ABSTRACT. levitation (SWAL) was investigated. Multiple ultrasonic bolt-clamped Langevin transducers (BLTs)

Transcription

1 ABSTRACT PARK, JOONG-KYOO. Feasibility of Non-contact Manipulation of a Small Object using Standing Wave Acoustic Levitation. (Under the direction of Dr. Paul I. Ro.) In this dissertation a novel method of non-contact manipulation using standing wave acoustic levitation (SWAL) was investigated. Multiple ultrasonic bolt-clamped Langevin transducers (BLTs) were used to generate pressure nodes in a unique acoustic standing wave field. Small light objects of any shape or material can be trapped in these pressure nodes. It was proposed that the frequency, amplitude and phase of standing waves can be modulated to transport the object along desired trajectories. From simulation and experiments, phase modulation proved to be superior to modulating the other parameters and produced smooth motion long range capability and was simple to control. Furthermore, the angle between the two transducers was found to affect the trajectory of the trapped object during phase modulation. At certain tilt angles, modulating a combination of parameters resulted in sinusoidal and elliptic paths of the object both in simulations and experiments. To understand the nature of levitation forces acting on objects, analysis of non-linear second order radiation pressure was conducted for a simple case. In accordance with the analysis of the radiation pressure, a finite element method was employed to validate the complex radiation pressure field and its levitation forces. According to the simulation results, radiation pressure increased at 180 n degree phase angles (n=0, 1, 2, 3 ) if the distance between two facing transducers is changed by a certain fraction of the wave length. This observation led to proposing a new distance modulation technique to enhance the acoustic levitation forces. The distance modulation technique changes the distance between two opposing transducers at the certain phase angles to increase levitation forces without moving the pressure nodes. This was proven numerically and experimentally. The results showed that the additional distance modulation can increase overall levitation force more

2 than two times and it allows for longer controlled movements than that achieved by phase modulation alone. A three-transducer experimental system was developed for SWAL. A three-channel function generator controlled by a micro-controller was adapted for parameter modulation. Stepper motors and servo motors were attached to the transducers for the linear and angular movements and two other micro-controllers operated the motors. An integrated graphical user interface (GUI) was developed to control each component. A USB camera and object tracking algorithm served as the feedback sensor for the controller. For two-dimensional motion control, direct inverse control using artificial neural networks (ANN) with PID feedback was adopted to follow a desired trajectory. Two different operational methods were developed for control bases. The first uses two BLTs attached to two horizontal linear actuators, and a vertical linear actuator moves the entire structure. In this setup, distance modulation was applied for accuracy and stability. In the second method, three BLTs were attached to the two horizontal linear actuators and one rotational servo motor respectively to form a Y-shape. Angular modulation of the lower servo motor was adapted to achieve straight movement of objects in the acoustic field. Experiments were performed for each method with two different trajectories: linear and circular. The results show that the second method has a higher overall control error than the first due to the complexity of the pressure field generated by the larger number of transducers. In addition, circular trajectory control had a higher mean square error (MSE) than the linear trajectory because the phase modulation is only used for single axial motion control. This causes both x- and y- axial movement and this extra error results in more frequent movement when following a complex circular trajectory. The results of experiments confirm that two-dimensional motion control using acoustic levitation can be achieved with acceptable errors.

3 Copyright 2014 by Joong-Kyoo Park All Rights Reserved

4 Feasibility of Non-contact Manipulation of a Small Object using Standing Wave Acoustic Levitation by Joong-Kyoo Park A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Mechanical Engineering Raleigh, North Carolina 2014 APPROVED BY: Dr. Gregory D. Buckner Dr. Yun Jing Dr. Yong Zhu Dr. Paul I. Ro Committee Chair

5 DEDICATION To my father. ii

6 BIOGRAPHY Joong-Kyoo Park was born in South Korea. He received a B.S. degree in Physics from Soonchunhyang University, Asan, South Korea in 1995 and a B.S. in Mechanical Engineering from Virginia Tech, Blacksburg, VA in He then received an M.S. in Mechanical Engineering from the University of Tennessee, Knoxville, TN in He enrolled in graduate school in the department of Mechanical and Aerospace Engineering at North Carolina State University in iii

7 ACKNOWLEDGMENTS I would like to thank my academic advisor for this research, Dr. Paul I. Ro. He has always guided and trusted me during my research, and he has been a good mentor for not only my academics, but also for my life. I would also like to thank Dr. Gregory D. Buckner, Dr. Yong Zhu, Dr. Yun Jing, and Dr. Henry Lamb for serving on my advisory committee and providing me with support and encouragement. I would like to thank Ken Garrard, who has helped me with his broad knowlege. I d also like to thank Zack and Frank for their friship, advice, and suggestions. I would especially like to thank my father who has supported me financially and provided me with encouragement. I will never forget his love and devotion. I am also thankful to my mother, brother, and sisters for their support, and my wife and our children who give me love and support. iv

8 TABLE OF CONTENTS LIST OF TABLES... viii LIST OF FIGURES... ix Chapter 1: Introduction Acoustic Non-contact Manipulation Acoustic Radiation Force Piezoelectric Transducers Research Objectives Chapter 2: Standing Wave Acoustic Levitation (SWAL) Manipulation based on Parameter Modulations of Pressure Nodes using Two Transducers Abstract Introduction Near Field Acoustic Pressure Parameter Modulation Experiments Conclusions Chapter 3: Numerical and Experimental Study of Acoustic Levitation Force and Performance Enhancement for Standing Wave Acoustic Levitation (SWAL) by Distance Modulation Abstract Introduction Analysis of Acoustic Radiation Pressure and Levitation Force Distance Modulation Numerical Simulation of Distance Modulation v

9 3.6 Numerical Simulation for Acoustic Levitation Force Distance Modulation Experiments Conclusions Chapter 4: Experimental Setup for Standing Wave Acoustic Levitation (SWAL) System Abstract Introduction Three-Transducer Experimental Setup Servo and Stepper Motors Micro-Controller Units (MCUs) and Function Generator Object Tracking Integrated Graphical User Interface (GUI) Object Tracking Error Phase Modulation for the Three-Transducer Experimental Setup Two-Dimension Operational Methods using Phase Modulation Conclusions Chapter 5: Two-dimensional Motion Controls using Artificial Neural Network (ANN) for Acoustic Non-contact Manipulation Abstract Introduction Artificial Neural Network (ANN) Neural Network for Control Neural Network Control Design for SWAL Experiment Results Line Trajectory Control vi

10 5.4.2 Circle Trajectory Control Conclusions Chapter 6: Conclusions Parameter Modulations and Force Enhancement of SWAL Two-dimensional Motion Control using SWAL Recommations for Future Work REFERENCES APPENDIX Appix A Matlab Code Appix B Micro-controller Code (Linear Actuator) Appix C Micro-controller Code (Rotational Actuator) vii

11 LIST OF TABLES Table 3-1 Peak locations of experiment and simulation (λ=12.85 mm) Table 5-1 Experiment results of two-dimensional control viii

12 LIST OF FIGURES Figure 1-1 Acoustic levitation (Left: Hard-shell pill (dia. 3mm), Right: a water droplet)... 3 Figure 1-2 Traveling wave and standing wave... 4 Figure 1-3 Standing Wave Acoustic Levitation (SWAL)... 5 Figure 1-4 Bolt-clamped Langevin transducers (BLTs) Figure 2-1 A proposed SWAL design in two different tilt angles Figure 2-2 Near-field pressure of a circular piston Figure 2-3 Parameter modulation simulations Figure 2-4 Combination of parameter modulation simulations Figure 2-5 Experiment setup Figure 2-6 Frequency and amplitude modulation Figure 2-7 Phase modulation and 150 degree tilt angle Figure 2-8 Phase and amplitude modulation at 150 degree tilt angle Figure 3-1 Distance modulation Figure 3-2 Second order radiation pressure along the center line Figure 3-3 Validation of the distance modulation concept Figure 3-4 Radiation pressure at x=0 during distance modulation Figure 3-5 COMSOL simulations for levitation force Figure 3-6 The axial and lateral levitation forces Figure 3-7 Experimental setup (d=19.3 mm and f=26.7 khz) Figure 3-8 Position variations during the phase modulation Figure 3-9 Object y-position during distance modulation Figure 3-10 Phase modulation with distance modulation Figure 4-1 Model of two-dimensional manipulation system ix

13 Figure 4-2 Servo and stepper motor signal Figure 4-3 Microcontrollers and a step motor driver Figure 4-4 Four-channel DDS-based function generator system Figure 4-5 A USB camera and object tracking Figure 4-6 Integrated control interface using MATLAB GUI Figure 4-7 Normal distribution of a levitated object s position using object tracking (unit: mm) Figure 4-8 Simulations for two-dimensional system Figure 4-9 Phase modulation for long vertical movement Figure 4-10 Phase modulation at the left operation area Figure 4-11 Two different proposed operation strategies for motion control Figure 5-1 Two operational methods for ANN motion control Figure 5-2 Activation functions Figure 5-3 Structure of a basic neuron Figure 5-4 Direct inverse controls Figure 5-5 Training date collected with the distance modulation Figure 5-6 Training data collected for the first method Figure 5-7 Training date collected for the second method Figure 5-8 Motion controllers for each axis (method 1) Figure 5-9 Motion controllers for each axis (method 2) Figure 5-10 Method 1: Horizontal line trajectory Figure 5-11 Method 2: Horizontal line trajectory Figure 5-12 Method 1: Circle trajectory (d=3.2mm) Figure 5-13 Method 2: Circle trajectory (d=3.2mm) x

14 Chapter 1: Introduction The aim of this research was to investigate the feasibility of non-contact manipulation using acoustic levitation of light objects such as Styrofoam balls in air. The objects considered in this study had a size range of a few millimeters. However, the findings of this study are not limited by the size or number of materials or the media in which the objects are being levitated. The findings of this research work are applicable to objects as small as blood cells, either single or grouped together. The objects could be hard-shell medicine pills or soft synthetic drops. The vibrating media surrounding the objects could be air or liquid or even human tissues. In this research, characteristics of acoustic radiation forces and their manipulable parameters were studied, and control schemes for precise manipulation were investigated. To study the phenomenon of acoustic levitation, an experimental setup was designed and unique control strategies with feedback were developed. The details of the experimental setup and the control system are discussed in chapters two through five. This chapter briefly explains the concepts that were used in this research work. 1.1 Acoustic Non-contact Manipulation Non-contact manipulation is defined as a means of positioning objects in a medium such as air/water without any kind of physical contact with the object. It has applications ranging from industrial environments to research areas such as microgravity, chemical synthesis, bioengineering, and semiconductor device fabrication [1-4]. In micro-assembly processes, surface forces become dominant in comparison to gravitational or inertial forces since the components are small [5]. These adhesion/cohesion forces (electrostatic, van der Walls, and surface tension forces), create challenges 1

