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Magnetically levitated six degree of freedom micro-machining rotary table Dyck, Mark 2014

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Magnetically Levitated Six Degree of FreedomMicro-Machining Rotary TablebyMark DyckB.A.Sc., The University of British Columbia, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Mechanical Engineering)The University of British Columbia(Vancouver)December 2014c©Mark Dyck, 2014AbstractThis thesis presents a six degree of freedom magnetically levitated rotary tablethat has one unlimited rotation axis. The actuation force is achieved by the Lorentzforce. The underside of the actuator has an axial Halbach array mounted circumfer-entially near the outside edge. Force is produced in the stator coils which are madeusing a printed circuit board. The purpose of this table is for a micro-machining ro-tary table application. Benefits of this table are its compact, lightweight, no-frictionand high precision characteristics.Control of the table in six degrees of freedom is achieved by dividing the sta-tor into quarters. Each quarter is driven by a linear three phase current amplifier.For each quarter two forces can be generated, one in the levitation direction andone in the tangential direction. This creates eight independently controlled forcesallowing for full six degrees of freedom control. Position feedback for the stageis achieved by using four capacitive displacement measurement probes and fouroptical encoders around a circular optical grating. Performance of the table hasbeen tested and the results show that the closed loop bandwidth for all axes is be-tween ∼ 250Hz and ∼ 550Hz. Regulation error in the X,Y and Z axes is less than55nm while the A,B and C axes are better than 1.2µrad (0.248 arc seconds). Forcecapacity has been tested up-to 70N with a theoretical limit of 140N.iiPrefaceFor this project I was the lead investigator and was responsible for the majority ofthe design, development, manufacturing and testing of the project. Yusuf Altintasand Xiaodong Lu were the supervising authors on this project and were involvedin providing conceptual ideas, design suggestion and manuscript composition.Chapter 1. Figures 1.2, 1.5, 1.7, 1.8, and 1.9 are not the authors’ work, as notedby each figure.Chapter 3. Parts of this chapter, including some figures, appear in two papersthat have yet to be submitted to journals. The titles of the papers are ”Magnet-ically Levitated Six Degree of Freedom Rotary Stage” and ”Non-Contact, Com-pact, Vacuum Compatible High Precision Six Degrees of Freedom Rotary Stage”respectively. Authors of the papers are Xiaodong Lu, Mark Dyck and Yusuf Altin-tas.Chapter 4. Parts of this chapter also appear in two papers, same as Chapter 3.Chapter 5. Some of the results will also be published in the two papers men-tioned in Chapter 3.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Micro-Machining Overview . . . . . . . . . . . . . . . . . . . . 21.2 Current Technology . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Magnetically Levitated Rotary Table Architecture . . . . . . . . . 31.4 Previous Non-contact Table Work . . . . . . . . . . . . . . . . . 41.4.1 Multi-Degree of Freedom Planar Actuators . . . . . . . . 51.4.2 Multi-Degree of Freedom Rotary Actuators . . . . . . . . 92 Working Principle and Electro-Mechanical Design . . . . . . . . . . 142.1 Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.1 Force Ripple Cancellation . . . . . . . . . . . . . . . . . 202.2 Electro Mechanical Design . . . . . . . . . . . . . . . . . . . . . 21iv2.2.1 Magnetic Array Design . . . . . . . . . . . . . . . . . . . 212.2.2 Stator Design . . . . . . . . . . . . . . . . . . . . . . . . 312.2.3 Mechanical Structure Design . . . . . . . . . . . . . . . . 352.2.4 Force to motion system overview . . . . . . . . . . . . . 463 Metrology Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.1 Capacitive Sensors . . . . . . . . . . . . . . . . . . . . . . . . . 503.2 Optical Encoder Setup . . . . . . . . . . . . . . . . . . . . . . . 513.3 Initialization Procedure . . . . . . . . . . . . . . . . . . . . . . . 543.4 Geometric Distortion Effects . . . . . . . . . . . . . . . . . . . . 