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

Development of a Linear Ultrasonic Motor with Segmented Electrodes

Jacky Ka Ki Lau

Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto 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.

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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.

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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

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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

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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

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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

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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.

Page 1 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.

(+)

(-) (a) (b)

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)

Page 2 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].

Page 3 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.

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

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

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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

Page 6 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

Page 7 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 2nd 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

Page 8 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.

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

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

Page 10 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].

Page 11 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

Page 12 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.

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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.

Page 14 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

Thrust Holding Linear Max Speed Stroke Weight Principle of Force Force Size [mm] Motor [mm/s] [mm] [g] Operation [N] [N] Piezo LEGS 20 55 20 22 22 x 10.8 x 21 40 Stepping Linear 20N

PiezoWalk® 1 20 600 800 95 x 80 x 72 1250 Stepping N-216.2 PILine® 500 - 4 - 120 x 40 x 9 - Standing-wave U-164

Commercial 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 Salisbury et 8.5 - 6 - 45 x 27 x 43 - Inchworm al. 2009 Y.X. Liu et 1160 - 20 - ~99 x ~116 - Standing-wave al. 2010 W.S. Kim et 450 - 75 - Ø20 x 247 - Standing-wave Research al. 2008 C.H. Yun et 470 - 92 - Ø40 x 92 - Standing-wave al. 2001

Page 15 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

Page 16 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.

Page 17 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.

Ø250mm

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

Page 18 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.

Page 19

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.

Page 20

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

Page 21 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

Page 22 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.

Page 23 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.

y

x Piezoceramic

z

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)

Page 24 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

y x z

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.

Page 25

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.

Page 26

(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.

1.E-06

1.E-07

1.E-08 Displacement [m] UX UY

1.E-09 55000 57500 60000 62500 65000 67500 70000 Frequency [Hz] Figure 3.6: Drive-tip displacement results from harmonic analysis.

Page 27

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.

Page 28

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)

Page 29

[ ] [ ] (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-

Page 30 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.

Page 31

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.

Page 32

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.

Slider with mass, m

̇

Drive ̇ -tip

Piezoceramic

Figure 3.14: Dynamic model diagram [26].

Page 33 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.

Page 34 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.

Page 35 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.

Page 36 Table 3.1: FEA data of piezoceramic with varying thickness.

Dimension E(3,1) Freq. UX [m] UY [m] Phase [°] L W T [Hz] 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

0.20 25

0.18 23 0.16 21 0.14 19 0.12 17 0.10 15 0.08 13 0.06 11 0.04 Speed 9 Force

Estimated MaximumSpeed[m/s] 0.02 7 Estimated MaximumThrust Force[N] 0.00 5 7 7.5 8 8.5 9 9.5 10 10.5 11 Thickness [mm] 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

Page 37 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.

0.40 25

0.35 Speed 23 Force 21 0.30 19 0.25 17 0.20 15

0.15 13 11 0.10 9 0.05

Estimated MaximumSpeed[m/s] 7 Estimated MaximumThrust Force[N] 0.00 5 1 1.5 2 2.5 3 Aspect Ratio [X:Y] 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.

Page 38 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.

Page 39

[ ] (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.

Page 40 y Active Electrode x

Electrode Length

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.

Page 41

6.E-06 (a) 6.E-06 (b)

0.E+00 0.E+00

UY UY [m] UY [m]

-6.E-06 -6.E-06 -4.E-06 0.E+00 4.E-06 -4.E-06 0.E+00 4.E-06 UX [m] UX [m]

6.E-06 (c) 6.E-06 (d)

0.E+00 0.E+00

UY UY [m] UY [m]

-6.E-06 -6.E-06 -4.E-06 0.E+00 4.E-06 -4.E-06 0.E+00 4.E-06 UX [m] UX [m]

Figure 3.19: Drive-tip trajectory at active electrode length of (a) 20mm, (b) 30mm, (c) 40mm, (d) 50mm.

