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UBC Theses and Dissertations

A 3d printing and moulding method of the fabrication of a miniature voice coil motor actuator Yuan, Kaiwen 2015

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A 3D PRINTING AND MOULDING METHOD FOR THE FABRICATION OF A MINIATURE VOICE COIL MOTOR ACTUATOR  by Kaiwen Yuan B.Eng., Xi’an Jiaotong University, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  July 2015  © Kaiwen Yuan, 2015    ii Abstract The goal of this project is to apply 3D printing and moulding (3DPM) methods for the fabrication of a miniature magnetic actuator for optical image stabilization (OIS) applications. Polydimethylsiloxane (PDMS) and strontium ferrite (SrFe) nano powder were used as the main structural material. Young’s modulus and the magnetization of the material with SrFe-doping ratios ranging from 20% to 60% by weight were characterized. The actuator, consisting of four coils, an actuating plate, and a base supporter was assembled and tested with a Laser Doppler Velocimetry (LDV) system. A tilting angle of 0.6o was achieved with the application of 500 mA (50 turns/9 mm long coils). A Taguchi’s orthogonal experimental design was used in the finite element analysis (FEA) simulation to examine the effect of dimension variations on the eigenfrequencies. Frequency response of the actuator was characterized and the experimental results matched with the simulation results between 1 and 450 Hz showing less than 5% errors. A series of replica experiments were also performed and analyzed.     iii Preface  The research presented in this thesis was conducted in the University of British Columbia (UBC) MEMS Lab, in the Department of Mechanical Engineering under supervision of Dr. Mu Chiao.  All aspects of the work presented in this thesis, including literature review, device design, fabrication design and processes, material characterizations (except that Magnetization characterization was performed with help of Dr. Pinder Dosanjh, research engineer in Department of Physics, UBC), device characterizations was performed by the author of this thesis. Mr. Pan Zhao (PhD candidate in the Mechanical Engineering, UBC, supervised by Dr. Mu Chiao and Dr. Ryozo Nagamune) contributed to laser Doppler vibrometer (LDV) system control programming.              iv Table of Contents  Abstract ........................................................................................................................ ii Preface ......................................................................................................................... iii Table of Contents ........................................................................................................ iv List of Tables ............................................................................................................... vi List of Figures ............................................................................................................ vii List of Abbreviations ................................................................................................... x Acknowledgements ..................................................................................................... xi Dedication ................................................................................................................. xiii Chapter  1: Introduction ............................................................................................. 1 1.1 Magnetic Polymer and Actuators ................................................................... 2 1.2 Optical Image Stabilizer (OIS) ...................................................................... 3 1.3 Research Objectives ....................................................................................... 5 1.4 Thesis Organization ....................................................................................... 5 Chapter  2: Design, Fabrication and Characterization ............................................ 7 2.1 Design ............................................................................................................ 7 2.2 Fabrication ................................................................................................... 11 2.2.1 Material Preparation ................................................................................ 11 2.2.2 3D Printing ............................................................................................... 12 2.2.3 Moulding .................................................................................................. 14 2.2.4 Replica Experiments ................................................................................ 18 2.3 Characterization Methods ............................................................................ 20 v 2.3.1 Characterization of Material .................................................................... 21 2.3.2 Characterization of Actuator .................................................................... 22 Chapter  3: Results and Discussion .......................................................................... 24 3.1 Characterization of Material ........................................................................ 24 3.1.1 Young’s Modulus .................................................................................... 24 3.1.2 Magnetization Curve ................................................................................ 26 3.2 Dimensions .................................................................................................. 27 3.3 Finite Element Analysis ............................................................................... 29 3.3.1 Eigenfrequency ........................................................................................ 29 3.3.2 Magnetic Field and Forces ....................................................................... 35 3.4 Characterization of Actuator ........................................................................ 36 3.4.1 Stationary Test ......................................................................................... 36 3.4.2 Frequency Response ................................................................................ 38 3.4.3 Replica Experiments ................................................................................ 41 Chapter  4: Conclusions and Future Work ............................................................. 56 4.1 Conclusions .................................................................................................. 56 4.2 Future Work ................................................................................................. 57 Bibliography ............................................................................................................... 59 Appendices .................................................................................................................. 65 Appendix A Coils ................................................................................................... 65 Appendix B Diagram of control system ............................................................... 66   vi List of Tables  Table 2.1    Parameter settings of SLA 3D Printer ...................................................... 13 Table 2.3    Dimension of samples for SQUID test. .................................................... 22 Table 3.1    Dimensions of the prototype ..................................................................... 28 Table 3.2    Material properties of FEA 3D Model ...................................................... 30 Table 3.3    Three-factor and Three Level Taguchi Orthogonal Design ...................... 30 Table 3.4    Nine experiments settings of Three-factor and Three Level Taguchi Orthogonal Design for COMSOL ................................................................................ 31 Table 3.5    Relative permeability settings of FEA 3D Model .................................... 36 Table 3.6    The tilting rate for four sides with an 1 Hz sinusoidal current ................. 37 Table A.1   Parameters of core ..................................................................................... 65 Table A.2  Parameters of coil wires (Noted: in the project, 5 turns of wires were unwounded to guarantee enough length to be connected with PCB) .......................... 