speed

[mm/s]

E14 N/A N/A N/A N/A N/A N/A

E13-14 N/A N/A N/A N/A N/A N/A

E12-14 N/A N/A N/A N/A N/A N/A

E11-14 2 10.962 6.376 N/A N/A N/A

E10-14 22 70.326 43.461 9 27.583 16.940

E9-14 23 67.149 42.085 19 27.077 16.179

E8-14 22 67.375 40.994 17 26.383 18.927

E7-14 22 61.936 31.070 14 21.828 15.531

E6-14 18 24.858 4.351 14 13.668 7.736

E5-14 13 20.116 3.879 13 4.584 2.152

E4-14 8 13.462 1.149 8 3.420 0.811

E3-14 6 9.840 1.007 5 2.873 0.698

E2-14 4 4.372 0.622 3 1.718 0.373

Table F.3: Performance Data at 200 Vp applied voltage and Two Amplifiers

Active

Electrode(s)

70 N preload 50 N preload 30 N preload

Max. Force

[N]

Max. Speed

[mm/s]

Max. Force

[N]

Max. Speed

[mm/s]

Max. Force

[N]

Max. Speed

[mm/s]

E14 N/A N/A 5 12.368 N/A N/A

E13-14 14.5 10.991 10 47.035 0.5 8.617

E12-14 25 52.170 15 117.732 2 29.772

E11-14 35.5 154.007 25 141.776 12 62.767

E10-14 36 201.524 27 174.281 21 109.286

E9-14 34.5 223.348 27 202.568 19 118.601

E8-14 30 206.702 27 195.489 19 142.725

E7-14 29.5 195.840 25 181.017 19 102.139

E6-14 29.5 179.581 23 166.232 16.5 76.311

E5-14 26 145.107 20.5 155.443 8 48.721

E4-14 18.5 94.821 18.5 125.600 2.5 32.002

E3-14 17.5 35.004 16 98.081 1 20.116

E2-14 15 17.238 10 29.640 N/A N/A

Appendix G : Piezoceramic and USM Drawings

This appendix contains all the drawings related to this project.

Piezoceramic:

1. UTUSM-001-RC - USM Piezoceramic

2. UTUSM-012-RA - Piezo Drive Tip

Initial RmMT USM Assembly:

1. UTUSM-A01-RA - Assembly Drawing

2. UTUSM-002-RA - USM Right Cover

3. UTUSM-003-RA - USM Side Wall

4. UTUSM-004-RA - USM Separation Plate

5. UTUSM-005-RA - USM Preload Plate

6. UTUSM-006-RA - USM Left Cover

7. UTUSM-007-RA - USM Encoder Bracket

8. UTUSM-008-RA - USM Mounting Bracket

9. UTUSM-009-RA - Slider Al Strip Support

10. UTUSM-010-RA - Slider Encoder Scale Support

11. UTUSM-011-RA - Test Rig Base

USM Stage Setup:

1. UTUSM-A02-RA - Assembly Drawing

2. UTUSM-020-RA - Adapter Base

3. UTUSM-021-RA - Side Support

4. UTUSM-022-RA - Preload Spring Support

5. UTUSM-023-RA - Preload Spring Plate

6. UTUSM-024-026-RA - Spring Plate and Covers

BOTTOM SURFACE.ELECTRODE DIMENSION ARE FROM THE 2.EDGE OF THE PIEZO TO THE FAR EDGE OF THE ELECTRODE. THE NEXT ELECTRODE STARTS AFTER A 0.25 GAP. PATTERN IS MIRRORED AT THE CL .THE PIEZO IS TO BE POLARIZED

BELOW.

3.ACCORDING TO THE ISO VIEWS DRAWING

NOTE:

A SINGLE ELECTRODE COVERS THE ENTIRE 1.