Page 42 0.6 50

45

0.5 40

0.4 35

30 0.3 25

0.2 20

Estimated SpeedEstimated [m/s] Maximum 15

0.1 Est. Max. Speed Curve Fit Estimated MaximumThrust Force[N] 10 Est. Max. Force Curve Fit

0.0 5 10 20 30 40 50 60 Active Electrode Lengtt [mm] 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).

Page 43 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.

GND

↓ ↓ ↓ ↓

A B

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

Table 3.2: Electrodes dimension.

Total Electrode Length when Electrode # Electrode Length [mm] 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.

Page 44

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.

Slider

Bottom Support Side Supports

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

Page 45 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.

Page 46 40 25N Load - 57.9 kHz 30N Load - 57.9 kHz 30

35N Load - 57.9 kHz

40N Load - 57.9 kHz 20 45N Load - 57.9 kHz 25N Load - 56.5 kHz 10

0

Slider Displacement Slider (µm) -10

-20 0 100 200 300 400 500 600 Time (µs) Figure 3.24: Slider displacement estimated from FE dynamic analysis with a 30 mm active electrode length.

30 25N Load - 57.5 kHz 25 30N Load - 57.5 kHz 20

35N Load - 57.5 kHz

15 40N Load - 57.5 kHz 10 45N Load - 57.5 kHz 5 0 -5

-10 Slider Displacement Slider (µm) -15 -20 0 100 200 300 400 500 600 Time (µs) 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.

Page 47 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.

Page 48

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

Page 49 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.

Page 50 90 180 85 Magnitude 80 Phase

75

)

70 ° 65 0

60 Phase (

Magnitude Magnitude (dB) 55 50 45 40 -180 40000 45000 50000 55000 60000 65000 70000 Frequency (Hz)

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.

Page 51

Figure 4.6: Original USM setup.

Figure 4.7: Final USM setup used.

Page 52 PXI Controller

Alternate FGEN and amplifier

USM and slider stage

DAQ breakout

Figure 4.8: Experimental setup workspace.

PXI Function NI LabVIEW Controller Generator

Switch USM Matrix Piezo

Digital Input Encoder

Figure 4.9: Experimental setup block diagram.

Page 53 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.

USM Pulley Stage

Weight Workbench

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.

Page 54 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.

60 Saturation

50

40

30 200 V Applied Voltage Current[mA] 20 100 V Applied Voltage

10 50 V Applied Voltage

0 0 10 20 30 40 50 60 Active Electrode Length [mm] 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

Page 55 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.

0.6 70 N Preload - 200 V Applied Voltage 70 N Preload - 100 V Applied Voltage 70 N Preload - 50 V Applied Voltage 0.5 50 N Preload - 200 V Applied Voltage Theoretical Max. Speed 0.4

0.3

0.2 Maximum Speed [m/s]MaximumSpeed 0.1

0.0 0 10 20 30 40 50 60 Active Electrode Length [mm] Figure 4.12: Maximum achievable speed result versus active electrode length.

50 70 N Preload - 200 V Applied Voltage 70 N Preload - 100 V Applied Voltage 45 70 N Preload - 50 V Applied Voltage 50 N Preload - 200 V Applied Voltage 40

Theoretical Max. Force

35 30 25 20

15 MaximumForce [N] 10 5 0 0 10 20 30 40 50 60 Active Electrode Length [mm] Figure 4.13: Maximum achievable force result versus active electrode length.

Page 56 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.

1.6E-08

1.4E-08

1.2E-08

1.0E-08

8.0E-09

6.0E-09 Slider Displacement Slider [m] 4.0E-09 9nm 2.0E-09

0.0E+00 0 100 200 300 400 500 Time [µs] Figure 4.14: Displacement response with one active electrode and 18 µs impulse.

Page 57 1.E-05

1.E-06

1.E-07

Smallest Smallest StepAchieved [m] 1.E-08

1.E-09 0 10 20 30 40 50 60 Active Electrode Length [mm] 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.