65      vii List of Figures  Figure 1.1    Schematic of typical OIS system ............................................................... 4 Figure 2.1    Exploded view of the actuator system, composed of lens holder, coils, and supporter ........................................................................................................................ 8 Figure 2.2    Top view and dimensions of the actuating plate ....................................... 9 Figure 2.3    (a) Top view and dimensions of the base supporter; (b) cross-sectional view and dimensions of the base supporter .......................................................................... 10 Figure 2.4    Stereolithography 3D printing mechanism .............................................. 12 Figure 2.5    Mould of actuating plate for Stereolithography 3D printing ................... 13 Figure 2.6    Fabrication process for the actuating plate .............................................. 15 Figure 2.7    Moulding sandwich with magnets clamping glass slides and magnetizing materials in mould........................................................................................................ 15 Figure 2.8    (a) a drop of PDMS (pre-polymer and crosslinker mixed with 5:1 w/w) on glass slide; (b) a drop of PDMS doped with 20% w/w SrFe nanopowder on glass slide; (c) a drop of PDMS doped with 40% w/w SrFe nanopowder on glass slide; (d) a drop of PDMS doped with 60% w/w SrFe nanopowder on glass slide .................................... 16 Figure 2.9    Assembling process of actuator ............................................................... 18 Figure 2.10    (a) Actuator with auxiliary magnet and glass slide before curing; (b) final actuator after curing ..................................................................................................... 18 Figure 2.11    15 actuating plates with 5 moulds and 3 batches .................................. 19 Figure 2.12     15 assembled actuators with 5 moulds and 3 batches (from left to right: 1st batch, 2nd batch and 3rd batch) ................................................................................... 20 viii Figure 2.13    System setup for characterizing the actuator ......................................... 23 Figure 3.1    Stress-strain curves of pure PDMS and PDMS doped with 20%, 40%, and 60% w/w SrFe composites ........................................................................................... 25 Figure 3.2    Elastic moduli of pure PDMS and PDMS doped with 20%, 40%, and 60% w/w SrFe composites ................................................................................................... 25 Figure 3.3    Mass magnetization curves versus applied magnetic field for composites with 20% to 60% strontium ferrite nanopowder added at 300 oK (26.86℃) ............... 27 Figure 3.4    Dimensions characterization under microscope ...................................... 28 Figure 3.5    3D Model of FEA simulation in COMSOL Multiphysics ...................... 30 Figure 3.6    Eigenfrequency study results of second experiment ............................... 32 Figure 3.7    Main effects plot for means of eigenfrequencies .................................... 33 Figure 3.8    Eigenfrequency study results of actual prototype ................................... 34 Figure 3.9    Magnetic flux density in the Y-Z plane of the simulated model; a) pure PDMS as the plate; b) 60% SrFe-doped PDMS composite as the plate ...................... 36 Figure 3.10    Relation between current and tilting angle for the four sides vertically down...................................................................................................................................... 37 Figure 3.11    Relation between current and tilting angle for the four sides vertically up...................................................................................................................................... 38 Figure 3.12    Frequency responses of the system and simulation results ................... 40 Figure 3.13     Frequency response curves of 15 actuators (B35 means the sample from 3rd batch with Mould5) ............................................................................................... 42 Figure 3.14     Frequency response curve of samples with Mould1 ............................ 42 Figure 3.15     Frequency response curve of samples with Mould2 ............................ 43 ix Figure 3.16     Frequency response curve of samples with Mould3 ............................ 43 Figure 3.17    Frequency response curve of samples with Mould4 ............................. 44 Figure 3.18    Frequency response curve of samples with Mould5 ............................. 44 Figure 3.19   Frequency response curve of samples from 1st batch ............................ 45 Figure 3.20    Frequency response curve of samples from 2nd batch .......................... 45 Figure 3.21    Frequency response curve of samples from 3rd batch .......................... 46 Figure 3.22     Relation between current and tilting angle for the four sides vertically up of B11........................................................................................................................... 48 Figure 3.23    Relation between current and tilting angle for the four sides vertically down of B11........................................................................................................................... 48 Figure 3.24    Relation between current and tilting angle for the four sides vertically up of B21 ............................................................................................................................... 49 Figure 3.25     Relation between current and tilting angle for the four sides vertically down of B21 ................................................................................................................. 49 Figure 3.26     Standard deviations of widths, lengths in four sides of each actuator (B1 to B3 means number of batch) ......................................................................................... 51 Figure 3.27     Errors of actuating plates dimensions relative to mould in different batches...................................................................................................................................... 53 Figure 3.28     Standard deviations of means of widths, lengths, diameters of 5 actuating plates in the same batch ............................................................................................... 55    x List of Abbreviations 3D 3-dimension ABS acrylonitrile butadiene styrene CAD computer-aided design CNC computer numerical control DIS or EIS digital image stabilization FDM fused deposition modeling FEA finite element analysis IPA isopropyl alcohol IS image stabilization LDV laser Doppler vibrometer LOC lab-on-chip MEMS microelectromechanical system OIS Optical Image Stabilizer PC polycarbonate PLA polylactic acid PPSU polyphenylsulfone PZT piezoelectric SLA stereolithography SLA stereolithography SLS selective laser sintering UV ultraviolet VCM voice coil motor    xi Acknowledgements  First and foremost I want to thank my supervisor Dr. Mu Chiao for his guidance and support. I am very grateful for this opportunity to work in his lab and under his wise supervision. I thank Dr. Jing-song Chu (Micromoulding Solutions Inc.), Dr. Simon Park (University of Calgary), Dr. Karan Cheung (The University of British Columbia), Dr. John Jackson (The University of British Columbia), Dr. Pinder Dosanjh (The University of British Columbia),  and Dr. Bonnie Gray (Simon Fraser University), for their guidance, support and sharing of laboratory facilities to make this project possible. I would like to thank Dr. Ryozo Nagamune (The University of British Columbia) and Dr. Steven Feng (The University of British Columbia) for being members of the defense committee. I would like to thank Mr. Pan Zhao, and my fellow lab mates Colin (Keqin) Chen, Hadi Mansoor, Payam Zachkani, Eric (Jiahua) Zhao, Aurora (Qianyu) Chen, Farzad Khademolhosseini, Hongbing Zhang, Zhengmu Wang, Yibo Zhang, Ali Shademani, Guanyi Cao at the UBC MEMS Lab for sharing knowledge, experiences and ideas. I would like to thank Jiaotong University Alunmi Association of Vancouver, giving me a sense of belonging and infinite chances of expanding my connections in Vancouver. I also would like to thank Mr. Louis-Victor Jadavji and Mr. Shamil Hargovan, two co-founders of Wiivv Wearables Inc., for offering me an opportunity to join this promising start-up and their cares, trust and patience. Special thanks are owed to my open-minded parents, whose have supported me throughout my years of education, my girlfriend Zhen Gong, without whom I could not xii make anything happen, Cuihong Peng, my great high school teacher, whose guidance and instructions keep benefiting and inspiring me, Li Li, my primary school Olympic Math Competition abecedarian, whose help I cannot use a simple sentence to describe.       