15 handling small objects using grippers or probes. These difficulties can be avoided by preventing any mechanical contact with these objects. In addition, contamination and damage of sensitive or fragile materials can be avoided using non-contact manipulation methods. Further, these methods can be used in cases where conventional contact methods would fail, such as the handling of liquids and aerosols. Acoustic levitation, one of the non-contact manipulation techniques, uses acoustic radiation pressure to enable the suspension of single or multiple objects. Figure 1-1 shows the levitation of a hard shell pill and a drop of water in the acoustic radiation field of standing waves created by two Bolt-clamped Langevin transducers (BLTs). Any object can be levitated if the surface area of the object in the pressure field is large enough to resist gravitational or external forces. The main advantage of acoustic levitation in comparison to other techniques, such as magnetic or electrostatic, is that this technique is indepent of the material of the object thereby allowing the handling of a variety of solids and liquids which need not be conductive or semi-conductive or dielectric. Examples of applications of acoustic levitation are spectroscopy and chemical reactivity [6, 7], separation of different density bio-particles and cell manipulation in microfluidics [8, 9], journal (or plain) bearings [10], clarification of interaction between droplet combustion and acoustic oscillation [11] and Martian dust mitigation [12]. 2

16 Figure 1-1 Acoustic levitation (Left: Hard-shell pill (dia. 3mm), Right: a water droplet) The acoustic levitation technique uses two types of waves to generate acoustic radiation pressure: traveling waves and standing waves, as shown in Figure 1-2. The traveling waves propagate through a medium, and transport energy while standing waves are stationary. Standing waves are typically generated by two traveling waves, an incident wave and a reflected wave, and have pressure nodes and antinodes. The pressure nodes are the positions where pressure is zero, and the antinodes are positions at which the pressure fluctuates between its maximum and minimum value. The frequency of the generated waves for acoustic levitation is generally above 20 khz which lies in the ultrasound domain. This implies that humans cannot hear this sound and would not be affected by it. 3

17 Wave Length (λ) (a) Traveling wave Node Anti-node Wave Length (λ) (b) Standing wave Figure 1-2 Traveling wave and standing wave In general, there are two different acoustic levitation types: Near-field Acoustic Levitation (NFAL) and Standing Wave Acoustic Levitation (SWAL). NFAL or squeeze film levitation is a phenomenon in which objects are levitated at a very small distance above a vibrating surface using ultrasonic acoustic surface waves (SAWs). NFAL, which can transport an object using squeeze film effects in near field, can levitate heavy objects. However, the object being levitated must have sufficient cross-sectional area in the transverse direction of the pressure wave to resist external forces such as gravity. An object transport system on the surface of the vibrating beam using NFAL was studied in [13, 14]. Several parameters of the traveling waves generated by two-mode excitation were identified as the factors of transportation. It was found that factors such as the mass of objects, the supplied electric power, the phase difference between the two transducers, and the excitation frequency not only affect the speed of the objects, but also the direction of transportation. 4

18 Conversely, SWAL uses standing waves and traps small objects at pressure nodes. SWAL can levitate various shapes; however, its limitation is its weaker acoustic radiation force which limits the object weight. A typical SWAL design, which has one transducer and one reflector, creates a standing wave as shown in Figure 1-3. Pressure nodes and anti-nodes are produced along the center line between the transducer and the reflector, and an object is trapped at a pressure node due to the time-averaged second-order forces generated by acoustic radiation pressure. These forces at pressure antinodes push the object axially; either up or down. Because of a gravitational force, a trapped object is usually located slightly below a pressure node. This conventional design may be improved by using a transducer and reflector having a concave surface to focus the acoustic radiation. In this research, SWAL was utilized to manipulate an object, but multiple transducers were used to generate standing waves. Figure 1-3 Standing Wave Acoustic Levitation (SWAL) 5

19 1.2 Acoustic Radiation Force Acoustic radiation force acting on an object has been the subject of a number of research projects. The earliest theory of acoustic radiation forces acting on a particle was developed by King [15], although Rayleigh [16] was the first to describe this force. Investigating the radiation force produced by a traveling wave and a standing wave on a rigid, incompressible spherical object, King s calculation revealed that the acoustic radiation force was much higher in standing waves than in traveling waves. Yosioka and Kawasima [17] exted this work to a compressible spherical object. Gor kov [18] found that the average flux of momentum through any closed surface that encloses the object is the amount of force acting on the object in an ideal fluid. Nyborg [19] derived the acoustic radiation force using the time averaged densities of kinematic and potential energies. Wang and Lee [20] reviewed the acoustic levitation due to acoustic radiation force acting on a rigid sphere in air and on a liquid object in a liquid medium. They also presented their findings on acoustic viscous torque and resonance frequency shift. Aside from the axial force, which acts in the direction of the acoustic radiation wave, the lateral force that is perpicular to the axial force was also investigated. The distribution of the lateral force [21] and the acoustic force in a pseudo standing wave for the transport of objects [22] was measured. The magnitude of the lateral force in the general field was found [23], and the experimental measurement was verified qualitatively with the theory [24]. As expected, the lateral force was found to be much weaker than the axial force [24-26]. The lateral force expression was derived from empirical particle trajectories [27]. In this section, acoustic radiation forces acting on a rigid spherical object in gas are analyzed. These forces were found from the mean excess pressure along one dimension. In an adiabatic process which is reversible and isentropic, the relationship between pressure and density can be simplified. 6

20 Using the state equation, the equation of continuity, the momentum equation, and the linearized wave equation for ideal gas which is irrotational and inviscid, the follow relation can be found, (1.1) where is acoustic pressure, and is speed of sound which is related to bulk modulus and density of the medium. If the pressure is assumed plane standing wave and a function of one-dimensional position (x) and time (t), the acoustic pressure, which is the solution of the wave equation, can be found as (1.2) where is the pressure amplitude,, is the wave number, the angular frequency, and a pressure node located at x = 0 is the boundary condition. Equations (1.1) and (1.2) are not sufficient to determine the acoustic radiation forces owing to the fact that the time-averaged pressure of Eq. (1.2) over one cycle is zero due to the term. Therefore, the time-indepent term of radiation pressure is found from a Taylor series [15]. From the equation of continuity and the momentum equation, Euler s pressure can be expanded as a summation of zero order, first order, second order, and higher order terms. The zero order represents static pressure, while the first order and the second order represent the time-depent term and the time-indepent term, respectively. The other terms, including the higher terms, can be neglected. The approximated acoustic pressure is calculated [18] as 7

21 ( ) (1.3) where is the velocity potential, the potential energy density, and the kinetic energy density. Due to the second order terms, which are the second and third terms in Eq. (1.3), the time-averaged value will not be zero. If the time-averaged pressure is zero, then the object surrounded by acoustic radiation would be oscillating, but would not move to a new location. The mean value of this equation is ( ) (1.4) This pressure is called the Langevin radiation pressure which represents a mean energy density [15, 20]. The diamond brackets denote the time averaging over one cycle. To calculate the radiation force acting on an object, the following acoustic radiation stress tensor by Brillouin is required [20]: (1.5) where is the Kronecker delta, the density of medium, and the particle velocity. From the acoustic radiation stress tensor, the acoustic force acting on an object is found using a surface integral to the normal component of the stress over a closed surface, 8

22 (1.6) From the axisymmetry and boundary conditions, only the axial component is considered, since the normal component of the velocity at the boundary is zero. Finally, the acoustic radiation force is calculated by integrating over a closed surface as ( ( ) ) (1.7) where is angle from the radiation axis, and is the object surface. Equation (1.7) gives the timeaveraged force acting on a moving spherical object. In the spherical coordinate system for the direction aligned with the positive y-axis, the simplified levitation force can be written as [20] (1.8) where is the radius of a spherical object, is the distance from a node in the axial direction, and is small. 1.3 Piezoelectric Transducers Acoustic waves are commonly generated by piezoelectric materials which expand or contract on the application of a voltage across them. The polarity of the applied voltage determines the expansion or contraction. If a sigmoidal voltage is applied, the piezoelectric transducer vibrates 9

23 following the applied power waveform. Normal piezoelectric transducers generate a small amplitude vibration which is typically less than a micrometer at resonance frequency. However, Bolt-clamped Langevin Transducers (BLTs) can generate high amplitude vibrations of several micrometers. Piezoelectric ceramic materials such as PZT (lead zirconate titanate) are preloaded to prevent damage from tensile stress due to high amplitude motion [28]. Piezoelectric ceramic materials are strong at high compression stress, but weak at high tensile stress. BLTs are usually attached to a booster and/or a horn in order to amplify the amplitude and dissipate heat. For this research, the BLTs manufactured by NGK Spark Plug Co. Ltd (DA2228) are used as shown in Figure 1-4. At normal room temperature, the resonant frequency is 26.7 khz which is ultrasonic, thereby enabling silent operation. Figure 1-4 Bolt-clamped Langevin transducers (BLTs) 10

24 1.4 Research Objectives The primary objects of this research are to understand the standing wave acoustic levitation (SWAL), and to design a novel SWAL system for precise non-contact manipulation in twodimensional space. To achieve this general goal, an extensive research investigation has been conducted with the following objectives: 1. Investigation of parameter modulation for a multiple transducer system to drive a levitated object. 2. Analysis of acoustic radiation pressure and levitation forces as well as the development of performance enhancement techniques. 3. Design of a novel levitation system for one- and two-dimensional motion control. 4. Development of a controller to follow a desired trajectory. This dissertation is divided according to the above goals. In Chapter 2, an analysis of the near-field acoustic levitation forces and an investigation of parameter modulation for a multiple transducer system to drive a levitated object are presented. Chapter 3 focuses on the simulations of acoustic radiation pressure and levitation forces and enhancement of those forces by distance modulation. Chapter 4 describes the novel design of an experimental levitation setup for one- or twodimensional motion control. Chapter 5 presents a neural network controller for two different setups and evaluation of the experimental results. Finally, Chapter 6 presents conclusions from this research and gives direction for future research. 11