Page 58 0.6 70 N Preload - 200 V Applied Voltage 50 N Preload - 200 V Applied Voltage 30 N Preload - 200 V Applied Voltage

0.5 Theoretical Max. Speed

0.4

0.3

0.2 MaximumSpeed [m/s]

0.1

0.0 0 10 20 30 40 50 60 Active Electrode Length [mm] Figure 4.16: Maximum achievable speed results with two amplifiers in parallel.

50 70 N Preload - 200 V Applied Voltage 50 N Preload - 200 V Applied Voltage 45 30 N Preload - 200 V Applied Voltage Theoretical Max. Force 40

35

30

25

20

MaximumForce [N] 15

10

5

0 0 10 20 30 40 50 60 Active Electrode Length [mm] 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

Page 59 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.

160 Saturation

140

120

100

80

60 Current[mA]

40

20

0 0 10 20 30 40 50 60 Active Electrode Length [mm]

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

Page 60 0.30 40

35 0.25

30

0.20 25

0.15 20

15

0.10 MaximumForce [N] MaximumSpeed [m/s] Speed 10

0.05 Force 5

0.00 0 0 10 20 30 40 50 60 Active Electrode Length [mm] Figure 4.19: Maximum performance at 70 N preload with two amplifiers in parallel.

Page 61 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.

Page 62 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.

Page 63 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

Page 64 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

Page 65 [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

Page 66 [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

Page 67 Appendix A : Geometric Optimization Supplementary Data

Table A.1: Performance data of piezoceramic USM with varying thicknesses

Dimension Estimated Maximum Force L W T Speed [m/s] [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) Estimated Maximum Phase Stiffness Freq. UX [m] UY [m] Speed Force L W T [°] [MN/m] [Hz] [m/s] [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

Page 68 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

Page 69 Table B.2: Performance estimate of a 60 x 30 x 9 mm piezoceramic USM with varying active electrode length

Estimated Maximum Electrode Length 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

Page 70 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)

Page 71 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.

Page 72 1.00E-04 2D - Thermal Model

3D - Piezoelectric Model

1.00E-05

Displacement (m) 1.00E-06

1.00E-07 45000 50000 55000 60000 65000 Frequency (Hz)

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.

Page 73 1.00E-04 2D - Thermal Model 3D - Piezoelectric Model

1.00E-05

1.00E-06 Displacement (m) 1.00E-07

1.00E-08 45000 50000 55000 60000 65000 Frequency (Hz)

Figure C.2: Drive-tip x-displacement of an asymmetrically excited 60 x 30x 9 mm piezoceramic.

1.00E-04 2D - Thermal Model 3D - Piezoelectric Model

1.00E-05

1.00E-06 Displacement (m) 1.00E-07

1.00E-08 45000 50000 55000 60000 65000 Frequency (Hz)

Figure C.3: Drive-tip y-displacement of an asymmetrically excited 60 x 30x 9 mm piezoceramic.

Page 74 170

120

70

) ° 20

Phase ( -30

-80

-130 2D - Thermal Model -180 3D - Piezoelectric Model 45000 50000 55000 60000 65000 Frequency (Hz)

Figure C.4: Drive-tip phase angle of an asymmetrically excited 60 x 30x 9 mm piezoceramic.

Page 75 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.

GND

↓ ↓ ↓ ↓

A B

Figure D.1: Top view of differential electrode voltage concept. The arrows shows the polarization direction of the piezoceramic.

Page 76 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.

y Elect. Elect. A B x

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.

Page 77 1.E-05 180 UX 150 UY Phase 120 90

1.E-06 60

)

30 ° 0

-30 Phase (

Displacement Displacement (m) 1.E-07 -60 -90 -120 -150 1.E-08 -180 50000 52000 54000 56000 58000 60000 Frequency (Hz)

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.