544 Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.1 Axis Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 Initial Controller Design . . . . . . . . . . . . . . . . . . . . . . 604.3 Plant Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4 Classic High Performance Controller Design . . . . . . . . . . . . 614.5 Controller Results . . . . . . . . . . . . . . . . . . . . . . . . . . 635 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 685.1 Control Measurements . . . . . . . . . . . . . . . . . . . . . . . 685.1.1 Plant Frequency Response . . . . . . . . . . . . . . . . . 695.1.2 Closed Loop Response . . . . . . . . . . . . . . . . . . . 695.2 Static Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.3 Regulation Error . . . . . . . . . . . . . . . . . . . . . . . . . . 755.4 Transient Response . . . . . . . . . . . . . . . . . . . . . . . . . 765.5 Dynamic Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . 765.5.1 Cross Dynamic Stiffness . . . . . . . . . . . . . . . . . . 845.5.2 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . 845.6 Power Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 876 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.1 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97vA Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 101A.1 Mechanical Drawings . . . . . . . . . . . . . . . . . . . . . . . . 101A.2 Setup Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118A.3 Suppliers Information . . . . . . . . . . . . . . . . . . . . . . . . 118A.4 Data Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120viList of TablesTable 3.1 Range of Motion . . . . . . . . . . . . . . . . . . . . . . . . . 49Table 4.1 Controller Parameters . . . . . . . . . . . . . . . . . . . . . . 63Table 5.1 Closed Loop Bandwidth Results . . . . . . . . . . . . . . . . 69Table 5.2 RMS Regulation Error . . . . . . . . . . . . . . . . . . . . . . 76viiList of FiguresFigure 1.1 Proposed System Overview . . . . . . . . . . . . . . . . . . 4Figure 1.2 ”Perspective view of the magnetically levitated stage; the mo-tor forces acting on each magnet array are shown as arrows;the stators are labeled I through IV” - Image and Caption from[1], [Precision Engineering, 22/2, Won-jong Kim, David L.Trumper, High-precision magnetic levitation stage for photolithog-raphy, 66-77, Copyright (1998), with permission from Elsevier] 6Figure 1.3 Hazelton et al. Six Degrees of Freedom (6DOF) Stage DesignOverview - Image from [2] . . . . . . . . . . . . . . . . . . . 6Figure 1.4 Hazelton et al. Stage Checkerboard Magnet Array - Image from[2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 1.5 Overview Image of Jansen et al. Actuator Design - Image takenfrom [3], c©2007 IEEE . . . . . . . . . . . . . . . . . . . . . 8Figure 1.6 Compter et al. Coil Arrangement Overview - Image taken from[4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Figure 1.7 Lu and Irfan-ur rab Planer Motor Overview - Taken from [5],[CIRP Annals - Manufacturing Technology, 61/1, XiaodongLu, Irfan-ur-rab Usman, 6D direct-drive technology for pla-nar motion stages, 359-362, Copyright (2012), with permis-sion from Elsevier] . . . . . . . . . . . . . . . . . . . . . . . 10Figure 1.8 Hollis et al. 6DOF Magnetically Actuated Wrist Join - TakenFrom [6], c©1991 IEEE . . . . . . . . . . . . . . . . . . . . . 11viiiFigure 1.9 Trumper and Liebman Online Public Disclosure of 6DOF Mag-netically levitated rotary stage - Image from [7] . . . . . . . . 12Figure 1.10 LaunchPoint Technologies High Power Density Halbach Ar-ray Motor - Taken from [8] . . . . . . . . . . . . . . . . . . . 13Figure 2.1 Halbach and Coils Cross Section View . . . . . . . . . . . . . 15Figure 2.2 Halbach Array Simplistic Magnetic Field . . . . . . . . . . . 22Figure 2.3 F*a Optimization Plot . . . . . . . . . . . . . . . . . . . . . 24Figure 2.4 Magnet Array Configuration (280mm OD, 200mm ID) . . . . 26Figure 2.5 Magnetic Field Simulation - Z-direction at -0.5mm below mag-nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 2.6 Magnetic Field Simulation - Z-direction at -2.0mm below mag-nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.7 Magnetic Field Simulation - Tangential direction at -0.5mmbelow magnets . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.8 Magnetic Field Simulation - Tangential direction at -2.0mmbelow magnets . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 2.9 Fundamental Frequency of Halbach Array Along Radius . . . 29Figure 2.10 5th Harmonic Frequency of Halbach Arrays Along Radius . . 29Figure 2.11 9th Harmonic Frequency of Halbach Arrays Along Radius . . 30Figure 2.12 13th Harmonic Frequency of Halbach Arrays Along Radius . 30Figure 2.13 6 Phase Commutation Diagram . . . . . . . . . . . . . . . . 32Figure 2.14 Printed Circuit Board (PCB) Stackup Used . . . . . . . . . . . 34Figure 2.15 Manufactured PCB . . . . . . . . . . . . . . . . . . . . . . . 35Figure 2.16 Layer 1 PCB Layout . . . . . . . . . . . . . . . . . . . . . . 36Figure 2.17 Layer 2 PCB Layout . . . . . . . . . . . . . . . . . . . . . . 37Figure 2.18 Assembled System Overview Testing Setup . . . . . . . . . . 38Figure 2.19 Honey Comb Panel with Magnet Spacer Mounted to Bottom . 39Figure 2.20 Bottom View of Table . . . . . . . . . . . . . . . . . . . . . 39Figure 2.21 Magnet Assembly Jig . . . . . . . . . . . . . . . . . . . . . . 40Figure 2.22 Horizontal Magnet Assembly . . . . . . . . . . . . . . . . . 41Figure 2.23 Third Magnet Assembly . . . . . . . . . . . . . . . . . . . . 42Figure 2.24 Completed Magnet Assembly . . . . . . . . . . . . . . . . . 42ixFigure 2.25 Cross Section of Rotary Table Assembly . . . . . . . . . . . . 43Figure 2.26 Assembled Stator Assembly . . . . . . . . . . . . . . . . . . 44Figure 2.27 Metrology Hub Bottom View . . . . . . . . . . . . . . . . . . 45Figure 2.28 Side View of Metrology Hub . . . . . . . . . . . . . . . . . . 45Figure 2.29 Non-Desirable Force Path . . . . . . . . . . . . . . . . . . . 46Figure 2.30 Desirable Force Path . . . . . . . . . . . . . . . . . . . . . . 47Figure 2.31 Acting Location of Actuation Forces . . . . . . . . . . . . . . 48Figure 3.1 Non-Contact Sensor Overview . . . . . . . . . . . . . . . . . 50Figure 3.2 Optical Encoder Monitoring . . . . . . . . . . . . . . . . . . 53Figure 3.3 Geometric Encoder Error Diagram . . . . . . . . . . . . . . . 55Figure 4.1 Z Force Acting Location . . . . . . . . . . . . . . . . . . . . 58Figure 4.2 Translation Force Magnitude . . . . . . . . . . . . . . . . . . 59Figure 4.3 Closed Loop Control Overview . . . . . . . . . . . . . . . . 61Figure 4.4 A and B Axis Plant Frequency Response . . . . . . . . . . . 64Figure 4.5 C Axis Plant Frequency Response . . . . . . . . . . . . . . . 64Figure 4.6 X and Y Axis Plant Frequency Response . . . . . . . . . . . 65Figure 4.7 Z Axis Plant Frequency Response . . . . . . . . . . . . . . . 65Figure 4.8 A and B Axis Measured NLT FRFs . . . . . . . . . . . . . . 66Figure 4.9 C Axis Measured NLT FRF . . . . . . . . . . . . . . . . . . 66Figure 4.10 X and Y Axis Measured NLT FRFs . . . . . . . . . . . . . . 67Figure 4.11 Z Axis Measured NLT FRF . . . . . . . . . . . . . . . . . . 67Figure 5.1 Frequency Response Function (FRF) Measurement Method . . 69Figure 5.2 A-Axis Plant FRF . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 5.3 B-Axis Plant FRF Result . . . . . . . . . . . . . . . . . . . . 70Figure 5.4 C-Axis Plant FRF Result . . . . . . . . . . . . . . . . . . . . 71Figure 5.5 X-Axis Plant FRF Result . . . . . . . . . . . . . . . . . . . . 71Figure 5.6 Y-Axis Plant FRF Result . . . . . . . . . . . . . . . . . . . . 72Figure 5.7 Z-Axis Plant FRF Result . . . . . . . . . . . . . . . . . . . . 72Figure 5.8 A and B Axes Closed Loop FRF Results . . . . . . . . . . . . 73Figure 5.9 C Axis Closed Loop FRF Result . . . . . . . . . . . . . . . . 73Figure 5.10 X and Y Axes Closed Loop FRF Results . . . . . . . . . . . . 74xFigure 5.11 Z Axis Closed Loop FRF Result . . . . . . . . . . . . . . . . 74Figure 5.12 Current vs. Force Results . . . . . . . . . . . . . . . . . . . . 75Figure 5.13 A-Axis Staircase Trajectory (1µrad Step Size) . . . . . . . . 77Figure 5.14 B-Axis Staircase Trajectory (1µrad Step Size) . . . . . . . . 78Figure 5.15 C-Axis Staircase Trajectory (0.5µrad Step Size) . . . . . . . 79Figure 5.16 X-Axis Staircase Trajectory (20nm Step Size) . . . . . . . . . 80Figure 5.17 Y-Axis Staircase Trajectory (20nm Step Size) . . . . . . . . . 81Figure 5.18 Z-Axis Staircase Trajectory (60nm Step Size) . . . . . . . . . 82Figure 5.19 Step Response Results . . . . . . . . . . . . . . . . . . . . . 83Figure 5.20 Impact Hammer Experiment Setup . . . . . . . . . . . . . . . 