xiii Dedication       To My Parents   1 Chapter  1: Introduction 3-Dimension (3D) printing has been applied to rapid-prototyping and customization with advantages of low cost, speed, and ease of fabrication [1] in many fields, including medical applications and consumer electronics. 3D printing relies on an additive manufacturing process to build products layer-by-layer with software that processes computer-aided design (CAD) files. Sharing the same mechanism, 3D printers can print in multiple ways, such as with selective laser sintering (SLS), fused deposition modeling (FDM), stereolithography (SLA), etc. [2]. Diverse printing materials like acrylonitrile butadiene styrene (ABS), polylactic acid (PLA), polycarbonate (PC), polyphenylsulfone (PPSU), and nylon can be used. High-resolution 3D printing methods such as stereolithography (SLA) can allow 3D printing to rapidly fabricate devices and parts with a high precision  [1]. Nevertheless, in comparison to traditional injection molding and other technologies, 3D printing is not economical for large-scale production [3] and the materials for high resolution 3D printing are less diverse. For example, an SLA printer can only use photopolymer resin that is solidified with an ultraviolet laser. The application of 3D printing in injection moulding tooling (i.e., moulds and cooling channels) fabrication [4] and in vacuum-assisted resin transfer moulding [5] already shows advantages in both the quality and rate. In traditional moulding methods, for fabricating a mould, generally expensive, computer numerical control (CNC) end mills are required, which are both costly and brittle, especially for micro- or miniature-scale cases. For micro-mould fabrication, UV photolithography with clean-room conditions is always required [6], which limits the production efficiency and adds to the cost. The combination of moulding and 3D printing (for fabricating the toolings for the 2 moulding methods) provides a scalable, faster alternative at a lower cost than either traditional moulding methods or micro-mould fabrication. Several attempts have been made to use high-resolution 3D printing moulding (3DPM) in lab-on-chip (LOC) [7][8] and microlens fabrication [9]. The efforts simplify the micro-fabrication process, shorten the machining duration and reduce the cost. Nevertheless, so far, little research has been conducted on 3DPM applications for actuator fabrication or magnetic material, which require more considerations such as actuator assembly and accessory components to magnetize the material.  1.1 Magnetic Polymer and Actuators Generally, an actuator is one of five components for any control system, which also includes plant, sensor and transducer, signal modification units, and controllers [10]. Magnetic actuators are an important type of actuators, and they have been applied to drug delivery [11][12], disk drives [13], cellular migration [14], and so on. Compared to electrostatic actuators, magnetic actuators have advantages in operating wirelessly and at lower voltage. To achieve and control both desired mechanical and magnetic properties, magnetic particles should be loaded into polymers to form composites and be actuated with coils. By adding strontium ferrite micropowder into a commercial epoxy resin and actuating it with a planar coil, large deflections are possible [15][16]. Pallapa et al. [17] used lithography and micromoulding techniques to mix Nd-Fe-B powder into a PDMS matrix and the actuator was actuated with printed circuit board planar coils. In other 3 experiments, a micromirror scanner was demonstrated using a maximum 20mT magnetic field [17]. In any case, few authors have reported adding strontium ferrite nanopowder into a PDMS to form actuators. PDMS, a porous, biocompatible (non-toxic) and easy to process material is preferable for the base material and convenient for post-processing (i.e., laser cutting and coating). Strontium ferrite powders also have advantages over other hard magnetic material candidates of low cost and chemical inertness [18]. Furthermore, for most miniature or micro-magnetic actuators, fabrication processes require clean-room conditions [14][17][19][20], which is both time-consuming and costly. Therefore, innovative methods need to be developed that simplify the fabrication process and reduce the cost.  1.2 Optical Image Stabilizer (OIS) Image stabilization (IS) is a good solution to correct the image blur that results from a photographer’s hand trembling. Optical image stabilization (OIS) and digital image stabilization (DIS or EIS) are two types of popular IS methods. DIS shifts the electronic image from frame to frame to counteract the motion [21] or uses filters (i.e., Kalman filters) to track the movement of pixels and remove detected irregular global motion effects [22]. Although the cost of DIS is low, since no physical components like a gyroscope or actuators are added, it is less effective and may sacrifice resolution. Therefore, OIS, which modifies the optical path by an actuator to compensate for hand-tremble, is more advantageous and promising [23][24]. A typical OIS system [Figure 1.1] includes a gyroscope to measure hand tremor, an image sensor, an actuator to modify the 4 optical path, and a controller to process signals and give commands to the actuator. Lens shifting, module tilting, and image sensor shifting are commonly used technologies for OIS systems [23][25]. Actuating methods have been published, such as the voice coil motor (VCM) [23][26][27][28], moving mirrors methods [29], piezoelectric (PZT) methods [30], and microelectromechanical system (MEMS) based on thermal actuating methods [31][32]. VCM applies coils to actuate magnets, which are usually bonded with the lens holder, so that actuating displacement can be controlled by the current/voltage in the coils. As VCM has advantages in its low operating voltage, cost effectiveness, and stability, it has been the main method applied in the OIS industry [33][34]. Our previous publication [35] reported an innovative tilting lens VCM actuator concept and we demonstrated a conception macro prototype. As a follow-up to that research, we fabricated and tested a miniature prototype.   Figure 1.1    Schematic of typical OIS system  5 1.3 Research Objectives For OIS applications, the desired performance of the actuating system should include the actuator tilting in yaw (or pitch) direction of 0.6o [36] with a low energy consumption (less than 800 mA). For this project, the objectives are: 1) to apply high-resolution 3D printing moulding (3DPM) technology to fabricate a magnetic actuator, according to the above specifications. 2) to research the properties of a mixture of strontium ferrite nanopowder and PDMS as the filling material, to help us understand and predict the dynamic and stationary performance of the actuator. 3) to study the influences of dimension variations on performance, especially dynamic performance since errors in fabrication can lead to variations in the dimensions of parts. These can affect the performance. The results and conclusions will contribute to further research on control, based on this platform. The concept of an OIS system is based on previous work by our group [35]. The short-term goals of this project are to explore low cost fabrication methods and materials to develop a prototype of the miniature size concept actuator and to validate it in terms of compensating human hand-trembling. The long-term goal of the project is to develop advanced control theories based on this platform.  