25 Chapter 2: Standing Wave Acoustic Levitation (SWAL) Manipulation based on Parameter Modulations of Pressure Nodes using Two Transducers 2.1 Abstract In this chapter, an investigation of non-contact manipulation techniques based on parameter modulations of acoustic pressure nodes was undertaken in air. Standing wave acoustic levitation (SWAL) was observed when standing waves trapped small objects at pressure nodes. Two ultrasonic bolt-clamped Langevin type transducers (BLTs) generating traveling waves in order to generate a standing wave. Modulating parameters of the two traveling waves were used to manipulate a trapped object. Frequency, amplitude, and phase modulations of the two transducers were exploited. From simulation and experiments, phase modulation was prominent among other methods due to its long range and smooth controllability. It was also found that angles between two transducers affect the trajectory of the trapped object during the parameter modulations. Sinusoidal and elliptic paths of the object were observed experimentally through a combination of parameters at certain tilt angles. 2.2 Introduction The conventional SWAL design consists of a vibrating transducer, a reflector, an incident wave from the transducer and a reflected wave from the reflector creating a standing wave. This fixed-phase design is simple and easy to construct, but lacks the capability to manipulate the trapped object without moving an entire structure. Therefore, in this chapter, two BLTs without a reflector are 12

26 used for object manipulation. Figure 2-1 shows the proposed two-transducer design system at two different tilt angles. The two transducers generate two traveling waves in order to create one standing wave. Due to the superposition of the two traveling waves, pressure nodes can be manipulated by changing the wave parameters, and a trapped object follows the moving pressure nodes. It is discovered that frequency, amplitude, and phase modulations of two transducers can alter the position of these pressure nodes. Furthermore, different tilt angles between two transducers also affects the trajectory of the trapped object. Figure 2-1 A proposed SWAL design in two different tilt angles Several studies have shown that the movement of objects can be controlled by the modulation of transducer parameters. For instance, in [29], the phase difference between two transducers was manipulated to control the movement of the pressure node, and, in [30], oscillation of a moving object was observed by controlling the phase difference when two transducers were placed at an angle. 13

27 Frequency modulation was also used to transport objects along the sound wave direction in [31]. Another study used a line-focused transducer to move an object in which fifteen electrodes stacked together were switched one-by-one to shift the pressure nodes laterally [32]. In [33], two-dimensional manipulation was examined with frequency control. In this approach, two standing waves crossed orthogonally to move objects horizontally and vertically by the appropriate frequency shifting. The ultrasonic power density affected the trapping efficiency. Similarly, in [34], three ultrasonic transducers were used to perform two-dimensional manipulation in liquid. The axes of the sound beam were crossed at a 120 degree angle to one another in a plane, and the phase was changed to manipulate the objects. The aforementioned approaches all demonstrated a strong connection between transducer parameters (frequency and phase difference) and the motion of the object in air and in liquid. However, no approach has used a superposition of parameters of two transducers including amplitude modulation. In this chapter, a millimeter-sized Styrofoam sphere in air was manipulated in a twodimensional vertical plane by modulating a set of transducer parameters that include frequency, amplitude, phase, and tilt angles. These experiments revealed that a certain path shape, such as an ellipse, could only be achieved by modulating a combination of these parameters. 2.3 Near Field Acoustic Pressure Two incident plane waves of identical amplitude and frequency but opposite direction generate a single standing wave given by ( ) ( ) (2.1) 14

28 where is the pressure amplitude of each traveling wave, is the wave number, and the angular frequency. The wave amplitude of given by Eq. (2.1) is zero at x = 0. This standing wave was used to find the levitation forces generated by the two transducers. Equation (1.8) shows that frequency ( ), amplitude of incident pressure, and object size are the three parameters that affect the levitation force. This acoustic radiation force is a time-averaged static force with a constant amplitude and direction. The acoustic force is always directed toward the pressure node axially and laterally. However, the acoustic radiation force is generally too weak to levitate an object in air. Levitating a Styrofoam sphere with a density of 100 kg/m 3 using radiation forces requires a pressure amplitude of 660 Pa (SPL=147 db) when the transducer frequency is 26.7 khz. This pressure is difficult to achieve using conventional drivers. To generate the necessary radiation force, the drivers are placed close enough to each other to utilize the near-field effect. The near-field is the region within the Rayleigh distance from the driver surface where the pressure is high. The region beyond the Rayleigh distance is called the far-field region. The definition of the Rayleigh distance is shown in [35] as (2.2) where is the piston area, is the wave length, and is the radius of the piston. If the radius of the piston is 10 mm, the Rayleigh distance at 26.7 khz is mm, which is within the working range. The near-field pressure of this baffled circular piston is shown in Figure 2-2. The x-axis is the distance from the piston surface, and the maximum pressure reaches Pa (SPL= db). As frequency increases, the near-field pressure and Rayleigh distance also increases [35]. Therefore, much smaller objects, which are micro or nano sizes, can be levitated in the near-field with enough pressure to overcome adhesion forces like Van der Waals force. Another benefit of the two-transducer 15

29 design is an additional high pressure generated by reflection waves. With two transducers facing each other within the Rayleigh distance at certain frequencies, the incident and reflected waves are summed. Figure 2-2 Near-field pressure of a circular piston (Amplitude of the particle speed = 1m/s) 2.4 Parameter Modulation The main concept behind parameter modulation is to change the position of pressure nodes by manipulating certain parameters of the waveform so that the trapped object follows these moving nodes. This assumes that acoustic radiation forces are large enough to hold and move the object. Generally, the conventional method, which uses one transducer and a reflector, cannot achieve the same effect. As shown in Figure 1-3, a transducer generates traveling waves that are reflected from 16

30 the reflector with the same amplitude, the same frequency, and a fixed phase angle. These incident and reflected waves create standing waves. However, only the frequency parameter can change the position of pressure nodes to manipulate an object. In the proposed design, traveling waves, which are generated by two transducers, create a standing wave with a much higher acoustic pressure than that of the conventional method due to the near-field effects and reflection summation, as explained earlier. 17

31 Figure 2-3 Parameter modulation simulations ((a) Frequency modulation, (b) amplitude modulation, and (c) phase modulation) 18

32 The results of parameter modulation simulations performed by COMSOL are shown in Figure 2-3. In the simulation, the left and right sides are radiation boundaries where the transducers surfaces are located and frequency, amplitude, and phase difference are modulated. For the frequency modulation, the frequency of two transducers is changed from 10 khz to 40 khz simultaneously, and the result is shown in Figure 2-3 (a). As the wave length is decreased, nodes are moved to new locations. Initially two pressure nodes were generated at 10 khz, and, as the frequency was increased, the nodes moved toward the center, as indicated by the arrows. The amplitude modulation was also simulated at 26.7 khz, as shown in Figure 2-3 (b). As the pressure of one transducer was changed from 10 Pa to 2000 Pa, the pressure nodes moved slightly toward the lower pressure transducer. Figure 2-3 (c) shows the phase modulation from 0 to 360 degrees. From the simulation, the pressure nodes moved from one to the other. However, the pressure amplitude changed during phase modulation. The pressure amplitude peaked at a 0 or 360 degree phase angle, while the amplitude was at its minimum at 180 degrees. Finally, a combination of phase modulation with a 150-degree tilt angle between transducers was simulated, as shown in Figure 2-4. When the angle is 180 degrees, the transducers face each other (the opposite directions), and when the angle is 0 degrees, the transducers face the same direction. The 150-degree angle was arbitrarily chosen to match the experimental setup. As the phase of the upper transducer was changed from 0 to 180 degrees, the pressure nodes moved downward. The left contour plots in Figure 2-4 show the effective pressure, and the right plots represent normalized local velocities. Acoustic levitation occurs when objects are trapped at pressure nodes, the positions where pressure is zero or minimum. These pressure nodes are also antinodes of particle velocity. When a standing wave is generated, the absolute value of particle displacement magnitude is at its highest at the pressure node. This is also true for the particle velocity magnitude, although the particle displacement and the particle velocity have negative 90 degree phase difference with respect 19

33 to time. Therefore, instead of tracking pressure nodes, which may fall unnecessarily outside of the area of interest, tracking velocity antinodes is an easier way to visualize the movement of the pressure node where the object is trapped. On the right side of Figure 2-4, the gray circles represent local maxima of the normalized velocity antinodes, which are higher than 1.1 m/s. This value was chosen because it clearly distinguishes the nodes which have enough pressure to be used for levitation. Furthermore, the time-averaged value of the pressure was calculated as the effective values ( ); otherwise the time-averaged pressure over one cycle will be zero. In this simulation, the pressure nodes no longer moved linearly but along a curved path, as shown in the figure. A similar curved path was observed in the experiment as well. Increasing the tilt angle caused the node path to become linear, while decreasing the tilt angle caused the node path to become curved. Radiation forces were also found to decrease as the tilt angle decreased. Moreover, although the gravitational force was not considered in the simulation, it significantly affected the object movement in the modulation experiments, as shown in the experiments in the next section. 20

34 Figure 2-4 Combination of parameter modulation simulations (Left: effective pressure; right: normalized local velocity) 21

35 2.5 Experiments Figure 2-5 Experiment setup For experimental verification, a two-transducer system was designed, as shown in Figure 2-5. Two transducers were bolt-clamped Langevin type transducers (BLTs), and their peak-to-peak maximum displacement was around 10 µm at resonance frequencies and ambient room temperature. The resonance frequencies of the structure were found to be 26.7 khz, 38.1 khz, and 49.6 KHz for the first three modes. Each BLT was attached to a mechanical horn which was a cylinder shape made of aluminum alloy. The horn is usually designed not only to hold a transducer but also to amplify the longitudinal vibrations. However, in this setup, the simple horns held at a vibration node were attached to transducers without amplification. These horns were attached to a 3 degree of freedom (DOF) stand, which could move along the x and y axes as well as rotate. When the computer sent commands via a general purpose interface bus (GPIB) to a function generator to generate low-voltage 22

36 sinusoidal signals, the power supplier amplified the voltage signal going into the transducers. A camera captured the object position image, which was sent to the computer. The function generator could generate two indepent signals up to 600 khz. The amplitude range of the function generator was from 0 to 10 V p-p, where V p-p is peak-to-peak voltage. For these experiments, a polystyrene sphere whose mass was about 0.4 mg in air was manipulated in a one-dimensional 180 degree vertical line using the frequency and amplitude modulations. The results are shown in Figure 2-6. For the size comparison, a ruler was placed in the background away from the acoustic field in the gap. The first three frames show the effect of frequency modulation on the position of the object. Three distinct resonant frequencies of the BLT transducers and their stands were used. Figure 2-6 (a) shows the position of the object when both transducers were turned on at 49.6 khz. When the frequency of the upper transducer changed to 38.1 khz, the object experienced an appreciable drop. Again, when the frequency of the upper transducer changed to 26.7 khz, there was another drop of similar magnitude. The change of frequency resulted in the change of the common pressure node in the acoustic field equal to the amount of motion. This could be due to the equal wave length changes. 23