0.12 60

55

0.10

50 0.08 45

0.06 40

35 0.04

30 Estimated ThrustForce[N] Est. Max. Speed Curve Fit Estimated MaximumSpeed[m/s] 0.02 Est. Max. Force (Numerical) Curve Fit 25

0.00 20 0 50 100 150 200 Left Electrode Voltage [V] Figure D.4: Performance estimate of a 60 x 30 x 9 mm piezoceramic with differential electrode voltage at its y-displacement peak.

Page 78 1.6 6

1.4 5.5

1.2 5

1 4.5

0.8 4

0.6 3.5

0.4 3 Est. Max. Speed Curve Fit Estimated ThrustForce[N]

Estimated MaximumSpeed[m/s] 0.2 2.5 Est. Max. Force (Numerical) Curve Fit 0 2 0 50 100 150 200 Left Electrode Voltage [V] 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 Estimated Maximum Voltage E(3,1) Phase UX [m] UY [m] Freq. [Hz] [°] Force Left Right Speed [m/s] [N] 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

Page 79 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 Estimated Maximum Voltage E(3,1) Phase UX [m] UY [m] Freq. [Hz] [°] Force Left Right Speed [m/s] [N] 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

Page 80 Appendix E : Impendence Analysis Supplementary Data

Table E.1: Impendence analysis results subject to 30N preload

Piezoceramic #1 Piezoceramic #2 Active E(3,1) Resonant E(3,1) Resonant Electrode(s) Phase (°) Phase (°) Frequency (kHz) Frequency (kHz) 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

Page 81 Table E.2: Impendence analysis results subject to 50N preload

Piezoceramic #1 Piezoceramic #2 Active E(3,1) Resonant E(3,1) Resonant Electrode(s) Phase (°) Phase (°) Frequency (kHz) Frequency (kHz) 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

Page 82 Table E.3: Impendence analysis results subject to 70N preload

Piezoceramic #1 Piezoceramic #2 Active E(3,1) Resonant E(3,1) Resonant Electrode(s) Phase (°) Phase (°) Frequency (kHz) Frequency (kHz) 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

Page 83 Appendix F : Supplementary Data

Table F.1: Performance Data at 200 Vp applied voltage

50 N preload – 200 V applied voltage 70 N preload - 200 V applied voltage Active p p Electrode(s) Max. Force Max. Speed Avg. Speed Max. Force Max. Speed Avg. Speed [N] [mm/s] [mm/s] [N] [mm/s] [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

70 N preload – 100 V applied voltage 70 N preload - 50 V applied voltage Active p p Electrode(s) Max. Force Max. Speed Avg. Speed Max. Force Max. Speed Avg. Speed [N] [mm/s] [mm/s] [N] [mm/s] [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

Page 84 Table F.3: Performance Data at 200 Vp applied voltage and Two Amplifiers

70 N preload 50 N preload 30 N preload Active Electrode(s) Max. Force Max. Speed Max. Force Max. Speed Max. Force Max. Speed [N] [mm/s] [N] [mm/s] [N] [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

Page 85 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

Page 86 REVISIONS 29.875±0.01 REV. DESCRIPTION DATE 25.00 A INITIAL RELEASE 2011/11/11 B ADDED POLARITY IN ISO VIEW 2011/12/02 20.00 C UPDATED WITH "-1" AND "-2" 2011/12/12 GAP BETWEEN ELECTRODES 12.00 13X 0.25 9.00 6.00 3.00 A

DETAIL A SCALE 4 : 1

NOTE:

1. A SINGLE ELECTRODE COVERS THE ENTIRE BOTTOM SURFACE. 30±0.127 2. ELECTRODE DIMENSION ARE FROM THE 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 . 3. THE PIEZO IS TO BE POLARIZED ACCORDING TO THE ISO VIEWS DRAWING BELOW.