1.4 Thesis Organization This thesis is organized as follows: Chapter 1 introduces the project and provides background, including a description of the fabrication, materials, and applications. Long- 6 and short-term research objectives are also described. Chapter 2 describes the design of the actuator and the fabrication process. The set-up for characterization experiments is also introduced. Chapter 3 presents the results of the characterization of materials and actuator. Both stationary and frequency tests are described and a finite element analysis simulation is described. Replica experiments are demonstrated and analyzed as well. Chapter 4 provides the conclusions for the project and makes recommendations for future work.    7 Chapter  2: Design, Fabrication and Characterization 2.1 Design A final actuating system (Figure 2.1) consists of four parts: 1) actuating plate (or lens holder, with a ring magnet attached), 2) lens, 3) actuating coils (with Ni-Zn cores inside), and 4) a base supporter. In this thesis, we focus on parts 1, 3, and 4. The design refers to previous work from our group [35][37] that used coils to actuate a platform (the lens holder). Since folded beams [37] may cause difficulties in the demoulding, the design with one beam on each side was used to directly connect the parallel beams on the supporter and the center circle. The base supporter is composed of a horizontal base surface with a hole in the center, four symmetric hollow cylinders distributed around the hole to hold the coils, and four walls at the four sides. For each wall, a groove is present on top to fill the PDMS in the assembly process. The actuating parts include a ring neodymium magnet attached to the bottom and an actuating plate, which is the core part of the actuator. The actuating plate has four symmetric beams, at the end of which are four beams in parallel to the walls of the supporter. Four coils with Ni-Zn cores are placed into the hollow cylinders and the lens holder is mounted on top of the base supporter.  8  Figure 2.1    Exploded view of the actuator system, composed of lens holder, coils, and supporter  Figure 2.2 shows the dimensions of the actuating plate; the thickness is 1 mm. The entire length of the system is 12 mm, and four pairs of beams are folded at an angle of 61.87o and a 2 mm radius central circle. Figure 2.3(a) shows the top view and the dimensions of the supporter, and Figure 2.3 (b) shows the cross-sectional view and the dimensions of the supporter (the total height is 11.80 mm). The inner diameter and height of each hollow cylinder are 1.66 mm and 9.36 mm. The width, length, and depth of grooves are 0.6 mm, 7 mm, and 2 mm, respectively. All coils are wound with wires in the same direction. The coil has 50 turns and has a Ni-Zn core inside, with a length of 9 mm and an outer diameter of 1.35 mm.  9  Figure 2.2    Top view and dimensions of the actuating plate  10  Figure 2.3    (a) Top view and dimensions of the base supporter; (b) cross-sectional view and dimensions of the base supporter 11  When applying current with the same direction as the four coils, the force between the coils and the lens holder (including ring magnet and actuating plate) will cause the plate to translate vertically. When an opposite current is applied to two pairs of coils on the same side, the plate will rotate in yaw (around the x axis; Figure 2.2) or pitch (around the y axis; Figure 2.2). If a hole is drilled in the center of the plate, the lens can be mounted and when the plate rotates the light path will change, as shown in Figure 2.3(b). By changing the light path, the actuator can compensate for the hand-trembling effect with the help of sensors and controller. For hand tremor, the frequency can be as low as about 8-12 Hz [36].  2.2 Fabrication 2.2.1 Material Preparation A layer of 20% w/v polyacrylic acid (PAA, Sigma-Aldrich Corporation) solvent (in water) was spin-coated onto glass slides as a sacrificial layer at 2000 rpm for 30 s and then the PAA-coated glass slides were baked at 120℃ for 3 min. PDMS (Sylgard 184 Silicone Elastomer, Dow Corning Corporation) was used as the base material. Pre-polymer and crosslinker, two compounds of PDMS, were mixed at a 5:1 ratio by weight. Subsequently, strontium ferrite nanopowder (Sigma-Aldrich Corporation) was introduced at 3:2 (60%), 2:3 (40%), or 4:1 (20%) (strontium ferrite:PDMS) by weight, and mixed with a stick for at least 1 min.  12 2.2.2 3D Printing Stereolithography 3D printing (SLA 3DP) [38] is a 3D printing method that can achieve high resolution and it was applied in our project. The mechanism of SLA 3DP (Figure 2.4) uses UV light to solidify the photopolymer, layer by layer, so that the parameters such as slice thickness, burn-in exposure time, and normal exposure time are significant.   Figure 2.4    Stereolithography 3D printing mechanism  Asiga Freeform Pico (ASIGA, CA, USA), an affordable stereolithography (SLA) 3D printer with native XY pixel resolutions down to 27 μm and 250 nm Z-axis servo 13 resolution, was used to print the mould, with PlasWHITE (photopolymer, ASIGA, CA, USA) as the material and settings in Table 2.1. A flash mould (without bottom; Figure 2.5) was designed to ease the demoulding process, which typically has the most difficulties [39] due to large surface energy and friction force. After printing, the printed mould was immersed into isopropyl alcohol (IPA) for 5 min to remove uncured photopolymer. When dry, it was cured for 20 min in UV light (Pico Flash).   Figure 2.5    Mould of actuating plate for Stereolithography 3D printing The settings for the 3D printer were as follows: Parameters Value Unit Support Contact Width 0.4 mm Support Over-shoot 0.3 mm Slice Thickness 0.025 mm Burn-In Exposure Time 16.589 s Normal Exposure Time 2.745 s Table 2.1    Parameter settings of SLA 3D Printer  14 2.2.3 Moulding The fabrication procedures (Figure 2.6) for the actuating plate are as follows: 1) 3D printed mould mounted on PAA-coated side of the glass slide; 2) cylinder magnet (MAG400190, Main Electronic Supplies Ltd.) positioned at the bottom of the slide; 3) mixture of PDMS and strontium ferrite filled into the mould; 4) mould carefully covered with another PAA-coated glass slide and then clamped (Figure 2.7) with another cylinder magnet (MAG400185, Main Electronic Supplies Ltd), which also helps the magnetic powder align vertically during the curing process; 5) curing the moulded sandwich at 75℃ for 3 h (on a hot plate or in the oven) and then natural cooling; 6) magnets slowly removed and the cooled mould sandwich is immersed in water for 5 min to dissolve the PAA sacrificial layer; 7) slides are uncovered to obtain the mould with the solidified part inside; and 8) demoulding with tweezers or a thin stick. The 20% and 40% SrFe-doped mixtures (Figure 2.8 (b) and (c)) have viscosities that are low enough to stay in the liquid phase. In step (3), we just need to drop the liquid mixtures into the channels or the center and the liquid will automatically flow to fill the mould. Nevertheless, for the 60% SrFe-doped mixture (Figure 2.8 (d)), the mixture is mud-like (higher viscosity) and to fill the mould, flat tools, such as a glass slide, must be used to help fill and compress the materials into the mould. Although it seems to be more complicated, the 60% mixture is actually more advantageous than the 20% or 40% mixtures for the mould (or flash mould) we used, because the liquid mixtures tend to flow out, resulting in a waste of material and a failure to completely fill the mould. By attaching a magnet to the back of the glass slides during filling (Figure 2.6 (3)), the filling material will be attracted to the bottom because of its magnetic properties, and the 15 magnet will cause a virtual external compression, to increase the density and amount of SrFe in the mould volume.   