37 Figure 2-6 Frequency and amplitude modulation ((a) Upper: 49.6 khz and lower: 49.6 khz, (b) upper: 38.1 khz and lower: 49.6 khz, (c) upper: 26.7 khz and lower: 49.6 khz, (d) upper: 10V and lower: 300V, (e) upper: 300V and lower: 300V, and (f) upper: 300V and lower: 10V) The amplitude modulation of the two transducers was also tested by changing commanded voltages. As shown in the last three frames of Figure 2-6, a similar position change was observed along the axial direction with smooth motion when the supplied power was gradually changed. However, the amplitude modulation resulted in a significantly shorter drop, even at a near-maximum change of input voltage. Lastly, the phase difference between the two transducers was explored and was shown to provide the best results among all the parameters. The phase modulation resulted in the largest position changes, and, unlike the frequency modulation, the object moved smoothly without sudden jumps. In theory, an object can be moved for one wavelength distance when phase is changed for one cycle, i.e. from 0 to 360. A longer movement can be achieved by continuous phase changes. However, a loss of levitation force intensity was observed when the phase was modulated at near 180 degrees (out of phase). 24

38 Figure 2-7 Phase modulation and 150 degree tilt angle ((a), (b), and (c): upper transducer from 360 degree to 0 degree phase change, (d), (e), and (f): lower transducer from 0 degree to 360 degree phase change) The tilt angle between the two transducers also plays an important role in manipulating a trapped object. When an object is moved between two angled transducers, resultant pressure waves are no longer simple standing waves. Furthermore, the gravitational force affects the direction of the object movement as well. As shown in Figure 2-7, the phase modulation at an angle of 150 degrees resulted in the object moving along a zigzag path. A similar result has been reported in [18]. This phenomenon can be explained by reflected waves from the surface of the other transducer. The incident waves combined with the reflected waves create a wavy movement of the pressure nodes when the phase modulation is performed. Figure 2-8 illustrates another interesting movement pattern. Here, the object undergoes an elliptical motion generated by the combination of three parameters in a gravitational field. The amplitude modulation, the phase modulation, and the tilt angle are employed to trace the path. Such a path has never been reported to date. A combination of the tilt angle and amplitude modulation along 25

39 the gravitational force can significantly affect this motion. Likewise, the sequence of the combination of the parameters contributes to the generation of a different path. Figure 2-8 Phase and amplitude modulation at 150 degree tilt angle (Amplitude for the upper transducer at 400V and the lower transducer at 200V) 2.6 Conclusions The objective of this chapter was to investigate the acoustic non-contact manipulation of an object held in space by modulating parameters of two transducers in order to develop ways to find the best method for holding and prescribing its motion. Two BLT piezoelectric ceramic transducers without any reflectors were used to create a standing wave. At pressure nodes of this standing wave, acoustic radiation forces were able to trap a light object. By modulating frequency, amplitude, phase, and angle between the transducers, the position and motion of this trapped object was manipulated. From the simulations and the experiments, the amplitude and frequency modulations were not as effective in moving the object as the phase modulation. Especially for frequency modulation, the object was observed to move in sudden jumps rather than a smooth motion when frequency was 26

40 changed one resonant frequency to the next. Therefore, the phase modulation was the best among these parameters for manipulating the object s position and path. 27

41 Chapter 3: Numerical and Experimental Study of Acoustic Levitation Force and Performance Enhancement for Standing Wave Acoustic Levitation (SWAL) by Distance Modulation 3.1 Abstract This chapter presents the analysis of the acoustic levitation force for SWAL and a means to control its value. Observations have indicated that the horizontal axial phase modulation of the twotransducer model induces fluctuations in the levitation force acting on an object. Therefore, the accuracy and reliability of the system are affected by the oscillation of the trapped object due to weak levitation force. Distance modulation is proposed as a way to enhance the performance of the system. When the distance between the two transducers is changed, it has been observed that the acoustic radiation pressure was maximized at particular distances and phases while the location of the pressure nodes remained the same. To analyze this acoustic levitation force enhancement, the time-averaged second order radiation pressure was determined numerically. The levitation force was also calculated from the potential force for a rigid spherical object. Numerical and experimental analyses were conducted to determine the peak locations of the levitation force. Comparison of the experimental and numerical solutions gives a similar result except for a difference in position of. Based on these promising results, an experimental setup was designed to verify the enhancement in levitation force obtained with distance and phase modulation. The distance between the transducers was modulated with a predefined profile. The addition of distance modulation increased the overall levitation force by more than a factor of two. This allows operation at a distance that could not be achieved by normal phase modulation. 28

42 3.2 Introduction Attenuation was observed in the levitation force at certain angles during the phase modulation of the two-transducer model described in the previous chapter. It is important to maintain a strong levitation force during non-contact manipulation of an object. Otherwise, the object may not be susped, or manipulation or movement may be inaccurate. Power input adjustment is one way to maintain a strong levitation force. In this method, the driving power of transducers is increased when the levitation force is too weak and decreased when it is too strong in order to save energy. Although this method is intuitive and simple, the control action requires more energy and may induce other difficulties due to limited capability of power supplies and transducers. Several other researchers have conducted studies on increasing radiation pressure for acoustic levitation. In [36], an aluminum hemispherical shell having a diameter of 12 inches driven by a 130 segment PZT stack was used to focus acoustic radiation at a single fundamental frequency of 100 khz. It was also found that concave reflectors yielded the best positional stability. Since then, many researchers have used curved transducers and/or a concave reflector [37-40]. Another method of generating a strongly focused acoustic pressure field is the phased-array which is commonly used in medical applications and non-destructive testing (NDT). The phased-array consists of multiple transducers which are individually excited at predetermined time delays to steer or focus the acoustic beam [41]. In [42], the phased-array generated acoustic streaming was used to move liquid, manipulate liquid surfaces, and propel buoyant objects. Localized standing waves generated with two phased-arrays of 285 transducers have also been used to levitate objects [43]. Another possibility may be to use a conical Bessel beam propagating along an exted spatial distance with minimum diffraction [44-45]. However this technique has not been experimentally proven. 29

43 As described above, many methods using a large number of transducers or curved structures to enhance radiation pressure have been attempted. However, in this research, simple distance modulation is proposed to avoid the problems associated with the weakened levitation force for the horizontal axial phase modulation of the two-transducer model. The distance modulation is another way to maintain strong levitation force while it requires only one or two transducers with the same power consumption. This modulation adjusts the distance between the two transducers or between a transducer and a reflector in order to increase the radiation pressure so that enough levitation force can be generated for non-contact manipulation. In the case of the two-transducer setup, both the transducers are simultaneously moving the same distance in opposite directions. This movement ensures that the position of the pressure nodes stays constant so the levitated object s position does not change. Neither high energy consumption nor high performance transducers are required for distance modulation. To understand the relationship between levitation force and distance modulation, analysis of acoustic radiation pressure was conducted. In this study the maximum levitation force needed at a particular inter transducer distance to hold an object in a specified position (static) or move it by phase modulation (dynamic) was found. 3.3 Analysis of Acoustic Radiation Pressure and Levitation Force The theory of acoustic radiation pressure and force acting on a rigid spherical object was discussed in Chapter 1. The radiation pressure was found as the time-averaged value of the potential energy density and kinetic energy density. To solve the time-averaged PDEs numerically, transient simulation over at least one time period was required. Solving this transient acoustic problem with finite element analysis required small time steps and a fine mesh geometry. If the structure and 30

44 boundary conditions are complex, large computational resources (time and memory) are needed. In this chapter, the radiation pressure is defined in the frequency domain and numerically calculated with steady-state simulations. The levitation force is derived from the non-linear, second-order Langevin radiation pressure expressed in Chapter 1. The radiation pressure is the time-averaged value over one period, and Eq. (1.4) can be rewritten as 1 1 p p u o (3.1) oco where is the speed of sound, the density of the medium, is acoustic pressure, is the particle velocity, p 2 1 T 2 p dt T, 0 u 2 1 T 2 u dt T, and T is the time period. The RMS (root-mean- 0 square) or the effective value of acoustic pressure is defined as prms 1 T 2 p dt 0 1/2 T (3.2) and the squared value of the effective acoustic pressure can be expressed as 2 1 T 2 2 RMS 0 p p dt p T (3.3) Similarly, the RMS particle velocity is 31

45 2 1 T 2 2 RMS 0 u u dt u T (3.4) Therefore, the radiation pressure can be re-written as 1 1 p p u (3.5) RMS o RMS 2 oco 2 The RMS values in the expression can be easily found if the wave equation for a single frequency is expressed as the Helmholtz equation: 2 2 p x y z p x y z (,, ) (,, ) 0 c (3.6) j t where is the complex pressure from p( x, y, z, t) Re( p( x, y, z) e ). The RMS values of pressure and particle velocity in the frequency domain can be calculated from their absolute values: prms 1 p( x, y, z) (3.7) 2 urms 1 u( x, y, z) (3.8) 2 Now the time-indepent radiation pressure is 32

46 p p( x, y, z) u( x, y, z) (3.9) o oco Since the average radiation pressure in the frequency domain is time-indepent, it can be solved easily using numerical techniques even though the boundary conditions are complex. To find the levitation force acting on an object, a surface integral of the normal component of stress over a closed surface is used, as shown in Eq. (1.7). If the object is a sphere whose radius is much smaller than the wave length, then the levitation force can be calculated using the potential of the forces [18]: p RMS RMS U 2 R o f f2 3 oco p( x, y, z) 3 u( x, y, z) R o f f2 3 oco 2 u (3.10) where c, c 2 o o f o f2 2 2 o, c and are the speed of sound and the density of the object, c o and o are the speed of sound and density of the medium and is the radius of a spherical object. If the object is a rigid solid and the medium is air ( ), then both f 1 and f 2 are 1. Finally, the levitation force can be calculated from U ˆ U i U ˆ F j U kˆ (3.11) x y z 33