REVISIONSREV. DESCRIPTION DATE

A INITIAL RELEASE 2011/11/11B ADDED POLARITY IN ISO VIEW 2011/12/02C UPDATED WITH "-1" AND "-2" 2011/12/12

UTUSM-001-X

USM Piezoceramic

C

DO NOT SCALE DRAWING

1

SHEET 1 OF 1

2011/11/11J.LAUUNLESS OTHERWISE SPECIFIED:

SCALE: 1:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

PZT-5 or Eqv.FINISH

MATERIAL


ANSI Y14.5M-1994INTERPRET GEOMETRIC TOLERANCING PER:

0.1

Mechatronics & Microsystems Design Lab

4

X.XX

5

PROHIBITED.

1 X.X

PROPRIETARY AND CONFIDENTIAL

0.01

DIMENSIONS ARE IN MMTOLERANCES: ANGULAR 0.5° X

THE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OFUNIVERSITY OF TORONTO. ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OFUNIVERSITY OF TORONTO IS

3rd Angle

CL

A

29.875±0.01

±0.127

3.006.009.0012.0020.0025.00

60

30±0.127

9.0

DETAIL A SCALE 4 : 1

13X 0.25

GAP BETWEENELECTRODES

UTUSM-001-2

UTUSM-001-1


A INITIAL RELEASE 2011/12/08

NOTE:

CUT AND MACHINE AN ALUMINUM OXIDE STRIP INTO SIZE.1.RECOMMENDED MCMASTER-CARR ALUMINUM OXIDE STRIP 2.PART# 87125K64

UTUSM-012

Piezoceramic Drive Tip

A


1

SHEET 1 OF 1


SCALE: 10:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

Aluminium OxideFINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01

DIMENSIONS ARE IN MM [IN]TOLERANCES: ANGULAR 0.5° X


3rd Angle

1.0

9.0

4.0

2011/12/08INITIAL RELEASEADATEDESCRIPTIONREV.

REVISIONSITEM NO. PART NO. DESCRIPTION QTY.1 575 003 666 Linear Bearing - Type R Size 2 22 575 013 404 Linear Bearing - Type RD Size 2 13 575 016 323 Linear Bearing - Cage AC Size 2 24 8977K314 USM - Preload Silicon Rubber 125 8977K314 USM - Separation Silicon Rubber 86 90592A009 Parts - Hex Nut - M3 57 91290A110 Parts - Socket Head Screw - M3 - 5mm 68 91290A115 Parts - Socket Head Screw - M3 - 10mm 129 91290A119 Parts - Socket Head Screw - M3 - 14mm 210 91290A136 Parts - Socket Head Screw - M3 - 40mm 511 92196A077 Parts - Socket Head Screw - 2-56 - 0.25in 212 92605A097 Parts - Set Screw - M3 - 3mm 513 CS-20-3-200 Slider - Al Strip 114 L130-C1 High Acc. Slider - Scale 115 M3500Si-M10 USM - Mercury 3500 Encoder 116 UTUSM-001 USM - Piezoceramic 217 UTUSM-002 USM - Right Cover 118 UTUSM-003 USM - Side Wall 219 UTUSM-004 USM - Separation Plate 120 UTUSM-005-1 USM - Side Preload Plate 421 UTUSM-005-2 USM - Bottom Preload Plate 222 UTUSM-006 USM - Left Cover 123 UTUSM-007 USM - Encoder Bracket 124 UTUSM-008 USM - Mounting Bracket 125 UTUSM-009 Slider - Al Strip Support 126 UTUSM-010 Slider - Scale Support 127 UTUSM-011 Test - Base 128 UTUSM-012 USM - Drive Tip 2

UTUSM-A01

2

Vertical Configuration

A


1

SHEET 1 OF 1


SCALE: NTS

REVDWG. NO.

ASIZE

TITLE:USM Assembly

3

416-978-6035

NAME DATE

DRAWN

NONE

AISI 304 SSFINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

?12

8

22

15

7

11

17

23

26

9

24

25

27 10

1

2

3

6

13

14

18

19

26

0.3µm A

AA

4.5 ±149.56.0

5.0

18.0

7.5

71

3 5.5

515.04X

5X M

1.8


R0.2



1

USM Right Cover

A


UTUSM-002

SHEET 1 OF 1


SCALE: 1:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

15.5

17 33.0

4X R3

41 15

10

27.0

15.0 31.5

6.0

11X M3 THRU

66.019.5

2.5

3.0

8.5

5.0

16.0

15 0.5

M3 THRU ALL

11

26.0

10.0

2X 15

71

5.0

15

22.5

0.5

2X M3 THRU

UTUSM-005-2 needs to fit into the slot.1.