Figure 2.6    Fabrication process for the actuating plate   Figure 2.7    Moulding sandwich with magnets clamping glass slides and magnetizing materials in mould  16  Figure 2.8    (a) a drop of PDMS (pre-polymer and crosslinker mixed with 5:1 w/w) on glass slide; (b) a drop of PDMS doped with 20% w/w SrFe nanopowder on glass slide; (c) a drop of PDMS doped with 40% w/w SrFe nanopowder on glass slide; (d) a drop of PDMS doped with 60% w/w SrFe nanopowder on glass slide  After obtaining the actuating plate, the base supporter was also printed using the SLA 3D printer with the same settings as shown in Table 2.1. The post-processing was the same as that of the moulding (i.e., printed part immersed in IPA for 5 min to remove uncured photopolymer, and after drying, the curing takes place for 20 min with UV light (Pico Flash)). To assemble the device (Figure 2.9), the coils (Senders Electronic Commerce Co., Ltd., more details in Appendix A) were first inserted into the four hollow cylinders with wires coming out. Then, a ring magnet (R211, K&J Magnetics Inc.) was attached coaxially to the center of the actuating plate. When placing the plate onto the glass slide, a drop of PDMS (pre-polymer and crosslinker mixed with 5:1 ratio by 17 weight) was dripped into the hole of the ring magnet. Afterwards, the plate was cured at 75℃ for 40 min to solidify the PDMS, and to further bond the ring magnet and the plate together. If the plate is directly mounted on the supporter, the strong attractive force between the core of the coils and the ring magnet, will cause the plate to snap immediately. Therefore, we filled PDMS (5:1) into the four grooves at the top of the walls of the supporter as a glue to bond the plate and supporter. Before mounting the plate, and to protect it from snapping, another R311 ring magnet was attached on the other side of the glass slide (Figure 2.9, step 4; and Figure 2.10(a)). Finally, the plate is mounted on top of the supporter, which is soldered with a flexible printed circuit board (FPCB) for testing. The device was cured at 75℃ for 1 h, and afterwards, the auxiliary parts were removed carefully. Figure 2.10 (b) shows the final actuator after curing. A hole in the center of the plate can be cut with a laser easily or a cylinder can be inserted during moulding to embed any lens. Because PDMS is also a promising optical material [9], in the future, we may be able to mould both the lens and the lens holder directly. In this project, for ease of characterization, we kept the center material to emulate the case with a lens.  18  Figure 2.9    Assembling process of actuator   Figure 2.10    (a) Actuator with auxiliary magnet and glass slide before curing; (b) final actuator after curing  2.2.4 Replica Experiments A series of replica experiments were performed to study the influences of fabrication errors on variations of frequency responses of actuators. Since air gap, which may have significant influences on magnitude/tilting angle [35], but negligible impacts on shape of frequency response curves, is not easy to be quantified in assembled actuators, in this part, we mainly focus on studies of bandwidths and locations of natural frequencies.  19 Firstly, 5 moulds (named as Mould1, Mould2, Mould3, Mould4 and Mould5) were printed with the same SLA 3D Printer. Each mould was used to replicate 3 actuating plates. The exact same procedures were followed to fabricate 15 actuating plates in total, as shown in Figure 2.11. 15 and actuators based on that were assembled, as shown in Figure 2.12. Frequency responses of all 15 actuators with 100mA were tested from 1Hz to 1000Hz as well as static tests of two samples.  Figure 2.11    15 actuating plates with 5 moulds and 3 batches  20  Figure 2.12     15 assembled actuators with 5 moulds and 3 batches (from left to right: 1st batch, 2nd batch and 3rd batch)  2.3 Characterization Methods To understand the material properties and obtain parameters for further simulation, a tensile test of material and magnetization test were performed to calculate Young’s modulus, coercivity, remanent magnetic moment (unit weight), etc. For actuator performances, both stationary and dynamic tests were done with a laser Doppler vibrometer (LDV) system.  21 2.3.1 Characterization of Material Sample preparation procedures were similar (but not identical) to those above: 1) PDMS (5:1 ratio of pre-polymer and crosslinker by weight) was mixed with strontium ferrite with 20%, 40%, and 60% strontium ferrite:PDMS ratios by weight; 2) mixture was stirred with a stick for at least 1 min in petri-dishes (since the viscosity of the 60% mixture is low, even using a glass slide to help smear the mixture, obtaining a uniform layer was difficult); 3) the sample was placed into an oven at 75℃ for 3 hours with MAG400350 (Main Electronic Supplies Ltd) at the bottom, and followed with natural cooling; 4) samples were cut with a knife for characterizations. A Wyko profiler (VEECO Metrology Group, AZ, USA) was used to measure the thickness of samples and digital calipers were used to measure their length and width. The tensile test of composites were measured with a thermo-mechanical analyser (TMA 2940-Q series, TA Instruments, DE, USA). Testing was performed at room temperature and the applied force was ramped with 0.05 N min-1 from 0 to 0.1 N or 0.2 N. After obtaining the data for each sample, the end of pre-loading was set as the start point. Strains and stresses were obtained by dividing the dimension changes by length (including pre-loading length) and dividing the forces by section areas. Young’s modulus was calculated with the slope of each curve; the effect of temperature on Young’s modulus was ignored here. A Superconducting Quantum Interference Device (SQUID) (Quantum Design, CA, USA) was used to characterize the magnetic moment (emu) versus the applied magnetic field (kOe) at 300oK (26.86℃). Samples (Table 2.2) were prepared exactly as described for the moulds in the Fabrication section. 22  Ratio of Strontium Ferrite Length (mm) Width (mm) Thickness (mm) Mass (g) 20% wt. 2.57 2.2 1 0.00681 40% wt. 2.09 2.35 1 0.00692 60% wt. 2.29 2.41 1 0.01061 Table 2.2    Dimension of samples for SQUID test.  2.3.2 Characterization of Actuator A laser Doppler vibrometer (LDV) system (Figure 2.13) was used to characterize the actuator. The system (diagram of software side in Appendix B) included: 1) a dSPACE DS1003 platform for control of algorithm implementation, 2) a DC power supply, 3) an amplifier for converting control voltage from dSPACE to current for the coils of the actuator prototype, 4) a laser Doppler vibrometer (LDV) to measure the tilting (rotating) angle, and 5) the prototype with reflective tape attached at the top center to strengthen the signal. A 1 Hz sinusoidal current with amplitude ranging from 100 mA to 500 mA was first applied to the actuator. The direction of the current in coils on the A and B sides (or the C and D sides) (Figure 2.10 (a)) were made opposite so that the actuator could rotate (tilt). The frequency response of the device was also measured with a 100 mA current, ranging from 1 to 1000 Hz at the B side. In both stationary and dynamic characterization tests, a 1.25 mm by 1.25 mm square reflecting tape was cut and attached to the top of the actuating plate, with each edge parallel to the corresponding wall of the base supporter, to strengthen the signal. The laser was focused on the edge of the tape at each side to ensure that the rotating radius was 1.25 mm. 23   Figure 2.13    System setup for characterizing the actuator     24 Chapter  3: Results and Discussion 3.1 Characterization of Material 3.1.1 Young’s Modulus Young’s modulus (tensile modulus) is a measure of the stiffness of an elastic material, defined by the following equation:  Where E is the Young’s modulus; A0 is the cross-sectional area through which the force is applied; ΔL is the length change; and L0 is the original length. Figure 3.1 shows the stress-strain test results for the pure PDMS and PDMS composites with 20%, 40%, and 60% wt SrFe nanopowder loaded, and Figure 3.2 shows the elastic modulus of the samples. Young’s moduli of pure PDMS is 1.53 MPa, which is consistent with [19]. For the 20% and 40% samples, with addition of SrFe, the elastic modulus of the PDMS increased by 15.69% and 47.71%, respectively. Previous authors [19] implied that a reduction in Young’s modulus could result in poor interactions between the PDMS matrix and addition of powders. The results suggest that for the 20% and 40% cases, when the mixtures were still liquid, SrFe and PDMS show good compatibility and SrFe may not prevent the possibility of crosslinking. For the 60% case, the elastic moduli decreased by 47.71%, possibly because the viscoelastic solid mixture might not have been thoroughly crosslinked, which would lead to a low modulus [40][41].  