47 3.4 Distance Modulation The basic concept of distance modulation is varying the positions of the transducers to increase radiation pressure amplitude during the phase modulation without changing the location of pressure nodes. It has been experimentally shown that a variation in the distance between two transducers affects the vertical movement of an object. In this research, a horizontal two-transducer setup is used to observe levitation forces. A weaker levitation force results in a lower vertical position for the object due to constant gravitational force. A novel method which increases the levitation force and maintains the position of the pressure nodes is proposed, as shown in Figure 3-1. Transducer Transducer Pressure node Transducer Transducer (a) Two-transducer (out of phase) Transducer Pressure node Reflector Transducer (b) Single transducer with a reflector Figure 3-1 Distance modulation 34

48 In Figure 3-1 (a), two transducers are generating a standing wave at the same constant frequency while moving by the same distance in opposite directions. As a result, the pressure nodes remain at the same position and only the levitation force amplitude changes. The same method can be applied to the single transducer system with a reflector as demonstrated in Figure 3-1 (b). In this case, because a pressure anti-node is always generated on the reflector surface, only the single transducer must be moved to keep the pressure node locations unchanged. In this chapter, only the case of the two parallel transducers is considered. 3.5 Numerical Simulation of Distance Modulation To numerically simulate distance modulation, a time-harmonic calculation was performed. The results were obtained by the pressure acoustics module (acpr) of COMSOL 4.3a. The frequency domain study in the stationary analysis was used. The air domain was meshed with a total of 15,262 triangular elements, and solved by MUMPS (Multi-frontal Massively Parallel sparse direct Solver). For boundary setup, the sound hard boundary was applied to the transducers, and the plane wave radiation boundary was used with zero incident pressure for surrounding walls. The pressure boundary with phase was applied to the vibrating surfaces of the transducers. The excitation frequency was 26.7 khz ( ) for two parallel transducers. For the first simulation, the distance between two transducers was fixed at mm, and the radiation pressure was calculated along the center line. Two phase angles, 0 degrees and 180 degrees, were chosen to compare extreme scenarios. From the simulation results shown in Figure 3-2, the maximum value for a 0 degree phase angle was Pa, while the maximum value for a 180 degree phase angle was less than Pa. This difference was large enough to cause oscillation along the y-direction during phase modulation. Figure 3-2 demonstrates that the radiation pressure was time-indepent with several positive and 35

49 negative peaks along the distance. Because the radiation pressure does not fluctuate, the positive pressure always pushes an object out while the negative pressure always pulls the object in. Therefore, the negative pressure peaks represent the pressure nodes of a standing wave, and the positive pressure peaks represent the anti-nodes. The center peaks have higher values than the others because of the summation of two non-plane waves from circular plates. If an object is trapped in one of the negative peaks, two neighboring positive peaks are located axially while no peak is located laterally. This creates for more stability along the x-axis than the y-axis. If an object is located away from the pressure nodes, the higher pressures surrounding the object will push it toward a local minimum, which is a pressure node. 36

50 Radiation Pressure (Pa) Radiation Pressure (Pa) 200 Radiation Pressure Center line Distance (mm) (a) 0 degree phase angle 1 Radiation Pressure (b) 180 degree phase angle Distance (mm) Figure 3-2 Second order radiation pressure along the center line Validation of the distance modulation concept was conducted with a second simulation using distance changes from mm (= ) to mm (= ), as shown in Figure 3-3. The frequency is the same as before (26.7 khz), and four different phase angles (0, 90, 127 and 180 degrees) were chosen. The negative peaks of the radiation pressure represent the pressure nodes. When the phase angles were 0 degrees and 180 degrees, the x-position of the peaks remained constant while the amplitude of the pressure changed. In other words, the pressure nodes do not change their locations 37

51 during the distance modulation at these two phase angles. However, as shown in Figure 3-3 (b) and (c), the location of negative peaks (pressure nodes) changed during the distance modulation at phase angles of 90 degrees and 127 degrees. Similarly at a 127 degree phase angle, the largest peaks at 0 and 180 degree phase angles (blue starred and green starred lines) show up simultaneously with similar magnitude and location. It is safe to claim that the distance modulation is only effective for radiation pressures at degree phase angles, where n is 0, 1, 2, and so on. Instability and even pressure shifting is expected at other phase angles. 38

52 Pressure nodes (a) 0 degree phase angle (b) 90 degree phase angle (c) 127 degree phase angle (d) 180 degree phase angle Figure 3-3 Validation of the distance modulation concept After finding the specific phase angles which create stationary node positions, the distance where maximum radiation pressure is generated can be accurately measured. The radiation pressure was measured at the center (0, 0) while changing the distance from 1.6 mm to 48.2 mm with the phase angles 0, 90 and 180 degrees, as shown in Figure 3-4. Since the radiation pressure is measured at the midpoint of the two transducers, the pressure is always positive (antinode) when the phase is 0 degrees and negative (node) when the phase is 180 degrees. There are pressure peaks at the distances 39

53 where the levitation forces surrounding a node have high intensity. When the phase is 0 degrees, the peak values are observed at 2n 1 d, where n=1,2,3. When the phase is 180 degrees, the peak 2 values are observed at 2n d n, where n=1,2,3. When the phase is 90 degrees as shown in 2 Figure 3-4 (b), the positive and negative peak values are observed at both of these distances. This implies that the center point becomes a pressure node and an antinode with changing distance. It was also observed that the pressure at each peak decreases exponentially with increasing distance between the transducers. 40

54 Radiation Pressure (Pa) Radiation Pressure (Pa) Radiation Pressure (Pa) Radiation Pressure Change by Distance Modulation X: 6.59 Y: 1155 X: Y: Distance (mm) (a) 0 degree phase angle X: Y: 70.3 X: Y: Radiation Pressure Changed by Distance Modulation X: 6.59 Y: X: Y: X: Y: X: Y: X: Y: X: 39.3 Y: Distance (mm) (b) 90 degree phase angle X: Y: Radiation Pressure Change by Distance Modulation X: Y: X: 39.3 Y: X: Y: Distance (mm) (c) 180 degree phase angle Figure 3-4 Radiation pressure at x=0 during distance modulation 3.6 Numerical Simulation for Acoustic Levitation Force The levitation force can be calculated analytically using Eq. (3.10) and Eq. (3.11). First, the force potential was calculated for a spherical object of 1 mm radius. In order to have a pressure node at the center (0, 0), a phase angle of 180 degrees was applied. The pressure amplitude of the incident waves was 630 Pa for the out-of-phase case, with the density of air and the speed of sound at 20 ºC given as 1.2 kg/m 3 and 343 m/s, respectively. The operating frequency was 26.7 khz, which is the resonance frequency of the transducers. The x-component of the force, F x, is the axial force along the 41

55 sound beam axis, while the y-component of the force, F y, is the lateral force that is perpicular to the sound beam. The levitation forces were calculated from the potential of the force differentiated with respect to x and y, and they are shown in Figure 3-5. A positive value of the force indicates that an object is being pushed upward (y-component) or to the right (x-component). When the phase is 180 degrees, the pressure nodes reside in three locations: x = -7.5, 0, and 7.5 mm, where the force is zero and the surrounding forces are pushing the object toward the pressure nodes. At the pressure antinode, the force pulls the object away from the anti-node, causing it to become unstable. 42

56 Pressure nodes (a) x-component of the force (F x ) (b) y-component of the force (F y ) 2 2 (c) Total force ( F F F ) total x y Figure 3-5 COMSOL simulations for levitation force The simulation results were compared with the analytical results at the center (0, 0) pressure node. The axial and lateral forces were calculated along the x-axis and y-axis, and the results are shown in Figure 3-6. The maximum values of these forces around the center node were 4.7e-6 N and 6e-7 N, respectively. Thus, the axial force was nearly eight times as strong as the lateral force. 43

57 Levitation Force (N) Levitation Force (N) 5 x Acoustic Levitation Force at y=0 FEM Analytical 8 x Acoustic Levitation Force at x= Distance (mm) (a) Axial Force Distance (mm) (b) Lateral force Figure 3-6 The axial and lateral levitation forces As shown in Figure 3-6(a), the analytical result calculated using Eq. (1.8), matched the simulation result reasonably well, although the analytical result was generally smaller. This is because a plane standing wave was assumed when the analytical equations were derived. As a result, the amplitude of the axial force remains the same along the distance. However, in the simulation results, forces near the center line were larger because the acoustic pressure within the Rayleigh distance exhibited higher amplitude than an incident wave, as shown in Figure 2-2. In the two-transducer system, the summation of these two traveling waves has higher pressure at the middle. For the distance modulation analysis, it was found that the levitation force cannot be used to represent locations of both pressure nodes and maximum radiation pressure because the actual force is zero at these locations as proved in earlier analysis and the simulations. The maximum levitation forces occur between nodes and antinodes while pushing or pulling an object to keep it at a pressure node. Zero forces can be found in many places between the transducers and also in an acoustic field with no vibration. Therefore, in this research, the radiation pressure whose maximum value is located in a pressure node was used instead of the levitation force. 44

58 3.7 Distance Modulation Experiments A new experimental setup was built to verify the results produced by numerical simulation on distance modulation. As shown in Figure 3-7, two linear actuators that can be moved with stepper motors were installed to indepently change the positions of transducers. A USB camera was used as a position sensor for object tracking (more on this experimental setup will be explained later in Chapter 4). Styrofoam balls were chosen as the objects to be levitated, and the locations of these balls represented the pressure nodes. Figure 3-7 shows the positions of objects at phase angles of 0 and 180 degrees when the distance between the transducers is 19.3 mm. The white dots are the Styrofoam balls trapped in pressure nodes, and the red dots are reference points used to calibrate the Cartesian coordinate system with the camera. As shown in Figure 3-7 (b) the y-position of the two objects near the transducer surfaces was lower than the ball in the center because of the weak levitation force versus gravity. (a) 0 degree phase angle (b) 180 degree phase angle Figure 3-7 Experimental setup (d=19.3 mm and f=26.7 khz) 45

59 X position (mm) Y position (mm) Using this new experimental setup, phase modulation was performed, and the position change of an object was monitored by the camera during the phase change from 0 degree to 720 degrees. The results are shown in Figure 3-8. The x-position of the object had minimal oscillation, while the y- position varied significantly. The y-position of the object was influenced by the gravitational force which pulled down on the object while the x-position of the object was in equilibrium with the axial forces. When the levitation force is weak, the y-position of the object is affected negatively. In other words, the ball falls down if the levitation force is weaker than the gravitational force. Therefore, the y-position variation represents a proportional change of levitation force during the phase modulation. X position variation during the phase modulation (0 o ~720 o ) Phase ( o ) (a) x-position Y position variation during the phase modulation (0 o ~720 o ) Phase ( o ) (b) y-position Figure 3-8 Position variations during the phase modulation The distance modulation experiment was conducted based on two observations acquired from the analytical and simulation results. First, the position of the pressure nodes remain the same during the distance modulation when the phase angle is 180 n degree, where n = 0, 1, 2, and so on. Secondly, the levitation force is at its maximum at a distance of 2 n 1, where n=1,2,3, for