CL 9.0 60±0.127

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/11/11 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM UTUSM-001-1 TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 USM Piezoceramic PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY PZT-5 or Eqv. REPRODUCTION IN PART OR AS A WHOLE UTUSM-001-X UTUSM-001-2 FINISH C WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

9.0

4.0

1.0

NAME DATE NOTE: Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto 1. CUT AND MACHINE AN ALUMINUM OXIDE STRIP INTO SIZE. UNLESS OTHERWISE SPECIFIED: 416-978-6035 2. RECOMMENDED MCMASTER-CARR ALUMINUM OXIDE STRIP DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: PART# 87125K64 X 1 X.X 0.1 X.XX 0.01 Piezoceramic Drive Tip PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY Aluminium Oxide REPRODUCTION IN PART OR AS A WHOLE UTUSM-012 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 10:1 SHEET 1 OF 1 5 4 3 2 1 ITEM NO. PART NO. DESCRIPTION QTY. REVISIONS 1 575 003 666 Linear Bearing - Type R Size 2 2 REV. DESCRIPTION DATE 2 575 013 404 Linear Bearing - Type RD Size 2 1 27 10 19 A INITIAL RELEASE 2011/12/08 3 575 016 323 Linear Bearing - Cage AC Size 2 2 4 8977K314 USM - Preload Silicon Rubber 12 18 5 8977K314 USM - Separation Silicon Rubber 8 13 6 90592A009 Parts - Hex Nut - M3 5 6 7 91290A110 Parts - Socket Head Screw - M3 - 5mm 6 2 8 91290A115 Parts - Socket Head Screw - M3 - 10mm 12 9 91290A119 Parts - Socket Head Screw - M3 - 14mm 2 25 10 91290A136 Parts - Socket Head Screw - M3 - 40mm 5 3 11 92196A077 Parts - Socket Head Screw - 2-56 - 0.25in 2 12 92605A097 Parts - Set Screw - M3 - 3mm 5 1 13 CS-20-3-200 Slider - Al Strip 1 14 L130-C1 High Acc. Slider - Scale 1 15 M3500Si-M10 USM - Mercury 3500 Encoder 1 14 16 UTUSM-001 USM - Piezoceramic 2 9 26 17 UTUSM-002 USM - Right Cover 1 18 UTUSM-003 USM - Side Wall 2 26 19 UTUSM-004 USM - Separation Plate 1 20 UTUSM-005-1 USM - Side Preload Plate 4 21 UTUSM-005-2 USM - Bottom Preload Plate 2 23 22 22 UTUSM-006 USM - Left Cover 1 23 UTUSM-007 USM - Encoder Bracket 1 17 ? 24 UTUSM-008 USM - Mounting Bracket 1 25 UTUSM-009 Slider - Al Strip Support 1 7 12 26 UTUSM-010 Slider - Scale Support 1 8 27 UTUSM-011 Test - Base 1 28 UTUSM-012 USM - Drive Tip 2 15

11 24

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 USM Assembly X.XX 0.01 Vertical Configuration PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AISI 304 SS REPRODUCTION IN PART OR AS A WHOLE UTUSM-A01 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: NTS SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE 11X M3 THRU 41 15 A INITIAL RELEASE 2011/12/06 17 33.0

31.5 10 15.0

6.0

15.5

4X R3 27.0 3.0 19.5 66.0 2.5 0.3µm A

4.5 49.5±1 5.0 4X 15.0 5.5 6.0 7.5 5X M3 5

A A 71 1.8 18.0

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/06 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 R0.2 X.XX 0.01 USM Right Cover PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DETAIL A DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV SCALE 2 : 1 UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-002 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08 +0.1 5.0 33.0 5.0 0.0 1.0 16.5 1.0 2.5