25  Figure 3.1    Stress-strain curves of pure PDMS and PDMS doped with 20%, 40%, and 60% w/w SrFe composites   Figure 3.2    Elastic moduli of pure PDMS and PDMS doped with 20%, 40%, and 60% w/w SrFe composites  In our case, the 60% SrFe-doped mixture was used. A low Young’s modulus of the composite is advantageous for magnetic actuation since a weaker magnetic field is needed for lower forces (less stress per unit section area), while providing the same strain 26 (dimension change with unit length). Nevertheless, for a simple beam or plate, natural frequencies are proportional to the root of Young’s modulus. The actuating plate can be viewed as a combination of four beams and a circle plate. A lower Young’s modulus means lower natural frequencies, which may not be beneficial for control in our case. Higher natural frequencies will help the system stay away from resonance.  3.1.2 Magnetization Curve Figure 3.3 shows the M-H hysteresis curves for the samples in Table 2.2. The coercive force is consistent for all three samples, with an average value of 4.25 kOe and the remanent magnetic moment (unit weight) is proportional to the by-weight ratio of strontium ferrite-PDMS, which is also consistent with the findings of other authors [16][18]. The coercivity is 1.85 times larger than that reported [18], which could result from magnetization during curing [42]. An external magnetic field during mixture solidification can help magnetic particles align themselves in the vertical direction. Therefore, the aligned sample will show larger coercivity, which is advantageous since the sample will be more difficult to get demagnetized. The stress-strain and M-H hysteresis results were applied to a finite element analysis (FEA) to estimate the force and magnetic field. 27  Figure 3.3    Mass magnetization curves versus applied magnetic field for composites with 20% to 60% strontium ferrite nanopowder added at 300 oK (26.86℃)  3.2 Dimensions An SZ61 zoom stereo microscope (Olympus Co. Japan) was used to characterize the top view of the actuator, and ImageJ (National Institutes of Health, USA) software was used to calibrate and measure the dimensions (Figure 3.4 and Table 3.1). The beams at the A, B, and C side were found to have a relatively uniform beam width, with an average width of 0.7953 mm (standard deviation of 0.00404 mm). Nevertheless, the beam at the D side was 10.6% shorter than the average width of the others. For four beams, the average width was 0.7743 mm (standard deviation of 0.04296 mm). The variation may be due to the fact that the SLA printer generates pillars to support the printed part, and the surface of each side may not be even after the pillars are removed. We used sandpaper to file the uneven sides manually; however, some errors may have caused the asymmetric errors. In the future, the errors could be reduced by using a polishing/sanding machine instead of manual filing. The average beam length was 3.5463 mm (standard deviation of 28 0.1744 mm). The variation of lengths may have been the result of the assembly. As the ring magnet and the cores of coils would attract each other, the errors in the ring magnet/plate circle and hole in the base supporter, being non-coaxial, may contribute to variations in bending even without a current. The measurements show shorter beam lengths at the B and D sides, probably because of the center of the plate shifting closer to the B and D sides. Assembling errors, along both the C and D sides, may be due to variations in the diameters (Table 3.1) and could be reduced with an optimized design for the base supporter (i.e., with grooves to hold the parallel beams).  Figure 3.4    Dimensions characterization under microscope  Beam Width (mm) Beam Length (mm) Diameter (mm) A 0.799 3.647 3.700 B 0.796 3.408 C 0.791 3.740 3.862 D 0.711 3.390 Table 3.1    Dimensions of the prototype 29 3.3 Finite Element Analysis 3.3.1 Eigenfrequency For the actuating plate, the effect of variations in beam width, beam length, and radius (Figure 2.2) on the eigenfrequencies were analyzed. A finite element analysis (FEA) was performed with the Solid Mechanics module and the eigenfrequency study was conducted in COMSOL Multiphysics (Canadian Microelectronics Corporation, Canada). The 3D model is shown in Figure 3.5. The model consists of four parts: actuating plate, ring magnet, PDMS in middle and four PDMS bars. All parts were unioned and four PDMS bars were set as a fixed constraint. Table 3.2 shows the materials and property settings. A three-factor and three-level factorial experiment design (with L9 Taguchi Orthogonal Array [43]) was used to study the influences of beam width, beam length, and radius on normal modes (or natural frequencies). Taguchi Orthogonal Experiment Design is a commonly used method for increasing the efficiency of experiments. If checking three factors and three-levels one by one, 27 experiments would be needed; whereas, with the Taguchi Orthogonal Experiment Design, only 9 experiments are needed. A 30% increase or decrease for three factors from the designed model (Figure 2.2) was applied to generate the high and low levels. The design of the experiment is shown in Table 3.3 and the L9 experiment settings are shown in Table 3.4. 30  Figure 3.5    3D Model of FEA simulation in COMSOL Multiphysics  Parameters Density (kg/m3) Young’s Modulus (MPa) Poisson Ratio Actuating Plate 1922.48 0.8 0.49 Ring Magnet 7400 160000 0.3 PDMS 970 1.53 0.49 Table 3.2    Material properties of FEA 3D Model   Level Beam Width (mm) Beam Length (mm) Radius (mm) High (H) 1.001 5.031 2.60 Medium (M) 0.770 3.870 2.00 Low (L) 0.539 2.709 1.40 Table 3.3    Three-factor and Three Level Taguchi Orthogonal Design    31  Number Beam Width Beam Length Radius 1 1.001 5.031 2.60 2 1.001 3.870 2.00 3 1.001 2.709 1.40 4 0.770 5.031 2.00 5 0.770 3.870 1.40 6 0.770 2.709 2.60 7 0.539 5.031 1.40 8 0.539 3.870 2.60 9 0.539 2.709 2.00 Table 3.4    Nine experiments settings of Three-factor and Three Level Taguchi Orthogonal Design for COMSOL  Figure 3.6 shows 6 normal modes between 0 and 450 Hz in experiment 2 (Table 3.4). It suggests that one translation mode, four tilting modes, and one horizontal rotating mode will occur, which also means that in the frequency response curve, 6 peaks would be seen. The frequency difference between the 2nd mode and 3rd mode is as small as 1 Hz and the difference between the 5th mode and 6th mode is as small as 0.5 Hz. Therefore, in this case, four obvious peaks would be predicted in the frequency response curve.  32  Figure 3.6    Eigenfrequency study results of second experiment  Figure 3.7 shows the main effects plot for the means of the eigenfrequencies. For all normal modes, within the ranges, the relation between beam width and eigenfrequencies is positive, and the relation between beam length (and radius) and eigenfrequencies is negative. To prevent the system from resonance with dimensions within these ranges, the beam width should be increased and the beam length and radius should be decreased. 33 Nevertheless, a smaller beam length and radius means a smaller size for the actuating plate, and a larger beam width would require smaller space in between the beams, which would increase the possibility of damage during the demoulding process and require higher resolution of the 3D printer. Therefore, a trade-off must be considered between the performances and fabrication difficulties. In any case, the difficulties in moulding need to be quantified and the likelihood of demoulding damage should be considered in arriving at the optimal dimensions. Within the parameters that were examined in this project, medium-level dimensions would be a reasonable design as it is close to the optimal dimensions.   Figure 3.7    Main effects plot for means of eigenfrequencies  Figure 3.8 shows 6 normal modes between 0 and 450 Hz for the prototype with dimensions as shown in Table 3.1. It also suggests the same modes as in Figure 3.6: one translation mode, four tilting modes, and one horizontal rotating mode. The frequencies are between a medium- and a high-level (Figure 3.7). These results are from comparisons 34 using medium-level parameters, larger beam widths, smaller beam lengths, and smaller radius. Asymmetry also causes the differences in the fourth mode (Figure 3.7 (d) and Figure 3.6 (d)).   