60 degree and n, where n=1,2,3, for 180 degrees. For instance, if the phase angle is changed from 0 degrees to 360 degrees, there are three points (0, 180 and 360 degrees) of maximum levitation force. In this case, the initial distance of 25.7 mm (= 2 ) at 0 degree, the middle distance of 19.3 mm (= ) at 180 degrees, and the last distance 25.7 mm (= ) at 360 degrees will maximize the levitation forces at the three locations during the phase modulation. To verify the distances for the maximum levitation forces from the simulation, a second experiment was conducted with the same configuration. The positions of an object were measured while the distance was increased from 12 mm until the object fell. Figure 3-9 shows the results at 0, 90 and 180 degree phase angles. The y-position changed during the distance modulation and several peaks were observed at particular locations. At the 0 degree phase angle, two maxima occurred at d=15.2 mm and 28.8 mm as shown in Figure 3-9 (a), while at the 180 degree phase angle, two maxima occurred at d=21.8 mm and 35.6 mm as shown in Figure 3-9 (c). The 90 degree phase angle combined the 0 and 180 degree cases plus one more location of d=42.4 mm. Finally Figure 3-9 (d) shows the y-positions of all cases in one plot to highlight the overlap of maximum y-positions at certain distance values. From this figure, two facts are evident. First, the location of maximum y- positions is almost the same though the value is lower when the distance is longer. This implies that the strength of the maximum radiation pressure is similar or is high enough to hold the object regardless of the phase angle. Second the locations of the peaks are equally spaced through 0 and 180 phase angles, although some locations are missing. This spacing is related to the wave length, and the approximate fraction of the wavelength is described as 2n 1 d where n = 3, 4, 5, and so on. In 4 addition, it is observed that, unlike simulation results, the x-position fluctuated as well but remained the same at 0 and 180 phase angles while changing the distance. This is because of the uneven radiation pressure resulting from the near-field effect. The pressure close to the center is higher than 47

61 Y position (mm) Y position (mm) Y position (mm) Y position (mm) the neighbor pressures. Especially when the pressure becomes weak during distance modulation, higher pressure pushes the object away from the center. When the pressure becomes high again, the object moves back to its pressure node. 10 Y position variation during distance change (0 o ) Y position variation during distance change (90 o ) Distance between two actuators (mm) Distance between two actuators (mm) (a) 0 degree phase angle (b) 90 degree phase angle Y position variation during distance change (180 o ) Y position variation during distance change Distance between two actuators (mm) 2 Phase 0 o 0 Phase 90 o Phase 180 o Distance between two actuators (mm) (c) 180 degree phase angle (d) All cases (0, 90 and 180 degrees) Figure 3-9 Object y-position during distance modulation 48

62 Table 3.1 shows the peak locations of the experiment results. The locations were approximated with the fraction of the wavelength, and they were compared with the simulation results. The simulation results were smaller than the experiment results by a difference of. One possible reason for this consistent error is the unequal vibrating amplitude caused by slightly different resonance frequencies of two BLTs. Each transducer has a resonance frequency deping on material age, attached structure, and temperature even though they are same model. Furthermore, from the last peak location of the 90 degree phase angle, 42.4 mm is assumed as the missing distance in the 0 degree phase angle. In this case the object fell before reaching this separation. This information of the peak locations at 0 and 180 degree phase angles were used for next experiment. Table 3-1 Peak locations of experiment and simulation (λ=12.85 mm) Phase Distance between transducers D1 D2 D3 D4 D5 Approximation 5/4 λ 7/4 λ 9/4 λ 11/4 λ 13/4 λ (Experiment) (16.06 mm) (22.48 mm) (28.90 mm) (35.33 mm) (41.75 mm) mm 28.8 mm (42.4 mm) mm 21.8 mm 28.8 mm 35.6 mm 42.4 mm mm 35.6 mm Simulation mm mm mm mm 39.3 mm Approximation 4/4 λ 6/4 λ 8/4 λ 10/4 λ 12/4 λ (Simulation) (12.85 mm) (19.28 mm) (25.70 mm) (32.13 mm) (38.55 mm) Finally, distance modulation was superimposed with phase modulation to enhance the levitation. Using the same experimental setup, the phase angle and the distance were changed 49

63 simultaneously. For the first experiment, the phase angle was changed from 0 to 360 degrees while the distance was changed following this sequence, D3 (=28.8 mm) at 0, D2 (=21.8mm) at 180 and D1 (=15.2 mm) at 360. While the phase can be changed very quickly, it is impossible to change distance instantaneously. Therefore, the distance should be profiled along the phase angles. For example, when the distance difference is 7 mm (=D3 D2) at a phase change from 0 to 180 degrees, the value divided by 180 degrees, i.e., mm/, can be used for distance increment ( D). When the phase is 1 degree, the distance is D3-1 D (=28.76mm), when the phase is 2 degrees, the distance is D3-2 D (=28.72mm), and so on. This distance profile was used to avoid sudden or impossible movements of transducers. Furthermore, this profile can be used for any phase modulation regardless of initial and final phase angles. However, there are three disadvantages with this method. First is the limitation on object travel range. An object cannot travel outside of the profiled distance range. Second, levitation force can be enhanced only at degree phase angles. At other phase angles, the y-position of the object drops due to weak levitation force. Finally, x-position varies slightly according to the distance change. As mentioned previously, the x-position has not changed at degree phase angle even though distance is changed. However, since this method involves a change of distance at other phase angles, this causes un-inted x-axis movements from normal phase modulation. The results of the first experiment are shown in Figure 3-10 (a). The maximum y- axis variation improved from 2 mm to 1 mm when distance modulation was added. This proves that, in general, phase modulation is enhanced by superimposing it with distance modulation. 50

64 Y position (mm) X position (mm) Y position (mm) X position (mm) 0.5 Distance modulation (0 o ~360 o ) With distance modulation Without distance modulation 8 7 Distance modulation (0 o ~360 o ) With distance modulation Without distance modulation Phase ( o ) Phase ( o ) i) y-positon ii) x-position (a) Short manipulation (phase change from 0 degrees to 360 degrees) 1 0 Distance modulation (0 o ~720 o ) Distance modulation (0 o ~720 o ) With distance modulation Without distance modulation With distance modulation Without distance modulation Phase ( o ) Phase ( o ) i) y-positon ii) x-position (b) Long manipulation (phase change from 0 degrees to 720 degrees) Figure 3-10 Phase modulation with distance modulation For the second experiment, the phase was changed from 0 degrees to 720 degrees while the distance was changed from D5 (=42.4 mm) to D1 (=15.2 mm) at the same time. The results are 51

65 shown in Figure 3-10 (b). The maximum y-axis variation with the distance modulation was similar to the first experiment. However, without distance modulation, the maximum variation was 3 mm, and eventually the object fell at a 540 degree phase angle. The experiment was conducted again and it was confirmed that without distance modulation, the levitation force was too weak to hold the object. In addition, the x-position of the object followed a similar motion pattern as in the first experiment. 3.8 Conclusions The objective of this chapter was to investigate the levitation force and enhancement methods. Phase modulation proved to be one of the best ways to achieve acoustic levitation in Chapter 2; however, it was found that the levitation force varied with phase angle due to the formation of standing waves generated by two travelling waves. The levitation forces are weakest at a 180 degree phase angle (out of phase). Therefore, distance modulation in conjunction with phase modulation was proposed to enhance the weak levitation forces. It was observed that the distance variation between two horizontally-opposing transducers induced a y-positon change of a levitated object due to the strength of levitation force was varied against gravitational force. This implies that levitation forces may be improved by distance modulation. To analyze and simulate the distance modulation technique, the radiation pressure and the levitation forces were calculated numerically. As a result of the simulations, two observations were made and employed when implementing distance modulation. The first is that the location of the pressure nodes is fixed during the distance modulation when phase angles are degrees, where n = 0, 1, 2, and so on. The second is that there are peak distances where the levitation forces become maxima at the above phase angles. Therefore, if a distance is changed to the peak distance when a phase angle becomes degrees, then the levitation force can be maximized at that phase angle. 52

66 These observations were verified by experiments. It was also found that the peak distance of the simulation were smaller than the experiment by because of unequal amplitudes of the transducers. Finally, distance modulation was combined with the phase modulation, and the levitation enhancement was observed experimentally. The variation in the y-position of an object was reduced by one-half using distance modulation. The travel range of the object was limited without the additional distance modulation, as the experiment was not successful in keeping the object levitated beyond a certain range. In conclusion, the characteristics of the distance modulation were investigated and the enhancement of levitation forces was proven. This technique will be applied to a motion controller to improve its performance in Chapter 5. 53

67 Chapter 4: Experimental Setup for Standing Wave Acoustic Levitation (SWAL) System 4.1 Abstract A three-transducer experimental system for SWAL was designed and built. The setup was designed for acoustic manipulation of objects in two-dimensional space. Each motorized acoustic transducer can change its position and angle simultaneously, and a camera tracking system was developed to measure the position of the levitated objects. The sensors and actuators were integrated together and controlled by a Graphical User Interface (GUI). Static position data was also collected to determine the data accuracy of the object tracking. Overall object tracking error was evaluated by a probability density function with normal distribution, and it was found that vibrations of servo motors and the weak lateral levitation force caused most of the object tracking error. However, it was concluded that the overall object tracking error was less than 200 µm which was enough for millimeter scale operation. Numerical simulations of the radiation pressure and levitation force were conducted for the new experimental setup. Based on the simulations, a new phase modulation technique using three transducers was investigated and verified by experiments. Finally, two possible operation strategies for two-dimensional motion control were proposed. 54