7.5

+0.1 17.0 1 0.0 31.5 36.5±1 2

+0.1 5X 3.0 THRU 0.0 2.5 33.0 2.5 1.0 66.0

71 26.0 22.5 M3 THRU ALL 16.0

0.5 5.0 5.0 10.0

2X 15 15 0.5 2X M3 THRU 11 15 8.5

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM NOTE: TOLERANCES: ANGULAR 0.5° TITLE: 1. UTUSM-005-1 needs to fit into the 1 slot. X 1 X.X 0.1 2. UTUSM-005-2 needs to fit into the 2 slot. X.XX 0.01 USM Side Wall PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-003 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

+0.1 5X 3.0 THRU 41 0.0 4X R3 2.5

10

31.5 36.5±1

17

24 33.0 2.5 5 66.0

1.0

71

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 USM Separation Plate PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-004 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

0.0 1 10.0 - 0.1

0.0 17.0 1.0 - 0.1

UTUSM-005-1

0.0 10.0 1 - 0.1

0.0 33.0 - 0.1 1.0

NAME DATE Mechatronics & Microsystems Design Lab UTUSM-005-2 DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 USM Preload Plate NOTE: PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 1. The dimension at 1 needs to be the same as or less THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV than the height of UTUSM-003. UNIVERSITY OF TORONTO. ANY AL2024-T361 2. UTUSM-005-1 needs to fit into slot 1 in UTUSM-003. REPRODUCTION IN PART OR AS A WHOLE UTUSM-005-X FINISH A 3. UTUSM-005-2 needs to fit into slot 2 in UTUSM-003. WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 2:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE 41 15 A INITIAL RELEASE 2011/12/08 66.0 +0.1 2.5 33.0 5X 3.0 THRU 0.0

17

31.5 15.0

6.0 10 4X M3 THRU 15.5

4X R3 5.5 4X 15.0 3.0 0.3µm A 5X M3 THRU 49.5±1 18.0 5.0 5.5 4X 15.0 4.5 6.0 7.5

A 5X M3.0 5 A 71 1.8 NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 R0.2 X.XX 0.01 USM Left Cover PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV DETAIL A UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-006 FINISH A SCALE 2 : 1 WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

4.25±0.1

+0.1 2X 3.0 THRU 0.0 27.0 2.5

22 8 +0.1 9.9 8.26 11 5 3.0 0.0

1.8 8.48±0.08 2X #2-56 UNC THRU 18 HELICOIL INSERT 8.4±0.5 3.0

16.51±0.08

32 NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 USM Encoder Bracket PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-007 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 2:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

15.0

+0.1 2.5±1 10.5±1 20.0 4X 3.0 THRU 0.0

20 +1.0 5 31.0 2.5 15.0 2.5 0.0

+0.1 2X 3.0 THRU ALL 20 0.0

5

41 NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 USM Mounting Bracket PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AISI 304 SS REPRODUCTION IN PART OR AS A WHOLE UTUSM-008 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 2:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

175.0 12.5

CL 20.0

2X M3 THRU 7X M4 THRU 7X 25.0

200 17.0

A 3.0 1.0 1.5

DETAIL A NAME DATE Mechatronics & Microsystems Design Lab SCALE 4 : 1 DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Slider Al Strip Support PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-009 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08

8.5 175.0 12.5

17.0

+0.1 20.35±0.1 2X 3.0 THRU 0.0 +0.1 7X 4.0 THRU 0.0 7X 25.0 130.0 35.0 2X R5±2

200.0 3.0

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Slider Encoder Scale Support PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-010 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:2 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2011/12/08 66.0 20.0 67.0 23.0 8X M3 THRU 7.5