Figure 3.8    Eigenfrequency study results of actual prototype   35 3.3.2 Magnetic Field and Forces The same 3D model was imported into COMSOL with a 30 mm-radius sphere to be the air for the magnetic field and force analysis with the Magnetic Fields, No Currents (mfnc) module. Table 3.5 shows the relative permeability settings for this simulation. Equation (2) was used to constitute the magnetic field of the ring magnet and Equation (3) was used to define the actuating plate [44][45]:  where B is magnetic induction; H is magnetic field; M is magnetization; u0 is vacuum permeability; ur is relative permeability; and Br is remanence. For the N42 ring magnet [46], the remanence was set as 1.3 Tesla. According to Figure 3.3 and the mass and volume of the sample, the suggested value for the 60% SrFe-doped case, was magnetization of 37500 A/m. Nevertheless, since the actuating plate has two poles on two sides, 37500⋅(12.05-z) was used to define the magnetization, and 12.05 is the height of the actuating plate middle slice in the Z-direction. The outer surface of the sphere (air) was defined as zero magnetic scalar potential. The force on the ring magnet was calculated [47] with the software as an integral of surface stress tensor over all boundaries of the part. The results showed that global evaluation of force on the ring magnet in the Z-direction was 0.246 N, and setting the actuating plate as pure PDMS (i.e., zero-magnetization), the force on the ring magnet was 0.006 N. This implies that the actuating plate provides a large force (larger than 0.00069N [46], weight of the magnet) to attract the magnet than would be the case, otherwise, making it easier to assemble. This would also avoid the need to use further strengthening procedures with PDMS in the center, as 36 shown in Figure 2.9, step 2). This would reduce fabrication costs, in the future. Figure 3.9 shows the magnetic flux density distribution in the Y-Z plane for cases with and without magnetic powder doping. Parameters Relative Permeability Actuating Plate 1.2 Ring Magnet 1.05 PDMS 1.2 Air 1 Table 3.5    Relative permeability settings of FEA 3D Model   Figure 3.9    Magnetic flux density in the Y-Z plane of the simulated model; a) pure PDMS as the plate; b) 60% SrFe-doped PDMS composite as the plate  3.4 Characterization of Actuator 3.4.1 Stationary Test Figure 3.10 and Figure 3.11 show the relation between the actuating current and the tilting angle for four sides. All curves are quite linear, with R2 (coefficient of determination) larger than 0.99 and they perform a tilting rate of between 0.0011 and 0.0012 (Table 3.6), except for the C side that demonstrates a lower tilting rate. The shorter beam at the D side (Table 3.1) could cause this asymmetry. For the symmetric 37 side, the plate is able to be actuated by 0.6o (the maximum angle from human hand tremor [36]) with as low as a 500 mA current (50 turns/9 mm) or 1.11 mA/ (mm⋅ turn), operating at a much lower current than in other reported designs [28][32]. According to Ampere’s Law [45], the magnetic flux density is proportional to the turns of the coil, current, and is reciprocal to the length. Therefore, by increasing the turns of the coil, the current used and the thickness of the actuator can be reduced. We intend to make improvements in this regard in the future. Actuating Side Up Tilting Rate (o/mA) Down Tilting Rate (o/mA) A 0.0012 0.0012 B 0.0012 0.0011 C 0.0006 0.0009 D 0.0011 0.0011 Table 3.6    The tilting rate for four sides with an 1 Hz sinusoidal current   Figure 3.10    Relation between current and tilting angle for the four sides vertically down   38  Figure 3.11    Relation between current and tilting angle for the four sides vertically up  3.4.2 Frequency Response Figure 3.12 demonstrates the frequency response for the actuator tested with the same LDV system and a digital storage oscilloscope (TDS 2014, Tektronix Inc., USA). Three tested frequency responses curves show good repeatability. The tilting angle-frequency curve shows that at 104.11 Hz, 373.68 Hz, 459.73 Hz there are three peaks (natural frequencies). All normal modes are far from the operating frequency range, which is about 8-12 Hz [36] and the bandwidth is around 56 Hz, which means the ability to compensate undesired vibration under 56 Hz. Figure 3.12 also shows only 1st Mode (vertical translation), 5th and 6th Modes (tilting) were excited and that the simulation results (1st mode to 6th mode), which are close to the experimental result. The error at first peak is 2.72% and at second peak is 1.79%- 4.76% (since 5th and 6th Modes are close, in actual test, the peak may merge into one peak). Assumptions such as the Poisson ratio being unchanged, boundary conditions being ideal (as those in Figure 3.5), etc., and 39 the ignorance of details such as shape of PDMS in the center, effects of PDMS bonding on the performance, etc., may contribute to the differences between experimental and simulation results.  40  Figure 3.12    Frequency responses of the system and simulation results41 3.4.3 Replica Experiments Figure 3.13 shows frequency response curves of 15 actuators. Actuators were named as B11-B35, with first number representing batch and second number representing mould applied. For example, B35 means the sample was fabricated with Mould5 from 3rd batch. It shows that for all samples, resonance peaks will occur when frequency is larger than 367 Hz. However, between 10-50 Hz, noises (weak peaks) exist in all samples, which are not advantageous in terms of control since it is close to 8-12 Hz. Since the weak peaks in frequency range do not occur in FEA simulations, it could result from the bonding of PDMS in grooves of base supporter. Figure 3.14-3.18 shows frequency response curves of samples with Mould1, Mould 2, Mould3, Mould4 and Mould5 respectively. Figure 3.19-3.21 shows frequency response curves of samples from 1st batch, 2nd batch and 3rd batch. And Table 3.7 summarises the bandwidths and the standard deviations. It implies that samples with Mould2 in 3 batches show smallest standard deviation while samples with Mould4 in 3 batches show largest standard deviation, and that samples from 3rd batch show smallest standard deviation while samples from 1st batch show largest standard deviation. Table 3.8 summarises natural frequencies (frequency of first peaks occurring between 100-1000Hz) of 15 actuators and the standard deviations. Samples with Mould2 also show smallest standard deviation while samples with Mould1 show largest standard deviation. And samples from 3rd batch show smallest standard deviation while samples from 1st batch show largest standard deviation. Therefore, samples from 3 batches with Mould2 and samples with different moulds from 3rd batch, demonstrate best repeatability.   42  Figure 3.13     Frequency response curves of 15 actuators (B35 means the sample from 3rd batch with Mould5)    Figure 3.14     Frequency response curve of samples with Mould1  43  Figure 3.15     Frequency response curve of samples with Mould2   Figure 3.16     Frequency response curve of samples with Mould3  44  Figure 3.17    Frequency response curve of samples with Mould4   Figure 3.18    Frequency response curve of samples with Mould5 45  Figure 3.19   Frequency response curve of samples from 1st batch   Figure 3.20    Frequency response curve of samples from 2nd batch 46   Figure 3.21    Frequency response curve of samples from 3rd batch  Mould 1st batch 2nd batch 3rd batch Standard Deviation (Hz)  1 19.84 28.51 13.80 7.39 2 12.88 20.18 13.34 4.09 3 28.02 19.85 19.85 4.73 4 39.58 27.07 20.18 9.83 5 11.82 12.45 20.54 4.86 Standard Deviation (Hz) 11.58 6.45 3.64 N/A Table 3.7     Bandwidths of 15 actuators and the standard deviations 47   Mould 1st batch 2nd batch 3rd batch Standard Deviation (Hz)  1 373.68 649.38 N/A 194.9493 2 660.69 683.9 638.26 32.27235 3 N/A 527.84 575.44 33.65828 4 527.84 732.82 537.03 115.7835 5 N/A N/A 627.34 N/A Standard Deviation (Hz) 143.6367921 87.41211 47.11506 N/A Table 3.8    Natural frequencies of 15 actuators and the standard deviations  According to Table 3.7, all actuators except for sample B15 show a bandwidth larger than 12Hz, demonstrating the ability to compensate for undesired tremor below 12 Hz. Figure 3.22-25 show relations between current and tilting angle for the four sides vertically up and down of B11 and B21, which are all quite linear but asymmetric. The symmetricity could be improved by implanting ions to strengthen the mould.  