1

2.

2

2 slot.

NOTE:UTUSM-005-1 needs to fit into the 1



1

USM Side Wall

A


UTUSM-003

SHEET 1 OF 1


SCALE: 1:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

2.5

0.1

7.5

±1

33.0 2.5

36.531.5

5.0

0.0+0.1 THRU

0.1

16.5

+5.0

1.0

0.033.0

1.0

66.0

17.0

1.0

+0.0

5X 3.02.5

33.0

66.0

24

31.5

2.5

36.5±1

2.5

34X R

17

10

+ THRU0.1

5

5X 3.0 0.041



1

USM Separation Plate

A


UTUSM-004

SHEET 1 OF 1


SCALE: 1:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

1.0

71

UTUSM-005-2

10.0 -0.10.0

33.0 -0.10.0

1

USM Preload Plate

A


UTUSM-005-X

SHEET 1 OF 1


SCALE: 2:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

in UTUSM-003.1

1

1

3.2.

UTUSM-005-2 needs to fit into slot 2 in UTUSM-003.

NOTE:The dimension at 1 needs to be the same as or less 1.than the height of UTUSM-003.UTUSM-005-1 needs to fit into slot



1.0

1.0

UTUSM-005-1

-0.10.010.0

17.0 -0.10.0

4X

15

15.5

6.0 THRU4X M3

31.5

15.05.5

33.0

4166.0

0.1

10

17

15.0

3

+

4X R

2.5

3.0

THRU5X 3.0 0.0

5X M3 THRU

571

5.5

3.0

15.04X

5X M1.8

0.3µm A

AA

7.56.0

±149.518.0 5.0

4.5


R0.2

1

USM Left Cover

A


UTUSM-006

SHEET 1 OF 1


SCALE: 1:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle



4.25

2.527.0

±0.1

2X 3.0 0.0+0.1 THRU



1

USM Encoder Bracket

A


UTUSM-007

SHEET 1 OF 1


SCALE: 2:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

0.0+0.1

±0.0832

16.51

±0.5

±0.088.48

9.9 8.26 511

1.8

8.4

22

HELICOIL INSERT2X #2-56 UNC THRU

83.0

3.0

18

2.5 10.5 20.0

15.0

±1 ±1 4X 3.0 0.0+0.1 THRU



1

USM Mounting Bracket

A


UTUSM-008

SHEET 1 OF 1


SCALE: 2:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AISI 304 SSFINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

5

41

20

1.031.0 0.0+

5

2.520

15.02.5

2X 3.0 0.0+0.1 THRU ALL

CL

7X M4 THRU

12.5175.0

20.0

25.07X 2X M3 THRU

200



1

Slider Al Strip Support

A


UTUSM-009

SHEET 1 OF 1


SCALE: 1:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle


1.0 1.5

A

3.0

17.0

12.5

35.0

175.0

0.125.0

±0.1

130.07X

17.0

8.5

THRU

THRU2X 0.1+0.03.0

+0.07X 4.0

20.35

2X R5±2

1

Slider Encoder Scale Support

A


UTUSM-010

SHEET 1 OF 1


SCALE: 1:2

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle



200.0 3.0

23.0

66.0

25 15.0

2.0050.8

67.0 7.5

23.8 6.00152.4

THRU38X M

4X 6.4 THRU.25

20.0

1

TEST RIG BASE

A


UTUSM-011

SHEET 1 OF 1


SCALE: 1:2

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AISI 304 SSFINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

1. Secondary dimensions should only be used as a reference.NOTE:



100.0200.0 10.0

2012/08/01INITIAL RELEASEADATEDESCRIPTIONREV.