68 4.2 Introduction The study of object levitation and manipulation is exted to a two-dimensional case after having examined a one-dimensional case in previous chapters. In order to manipulate an object in two-dimensional space, a minimum of three transducers are required. The three-transducer system can generate standing waves in an infinite number of possible positions. In order to change the desired positions of the transducers, each one of them should be able to move linearly and rotationally. For automated motions, linear and rotational actuators controlled by microcontroller units (MCUs) were attached to the transducers. The parameter modulation is also complicated due to the large number of parameters. A camera was used as a position feedback sensor for levitated objects. Due to limited choices of non-contact position sensors, object tracking was done using a camera with due to its acceptable accuracy and cost-effectiveness. Some research projects have considered using multiple transducers. In [46], three pairs of acoustic transducers with vertical gas jet tube to support and position the liquid-phase processing materials. However, in that study a total six stationary transducers are used. Another researcher [34] uses three transducers which are arranged with an angle of 120 degrees to each other, and the phase of one of the transducers was changed to move particles in water. 4.3 Three-Transducer Experimental Setup The mechanical components of the two-dimensional system are shown in Figure 4-1. Three BLT type transducers with cylindrical horns were used. Each transducer is attached to a servo motor that controls rotation. Transducers 1 and 2 are attached to separate one degree-of-freedom (DOF) linear stepper motor, and the linear motors control the transducers to move along the x-axis indepently. Both linear stepper motors are coupled to a vertical linear motor which moves along 55

69 the y-axis, so that transducers 1 and 2 would vertically move together. Transducer 3 was set to face upward along the gravitational field, with only rotational motion allowed. Figure 4-1 Model of two-dimensional manipulation system Servo and Stepper Motors The servo motors used in the setup are Futaba Models S3003 and S3004 that have enough torque (4.1 kg-cm) and speed (0.19 sec/60º) to rotate the horn and transducer. A continuous Pulse- Width Modulation (PWM) signal is used to generate the rotational motion. The period of PWM signal is 20 ms, and the on-time ranges from 0.7 ms (0 deg) to 2.3 ms (180 deg), as shown in Figure 4-2 (a). Because the maximum duration is eight times smaller than the signal period, a single timer of 56

70 a MCU could be used to control all three servo motors. Each servo motor is connected to a potentiometer for feedback control. The two-phase stepper motors that drive the linear actuators are controlled by a Danaher MDM-7 motor driver, which requires square signals for rotational motions, as shown in Figure 4-2 (b). Each high-to-low transition falling edge rotates one step of the motor. The high and low transition should occur in 200 ns or less while the minimum duration for either the low or high is 1 µs (500 khz). One revolution of the stepper motor requires 4,000 steps because the micro-stepping function subdivides each step into 10 micro-steps electronically. The maximum speed is 1.25 rev/s or 70 rpm. The speed was lower than expected because of the mass of actuators and stands, but it was still fast enough for the experiments. The linear actuators do not have any feedback control because the stepper motors could provide reasonable positioning accuracy. (a) Servo motor (b) Stepper motor Figure 4-2 Servo and stepper motor signal 57

71 4.3.2 Micro-Controller Units (MCUs) and Function Generator Two Arduino Uno (ATmega328) microcontrollers are used to generate and s signals to the actuators, as shown in Figure 4-3. Four timers (both 8-bit and 16-bit) with the Clear Timer on Compare match (CTC) mode were used for accurate signal generation. Serial communication is used between the microcontrollers and PC, and the serial interrupt is used for immediate execution of a command. The command - which precisely controlled the speed, number of steps, direction, and servo angles - has its own protocol for each of the six actuators. Figure 4-3 Microcontrollers and a step motor driver 58

72 A four-channel function generator is used to generate a sine waveform for the BLT transducers, and the overall system of the function generator is shown in Figure 4-4. An evaluation board for the four-channel AD9959 Direct Digital Synthesizer (DDS) was chosen to indepently control the frequency, phase, and amplitude. The capability of the function generator is 500 MSPS (million samples per second) with 10-bit DACs that are used to generate the high frequency, highly accurate waveforms. The function generator provides two clocking options: an external clocking signal and an external crystal. The board has a low-pass filter for each channel, and a Serial I/O Port Interface (SPI) is provided to communicate with other devices. Each channel has a 32-bit frequency tuning word, 14-bits of phase offset, and a 10-bit output scale multiplier [47]. The output frequency of each channel is (4.1) where FTW is the frequency tuning word and is the system clock rate. The phase offset is (4.2) where POW is the phase offset word. Output amplitude scalar is (4.3) where ASF is the amplitude scale factor. The FTW, POW, and ASF are the integer numbers in the channel register. For example, if the ASF is BIN (=1023 = DEC), then the amplitude scalar is 1, which generates the maximum output. The minimum amplitude scalar is 0, and 59

73 the resolution of amplitude scalar is The phase and frequency can be set using the same procedure as the amplitude case. The resolution of phase is degrees, and the resolution of frequency is. If the system clock is, the resolution of frequency becomes 0.12 Hz. Figure 4-4 Four-channel DDS-based function generator system One drawback of the function generator was that the output voltage was only AVDD ± 0.5 V where AVDD = 1.8 V. Therefore, a high slew rate OP-amp was required to meet the ±10 V output voltage range and high frequency for the BLT power amplifier. Additionally, since the digital input voltage of the AD9959 chip was 3.3 V, instead of Arduino Uno, Arduino Due was used to 60

74 communicate with Serial I/O Port Interface (SPI), which operates at 3.3 V. The voltage for the DDS core is 1.8 V, which is uncommon as well Object Tracking Object tracking via computer vision was used as a position sensor for the levitation system. This method measures the position of an object over a time duration by capturing images and processing them using an intensive real-time computational processing technique. A single-camera is used to measure two-dimensional positions while a second camera is used for depth measurement. In this experimental setup, only the single-camera was used because the focus was solely on twodimensional position measurement. The contrast between the object and background was important because the object tracking uses color information to recognize an object from the background. For the SWAL system, a USB camera with a resolutions and 30 fps frame rate was used, as shown in Figure 4-5 (a). A total of six static reference points were used to calibrate the Cartesian coordinates for accurate measurement. The reference points represent pre-measured real distance, so an object s coordinates can be measured accurately based on the points regardless of location and angle of the camera. For the two-transducer setup, four red reference points were used; for the threetransducer setup, six red reference points were used as shown in Figure 4-5 (b) and (c). The pictures on the left show the binary images after red was extracted. The Region of Interest (ROI) with a grid provides guidance of the object manipulation within the experimental space. A cross line plotted in the camera view represents a coordinate of the object after the object tracking process, as shown in Figure 4-5 (b). Camera lens distortion was corrected during the image processing for better accuracy. When images were captured, full color images were converted to binary images with white color indicating 1 and black color indicating 0. For the levitation system, red color represented the 61

75 reference points while white color represented a levitated object; both of these colors were recognized as 1. During the calibration process, only red color was recognized as 1 while other colors, including white color, were recognized as 0. In this way, only the coordinates of the reference points were localized. During the object tracking process, only white color was recognized while other colors, including red, did not interfere with object recognition. For better visual performance, the color of the background and the horns was chosen to be black. 62

76 (a) A USB camera (b) Two-actuator setup (c) Three-actuator setup Figure 4-5 A USB camera and object tracking 63

77 There are four types of compensation strategy used in the setup for better object tracking performances. The first one is HSV (hue, saturation, value) color space conversion. Unlike RGB (red, green, blue) color space, HSV can separate the intensity components from image color and adjust only the intensity values [48, 49]. The threshold is used to adjust intensity of each channel to eliminate any unnecessary colors. The second strategy verifies the number of recognized objects after each captured image. If the number of objects is more or less than the desired number, then the image would be recaptured or the threshold would be readjusted. The third strategy transforms coordinates based on the reference points for distortion compensation of the camera lens. The last strategy applies morphology operations, such as erosion and dilation, in order to eliminate noise [50]. The procedures for the object tracking process are described as follows: (1) Adjust a camera view under the Region of Interest (ROI) and manually focus a camera. (2) Capture an image frame and convert it to an HSV image. (3) Apply the predefined threshold values to each channel. (4) Erode and dilate the image, and crop the image based on the ROI. (5) Find the centroid of the objects, and check the number of objects. (6) Locate the objects, and transform the coordinates based on the reference points Integrated Graphical User Interface (GUI) For an integrated control environment for the three-transducer system, a Graphical User Interface (GUI) was developed, as shown in Figure 4-6. The interface has three major areas. The first is for communication with other devices that have General Purpose Interface Bus (GPIB) and serial communication (RS-232). The GUI interface can control the function generator, servo motors, and 64

78 stepper motors precisely. The second area in the GUI is for object tracking. The right screen in the left corner displays an RGB image of the camera and the left screen displays a binary image of the reference points. HSV threshold values can be adjusted for both calibration and object tracking. Camera focus also can be adjusted for better images. For a better visual effect, ROI and grids are displayed on the images, and can be turned on/off manually. Further, the coordinates and object numbers are displayed in real time, and the captured images can be stored as a movie file. The last area is the control and data export area. In the control area, the distance modulation position control can be turned on and off, and variable values like PID gains and filter threshold can be adjusted. Furthermore, data can be collected and stored in computer files. The MATLAB GUI was utilized to develop this interface. While usable in the present study, execution speed and priority handling were not sufficient for multi-tasking jobs. Figure 4-6 Integrated control interface using MATLAB GUI 65

79 4.4 Object Tracking Error Mainly due to the non-spherical shape of the object and the quasi-standing wave, the levitation of object oscillated by itself without the influence of the object tracking error. In addition, the object tracking has its own error due to brightness, camera pixel size, and program algorithm errors. Thus, it was important to investigate the overall object tracking error for further experimental improvement. In order to verify the accuracy of object tracking, position data of the levitated object was collected, and a probability density function of normal distribution was plotted, as shown in Figure 4-7. The data was collected from operations with and without a servo motor to check for any mechanical error caused by the servo motor. 66

80 Density Density Density Density x data fit y data fit Data Data µ=13.42 σ=0.009 max=13.44 min=13.39 µ=9.76 σ=0.007 max=9.77 min=9.71 (a) Without servo operation x data fit y data fit Data µ=5.54 σ=0.030 max=5.64 min=5.45 (b) With servo operation Figure 4-7 Normal distribution of a levitated object s position using object tracking (unit: mm) (Left: x-component; Right: y-component) Data µ=8.63 σ=0.067 max=8.83 min=8.47 Figure 4-7 (a) illustrates a normal distribution of an operation without a servo motor. The data was collected in the two-transducer setup with λ (=28.9mm) distance and 0 degree phase angle. The standard deviations of the x- and y-components were 9 µm and 7 µm, respectively. The biggest 67