48  Figure 3.22     Relation between current and tilting angle for the four sides vertically up of B11  Figure 3.23    Relation between current and tilting angle for the four sides vertically down of B11 49  Figure 3.24    Relation between current and tilting angle for the four sides vertically up of B21  Figure 3.25     Relation between current and tilting angle for the four sides vertically down of B21  Mould dimension errors (errors caused by 3D printing and post process), moulding errors (errors result from fabrication process) and assembly errors (errors caused by 50 assembly process such as non-coaxial errors), will contribute to variations of the performances of the 15 actuators.  Dimensions, including beam widths, beam lengths and diameters, of all 15 actuators and 5 moulds were measured with same methods mentioned in 3.2 part (Chapter 3) to further understand errors. Figure 3.26 shows standard deviations of dimensions of each actuator as well as 5 moulds. It demonstrates that sample B32 (with Mould2 in 3rd batch) have best symmetricity of both lengths and width on four sides. 5 moulds have less than 0.03mm standard deviation (1.61%-2.90%) in beam width and 0.05-0.11mm deviation (1.37%-2.85%) in beam length, both of which are smaller than any of those in any actuators. What’s more, the standard deviation of diameters of all 5 moulds is 0.044mm, which means 1.11% errors. Therefore, moulding process would decrease the symmetricity and mould fabrication only contributing to 2.90% error in beam width, 2.85% error in beam length and 1.11% errors in diameter.  It could also be concluded that, according to those experiments, standard deviations in beam width and beam length in individual actuator are 0.024-0.158mm and 0.078-0.200 mm respectively. Based on the ideal design mentioned in Chapter 2, the errors of beam width and beam length on four sides for individual actuator are 2.02%- 5.18% and 3.10%-20.47%.  51  Figure 3.26     Standard deviations of widths, lengths in four sides of each actuator (B1 to B3 means number of batch) 52  Figure 3.27 shows errors of actuating plates dimensions relative to mould in different batches. These errors are calculated by standard deviations between means of respective dimension of actuator and corresponding mould, indexing errors during moulding process comparing to the corresponding mould. It could be shown that in these replica experiments, for diameter, errors are 0.69%-10.87%; for beam width, errors are 2.32%-22.75%; for beam length, errors are 0.38%-4.99%.   Table 3.9 shows maximum errors of dimensions of samples with 5 moulds. By comparing standard deviation of bandwidth in Table 3.7, it demonstrates that standard deviations of bandwidth are positive-related to errors in width. By referring to Table 3.8 (ignoring samples from Mould5), it implies that variations in natural frequency between 100-1000Hz are positive-related to errors in beam length.  53  Figure 3.27     Errors of actuating plates dimensions relative to mould in different batches 54   M1 M2 M3 M4 M5 Width 21.65% 13.96% 18.00% 22.75% 20.07% Length 4.99% 2.60% 3.40% 4.58% 1.40% Diameter 10.87% 4.76% 6.95% 8.57% 9.40% Table 3.9   Maximum errors of dimensions of samples with 5 moulds  Figure 3.28 shows standard deviations of means of widths, lengths, diameters of 5 actuating plates in the same batch. It implies that comparing to means of dimensions of moulds, 3rd batch demonstrates largest errors in both length and diameter. Referring to Table 3.7 and Table 3.8, 3rd batch showed lowest standard deviations both in bandwidth and natural frequency, which demonstrates no clear relations with errors in dimensions.  55  Figure 3.28     Standard deviations of means of widths, lengths, diameters of 5 actuating plates in the same batch 56 Chapter  4: Conclusions and Future Work 4.1 Conclusions In Chapter 1, we reviewed the background on 3D printing moulding (3DPM) methods, magnetic actuators, and optical image stabilizers (OIS). Challenges in the fabrication of micro/miniature magnetic actuators, current work on miniature OIS actuators, and the advantages of 3DPM methods were described. In Chapter 2, the design of the actuator was presented with its components and specific dimensions. The fabrication processes, including material preparation, 3D printing and moulding were described. Finally, the set-up for the characterization experiments and the preparation of the sample was introduced. In Chapter 3, the characterization of the material and the actuator was demonstrated. The results of the magnetization curves are consistent with previous works. Young’s modulus for the mixture of SrFe and PDMS (3:2 by weight) was a low value, so that the film of material could be actuated more easily. The actuator could be actuated to 0.6o with 500 mA (50 turns/9 mm). The comparisons of the finite element analysis simulation results with the experimental results were consistent. The actuator achieved high damping frequency responses, so that the system could easily become stable and no eigenfrequencies occurred within the range of operational frequencies. In replica experiments, we analyzed the moulding errors are 0.69%-10.87% for diameter, 2.32%-22.75% for beam width and 0.38%-4.99% for beam length. Mould fabrication errors are 2.90% for beam width, 2.85% error for beam length and 1.11% errors for diameter. We also disclosed that standard deviations of bandwidth are positive-related to errors in beam 57 width and that variations in natural frequency between 100-1000Hz are positive-related to errors in beam length.  In conclusion, we successfully applied 3D printing moulding methods to fabricate a miniature magnetic actuator for an optical image stabilizer. The Young’s modulus of the magnetization curve for the PDMS composite showed an advantage in the actuating. The actuator could achieve a 0.6o tilting angle with 500 mA (50 turns/9 mm), operating at a much lower current than in other designs [28][32]. The frequency response test also showed that the actuator could easily help the system become stable and experimental results match simulation results very well, showing less than 5% errors.  4.2 Future Work The current actuator shows good static and dynamic performances. Nevertheless, fabrication errors still exist that affect the performance, and have an impact on the stability of the system. The fabrication and assembly process still needs to be optimized, for example, by improving the mould sanding process to minimize any errors from the uneven surfaces. Ultimately, the effect of errors on the performance should be negligible. Since fabrication errors exist in the manufacturing industry, it would be meaningful to further study control theory using this platform, to achieve robust control in the fabrication of the actuator. With a new control theory and/or methods, even when the actuator dimensions vary slightly, the system could still be controlled with greater precision. 58 The current actuator has not been installed on any lens in our research center. With a laser cutter to cut a hole and the installation of a lens, additional optical experiments could be carried out. In our project, we only used 50 turns of the single-layer coils; however, the thickness of the actuator could be easily reduced by using shorter coils with more turns and multiple layers. This would be consistent with current trends in the design of today’s mobile phones. With more turns and layers of coils, the energy consumption could be reduced, to further lower the operation current. For example, with 300 turns (3 layers, 100 turns/layer) and 3 mm long coils, according to Ampere's Law [40], only half of the corresponding current would be needed to generate the same magnetic field. In this project, only the actuator part was fabricated and tested with a LDV system. A optical-electronic-mechanical system, with laser light sources, image sensor, gyroscope sensors, a controller, and the current actuator could be built to study the actual case of optical image stabilization and to test innovative control theories.     59 Bibliography [1] B. 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