REVISIONSITEM NO. PART NUMBER QTY.1 Current Base 12 UTUSM-020 Adapter Base 13 UTUSM-021 Side Support 24 UTUSM-022 Spring Support 15 USM - 001 - Piezoceramic 16 USM - 012 - Drive Tip 17 UTUSM-023 Preload Spring Plate 18 USM - Preload Silicon Rubber 69 USM - 005-1 - Side Preload Plate 2

10 UTUSM-025 Cover Bar 211 UTUSM-026 Spring Cover 112 UTUSM-027 Encoder Bracket 1

UTUSM-A02

USM Stage Setup

A


1

SHEET 1 OF 1


SCALE 2:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

N/AFINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

4

2

5

6

1

7

9

3

4

11 10

12

2

8

5

7

9



61.0

15.0

20.0

2.5

17.0

7.5 20.0

68.0

58.0

34.9

2X R2

2.5 4.0 THRU 36.5

4.26.0

5.0

20.0

13.5

2X

4.28.0

8X M3 THRU

6.5

26.5

2X 4.0 THRU

41.0

23.0 73.0

20.0 2X 5.0

2.0

9.0

A

PROHIBITED.

5 4

1


1

Adapter Base

3 2

UTUSM-020

SHEET 1 OF 1


X.XX


NONE

AL2024-T361FINISH

MATERIAL

INTERPRET GEOMETRIC TOLERANCING PER:

416-978-6035

NAME

X.X

DATE

0.1

SCALE 1:1

TITLE:

REVSIZE

A


DWG. NO.ANSI Y14.5M-1994


DRAWN

0.01



3rd Angle



UTUSM-021

Side Support

A


1

SHEET 1 OF 1


SCALE 2:1

REVDWG. NO.

ASIZE

TITLE:

23

416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361FINISH

MATERIAL



0.1


4

X.XX

5

PROHIBITED.

1 X.X


0.01



3rd Angle

10.0

15.0

5.0

M3 THRU

5.0 41.0

31.5

5.0

3.0 3X

5.0

2.5 20.0

R1 2.5 2.5



UTUSM-022

4 3 25

Preload Spring Support

A


1

SHEET 1 OF 1


SCALE 2:1

REV

PROHIBITED.

1

FINISH

MATERIAL


416-978-6035

NAME DATE

DRAWN University of Toronto

ANSI Y14.5M-1994

NONE


DWG. NO.

X.XX

A


TITLE:

SIZE

X.X 0.01

AL2024-T361

0.1



3rd Angle

10.0

10.0 5.0

20.0

M4

20.0

2.5

2X R1 10.0 5.0

15.0 2.5

2X 3.0



9.8

9.0

11.6

33.0

4.0

9.9

2X R1.0

A

2 1

Preload Spring Plate

3DO NOT SCALE DRAWING

UTUSM-023

SHEET 1 OF 1


SCALE 2:1

REVDWG. NO.

A45


416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361

X.X

FINISH

0.01

SIZE

PROHIBITED.

TITLE:1

X.XX

University of TorontoMechatronics & Microsystems Design Lab

ANSI Y14.5M-1994

0.1

MATERIAL




3rd Angle

20.0

5.0

9.9

3.0

9.9

A

2 1

Spring Plate and Covers

3DO NOT SCALE DRAWING

UTUSM-024-026

SHEET 1 OF 1


SCALE N/A

REVDWG. NO.

A45


416-978-6035

NAME DATE

DRAWN

NONE

AL2024-T361

X.X

FINISH

0.01

SIZE

PROHIBITED.

TITLE:1

X.XX

University of TorontoMechatronics & Microsystems Design Lab

ANSI Y14.5M-1994

0.1

MATERIAL




3rd Angle



UTUSM-024 Spring Plate 2:1

UTUSM-026 Spring Cover 2:1

UTUSM-025 Cover Bar 1:1

10.0

5.0

25.0

4X

2.5

15.0

3.0 THRU

2.5 20.0 68.0 2.5

73.0 2X 3.0 THRU

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