81 difference between mean and maximum/minimum values was 30 µm for the x-component and 50 µm for the y-component. These errors were small enough for millimeter scale operations. However, when the data was collected from an operation with an active servo motor, as shown in Figure 4-7 (b), the standard deviations were 30 µm and 67 µm for the x- and y-components, respectively. The biggest difference between mean and maximum/minimum values was 100 µm for the x-component and 200 µm for the y-component. These errors were more significant than the ones with an inactive servo motor. This was because the servo motor controller tries to stay at the same angle, which produced small oscillations. Each transducer is attached to a servo motor, and if the servo motor is active, the vibration of the servo motor influences the transducer. In addition, the y-component error was higher than that of the x-component because of the weak lateral levitation force acting along the y-direction. Nevertheless, it was concluded that the overall object tracking error was small enough for the two-dimensional setup. 4.5 Phase Modulation for the Three-Transducer Experimental Setup The radiation pressure and total force were numerically solved using COMSOL 4.3 as shown in Figure 4-8. The angle between each of the three transducers was 120 degrees, and the distance from the center to each transducer was 3λ, where λ = mm. The operation frequency was 26.7 khz. When all phase angles were 0 degrees, pressure nodes were created along the axial lines and the center was always a pressure anti-node surrounded by pressure nodes, as shown in Figure 4-8 (a). If the phase of one of the transducers increased while other phase angles remained constant, then pressure nodes in front of the transducer moved toward the center. This implies that this phase modulation moves a levitated object along the axial line. When the phase angles are 120 degrees 68

82 apart from each other, a pressure node is located at the center, surrounded by three major anti-nodes, as shown in Figure 4-8 (b). This makes it easy to position an object at the center. (a) 0 degree phase angles (b) 120 degree phase angles Figure 4-8 Simulations for two-dimensional system (Left: radiation pressure; right: total levitation force) In order to achieve object manipulation for a longer distance movement, a new configuration was found, as shown in Figure 4-9. The angle between the two upper BLTs was 140 degrees and the 69

83 other two angles were 110 degrees. The distances between the center and each BLT were λ, λ, and λ (14.5mm, 14.5mm, and 28.9mm). In this configuration, phase modulation was able to manipulate the object for more than a 100% longer distance movement than previously observed. Figure 4-9 (a) shows an experimental result where the phase was changed from 0 to 720 degrees. The radiation pressure was numerically solved as shown in Figure 4-9 (b) with the same geometric parameters as the experimental setup. It was observed that the pressure nodes (blue color) moved up as the phase was changed from 0 to 180 degrees. Since the overall radiation pressure did not change during the phase modulation, distance modulation was not required to increase the levitation force. In addition, because the bottom BLT faced up against the gravitational force, an object was stable during the phase modulation in the experiment. 70

84 (i) 0 phase angle (ii) 360 phase angle (iii) 720 phase angle (a) Experiment (i) 0 phase angle (ii) 90 phase angle (iii) 180 phase angle (b) Radiation pressure Figure 4-9 Phase modulation for long vertical movement Another configuration for the phase modulation was tested, as shown in Figure From the previous case, the two upper BLTs were moved to the left to maintain the same distance between each other while the bottom BLT was rotated to the left in order to move the object vertically upwards. Similarly, the same concept could be applied to move the object to the right by moving and rotating the BLTs to the right. In addition, if the bottom BLT was not rotated, the object would have moved diagonally from the center to the left or right towards the two upper BLTs. 71

85 (a) 0 phase angle (b) 360 phase angle (c) 720 phase angle Figure 4-10 Phase modulation at the left operation area 4.6 Two-Dimension Operational Methods using Phase Modulation In order to operate in a two-dimensional space, two unique strategies were proposed as shown in Figure If more than four BLTs are used for a two-dimensional operation, the BLTs do not need to move or rotate during operations because each pair of BLTs can maintain one-dimensional movement. In the experimental setup, a maximum of three transducers were used. Thus, additional linear or rotational motions of the mechanical components were required for the two-dimensional operation. Therefore, the proposed strategies were combinations of acoustic manipulations and mechanical movements. The first method used two BLTs with one linear stepper motor, as shown in Figure 4-11 (a). Phase modulation was used for movements along the x-axis while the linear motor was used for y-axis movement. The distance modulation was utilized to enhance the lateral levitation force. The second method consisted of three BLTs, two linear stepper motors, and one servo motor as shown in Figure 4-11 (b). The three BLTs were used for y-axis movement with the phase modulation, and linear motors were used for x-axis movement. In addition, when the linear actuator was moved far to the left or right, the transducer at the bottom was rotated towards the same direction in order to keep vertical movement of an object. 72

86 (a) Method 1 (b) Method 2 Figure 4-11 Two different proposed operation strategies for motion control 4.7 Conclusions In this chapter, an experimental setup of a three-transducer system for SWAL was designed and analyzed. Various mechanical and electrical components used in the setup were discussed. In the setup, three BLTs were used along with linear and rotational actuators. The servo motors, stepper motors and DDS function generator were all controlled by the micro-controllers. An integrated GUI is designed to provide a single-panel command post for controlling motors, a function generator, a USB 73

87 camera, object tracking, and a position controller. The object tracking algorithm was explained and verified the accuracy of the feedback sensor. Using a probability density function of normal distribution, overall object tracking error was investigated, and it was shown that the servo motor oscillations and the weak lateral levitation force were the main causes for the error. However, it was concluded that the overall levitation errors were acceptable for control actions. In order to understand the three-transducer configurations, numerical radiation pressure and levitation force were studied along with the phase modulation technique. Pressure nodes created by three BLTs could be manipulated along axial directions by phase modulation, and long vertical movements could be achieved without the distance modulation. Finally, two unique operation methods were proposed to operate an object in the two-dimensional system. The next chapter documents the analysis that was performed using these proposed methods with a controller to control 2-dimensional trajectories of the object. 74

88 Chapter 5: Two-dimensional Motion Controls using Artificial Neural Network (ANN) for Acoustic Non-contact Manipulation 5.1 Abstract Two-dimensional acoustic non-contact manipulation using phase modulation of multiple transducers for SWAL was investigated. For precise operations, artificial neural network (ANN) control was implemented. The two operational methods mentioned in Chapter 4 were adapted for the control bases. The first uses two BLTs and three linear actuators. In this setup, the distance modulation was applied for accuracy and stability. In the second method, three BLTs, two linear actuators, and one rotational servo motor were used. To maintain straightness of the vertical motion, angular adjustment of the bottom transducer was used. With each method, the inverse plant of the ANN with PID feedback control was adapted. A multilayer perceptron (MLP) network with one hidden layer was used for the structure of the inverse plant and was trained with the Levenberg Marquardt (LM) method. For accuracy improvement and straightness movement, distance and angular modulation were adapted. To reduce the noise from sensors and object oscillation, a low-pass filter was adapted with better feedback values. Experiments were performed for each method with two different trajectories, a line and a circle. The results show that the second method has higher overall mean square error (MSE) than the first because of the complexity of the pressure field generated by a higher number of transducers. In addition, the circle trajectory control has a higher MSE value than the line trajectory. From the results of the experiments, the two-dimensional motion control using acoustic levitation can be achieved with acceptable errors. 75

89 5.2 Introduction The goal of this chapter is to develop two-dimensional motion control schemes for the standing wave acoustic levitation (SWAL) system. It was found that the phase modulation is most effective for manipulation of an object in the two- or multi-transducer system. Other modulations such as angle between transducers and distance between transducers were successfully investigated as a way to move an object relative to the transducers or to enhance levitation forces. However, significant non-linear instabilities were observed in the SWAL manipulations. The oscillation or rotation of trapped objects is significant when dealing with imperfect axisymmetric objects or weak power acoustic transducers. The variation in amplitude of transducers also causes the instability during operation. The variation is due to the temperature of transducers, resonance frequency, modal shapes and degree of skew and jitter in waveforms generated by amplifiers. Other factors can be air flow from room air conditioning, light intensity and parallax error in the camera object tracking as well as aging of the transducers. Therefore, a controller of the non-linear dynamic system is required for precise manipulation to overcome disturbances and noise. Although many researchers have worked on acoustic non-contact manipulation, few have adapted the motion control for the acoustic levitation because of difficulty of designing a control model. Kozuka et al. [32] developed a method to control particles in two-dimensional space using frequency change and the electrode switching. Changing frequency alters the wave length and the interval between pressure nodes for vertical transport. Lateral transport was performed by the linefocused transducer with multiple electrodes and a reflector. However, no feedback controller was implemented, and the degree of accuracy was not analyzed. Takeuchi et al. [51] designed a twodimensional manipulation system with visual feedback. Four beam-width-compression leaky wave transducers (LWTs) were used to trap and transport particles. This method did not use the acoustic 76

90 levitation technique, and the particles were pushed by the transducers generating ultrasound waves in a beam. Recently, three-dimensional acoustic manipulation with three pairs of ultrasonic phased arrays was developed [52]. Each phased array was consisted of hundreds transducers arranged in a square area, and localized standing waves were generated. The sound pressure at the peak of the focal point could be as high as 2600 Pa (RMS). However, there was no motion control in this system. As discussed in Chapter 4, two methods were chosen for the two-dimensional control action. The first one, shown in Figure 5-1 (a), was based on the one-dimensional system used for distance modulation. Two BLTs were used for x-axis movement using phase modulation, and the y-axis linear actuator moved the levitated object vertically. In this scheme, control inputs for each axis were coupled due to the phase modulation resulted in both x- and y-axis movement, although the y-axis movement is not significant. A neural network was also used for the distance modulation to extract peak distance information from the position of an object. For the second method, three transducers were used, as shown in Figure 5-1 (b). The phase modulation between upper two BLTs and a bottom BLT manipulated an object in the vertical direction while the x-axis linear actuators moved the object horizontally. In this Y-shaped configuration, the bottom transducer acted against the gravitational force and higher levitation forces were generated by the three BLTs. Therefore, the distance modulation was superfluous in the second method. Calibrating the coordinate system using different configurations of reference points was necessary for each method. Figure 4-5 shows the locations of the reference points. 77

91 (a) Method 1 (b) Method 2 Figure 5-1 Two operational methods for ANN motion control Because of the nonlinear characteristics of the acoustic radiation pressure, it was not feasible to analyze the system to find the governing equations of a controller. Therefore, an Artificial Neural Network (ANN) was adopted for an approximation of the inverse dynamics of the unknown plant. The system identification was done with the MATLAB neural network toolbox Artificial Neural Network (ANN) Artificial neural networks are based on the structure of the human brain. The human brain is embodied with neurons which are linked to each other through drites (inputs) and axons (outputs). Signals transfer by chemical and electrical processes in a synapse. The synaptic gap and its adjustment lead to the storage of information or learning [53] Mimicking the processes of biological neurons, the perceptron, which is a mathematical model of the neuron, was developed by Rosenblatt in 1958 [54]. 78