25 15.0

50.8 2.00

23.8 152.4 6.00 4X 6.4.25 THRU

200.0 10.0 100.0

NOTE: NAME DATE Mechatronics & Microsystems Design Lab 1. Secondary dimensions should only be used as a reference. DRAWN J.LAU 2011/12/08 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 TEST RIG BASE PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AISI 304 SS REPRODUCTION IN PART OR AS A WHOLE UTUSM-011 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE: 1:2 SHEET 1 OF 1 5 4 3 2 1 ITEM NO. PART NUMBER QTY. REVISIONS 1 Current Base 1 REV. DESCRIPTION DATE 2 UTUSM-020 Adapter Base 1 A INITIAL RELEASE 2012/08/01 3 UTUSM-021 Side Support 2 4 UTUSM-022 Spring Support 1 1 5 USM - 001 - Piezoceramic 1 11 10 6 USM - 012 - Drive Tip 1 7 UTUSM-023 Preload Spring Plate 1 8 USM - Preload Silicon Rubber 6 6 9 USM - 005-1 - Side Preload Plate 2 4 10 UTUSM-025 Cover Bar 2 11 UTUSM-026 Spring Cover 1 12 UTUSM-027 Encoder Bracket 1 3

7 2

12 5 9 4

2

8

7

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2012/08/01 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 USM Stage Setup PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: 9 ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV 5 UNIVERSITY OF TORONTO. ANY N/A REPRODUCTION IN PART OR AS A WHOLE UTUSM-A02 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE 2:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS 7.5 58.0 REV. DESCRIPTION DATE A INITIAL RELEASE 2012/05/22 26.5 20.0 2.5 8X M3 THRU 15.0 2X R2 2X 4.0 THRU 8.0 4.2

20.0

13.5

34.9 41.0 20.0 17.0

5.0 6.5

36.5 2X 4.0 THRU 2.5 68.0 6.0 4.2 2.0 61.0

9.0

20.0 NAME DATE Mechatronics & Microsystems Design Lab 2X 5.0 23.0 DRAWN J.LAU 2012/05/22 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 73.0 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Adapter Base PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-020 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE 1:1 SHEET 1 OF 1 5 4 321 REVISIONS REV. DESCRIPTION DATE 5.0 A INITIAL RELEASE 2012/05/22 2.5 2.5 R1

3X 3.0

31.5

5.0

20.0 5.0 41.0 2.5

10.0 5.0

M3 THRU 15.0 NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2012/05/22 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Side Support PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-021 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE 2:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2012/05/22 10.0 2X R1 5.0

2X 3.0 20.0

2.5

2.5 15.0

M4

10.0 5.0

10.0 20.0

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2012/05/22 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Preload Spring Support PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-022 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE 2:1 SHEET 1 OF 1 5 4 321 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2012/06/04

33.0

4.0 9.0

9.9 11.6 2X R1.0

9.8

NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2012/06/04 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Preload Spring Plate PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-023 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE 2:1 SHEET 1 OF 1 5 4 3 2 1 REVISIONS REV. DESCRIPTION DATE A INITIAL RELEASE 2012/06/04

9.9

9.9

4X 3.0 THRU 3.0 5.0 UTUSM-024 Spring Plate 2:1

20.0 15.0

5.0 2.5 68.0 2.5 20.0 2.5 10.0 25.0

UTUSM-026 Spring Cover 2:1 2X 3.0 THRU 73.0 NAME DATE Mechatronics & Microsystems Design Lab DRAWN J.LAU 2012/06/04 University of Toronto UNLESS OTHERWISE SPECIFIED: 416-978-6035 DIMENSIONS ARE IN MM [IN] UTUSM-025 Cover Bar 1:1 TOLERANCES: ANGULAR 0.5° TITLE: X 1 X.X 0.1 X.XX 0.01 Spring Plate and Covers PROPRIETARY AND CONFIDENTIAL INTERPRET GEOMETRIC TOLERANCING PER: ANSI Y14.5M-1994 THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF MATERIAL SIZE DWG. NO. REV UNIVERSITY OF TORONTO. ANY AL2024-T361 REPRODUCTION IN PART OR AS A WHOLE UTUSM-024-026 FINISH A WITHOUT THE WRITTEN PERMISSION OF A UNIVERSITY OF TORONTO IS NONE 3rd Angle PROHIBITED. DO NOT SCALE DRAWING SCALE N/A SHEET 1 OF 1 5 4 3 2 1