84Figure 5.21 Dynamic Stiffness Results . . . . . . . . . . . . . . . . . . . 85Figure 5.22 Cross Axes Dynamic Stiffness . . . . . . . . . . . . . . . . . 86Figure 5.23 24Hz Z Axis Modal Shape . . . . . . . . . . . . . . . . . . . 87Figure 5.24 200Hz Z Axis Modal Shape . . . . . . . . . . . . . . . . . . 87Figure 5.25 1827Hz Z Axis Modal Shape . . . . . . . . . . . . . . . . . . 87Figure 5.26 Electrical Model of Motor . . . . . . . . . . . . . . . . . . . 88Figure 5.27 Power Analysis Experimental Setup . . . . . . . . . . . . . . 88Figure 5.28 Power Analysis Results for One Phase of One Quarter (Fortotal power multiply by 12) . . . . . . . . . . . . . . . . . . . 89Figure 5.29 Power Analysis Phase Measurement Results . . . . . . . . . . 90Figure 5.30 Raw current and voltage measurement at 1 revolution per sec-ond [Hz] rotation rate . . . . . . . . . . . . . . . . . . . . . . 90Figure 5.31 Phase A Coil with Z and θ Magnetic fields . . . . . . . . . . 91Figure 5.32 Voltage - Current Phase Vector Diagrams . . . . . . . . . . . 92xiGlossaryADC Analog to Digital ConvertersDOF Degree of FreedomEMF ElectroMotive ForceFRF Frequency Response FunctionLDV Laser Doppler VibrometerMAGTABLE Magnetically Levitated 6DOF TableNLT Negative Loop Transfer FunctionPCB Printed Circuit BoardRMS Root Mean SquareRPM Revolutions Per Minute6DOF Six Degrees of FreedomxiiAcknowledgmentsFirst and foremost I would like to thank my Lord, Saviour, and Creator, JesusChrist for providing me with the ability and opportunity to learn about and betterunderstand the electro-mechanical side of the world we live in. I would also like tothank my patient and loving wife for encouraging me as I followed my passion andcontinued my studies as a MASc. student. I am indebted to Dr. Altintas for takingme in as a MASc. student and for providing an invaluable environment for learning.The expertise and opportunities provided by Dr. Lu have also been invaluable forfurthering my understanding in this area of research. My parents, who gave me asolid foundation in both academics and mechanical hands on experience have beensuch a blessing and encouragement throughout my studies at UBC.I would like to thank the fellow students in both the Precision MechatronicsLaboratory and the Manufacturing and Automation Laboratory for making myMASc. an enjoyable experience and for providing insight and assistance whenrequired. A special thanks goes to Irfan Usman who was particularly helpful onthis project and was always willing to discuss any questions I had. Eric Buckley,Fan Chen and Keir Maguire where all an asset to this project as they providedfeedback and suggestions on many aspects of this project.The founding for this research was generously supported by NSERC and CAN-RIMT.xiiiChapter 1IntroductionThe goal of this thesis is to present and outline the design, manufacturing andtesting of a Six Degrees of Freedom (6DOF) magnetically levitated rotary tablethat has unlimited rotation around one axis and limited movement on all otheraxes. The main contributions of this project are:• Design and manufacture of a 6DOF non-contact rotary actuator based on thework done previously by [5] designed for micro-machining applications.• A method, design and implementation of a non-contact 6DOF position mea-surement system designed for the requirements of a micro-machining appli-cation.• Validation of the non-contact rotary table actuator design.• Validation of the non-contact metrology solution.The following chapters in this thesis are structured as follows:Chapter 1 outlines the need for a non-contact rotary table and discusses theprevious related work for 6DOF levitated planar actuators as well as the work donefor 6DOF magnetically levitated rotary motion actuators.Chapter 2 discusses the working principle behind the actuation force. Themagnetic field design process is outlined and analyzed. It also discusses in de-tail the mechanical design of the moving table and stator as well as the electrical-mechanical design of the stator.1Chapter 3 shows the design of the metrology frame. This involves showing themechanical layout as well as the derivation of the decoupling equations.Chapter 4 presents the controller design method and the resultant controllers.Results of the designed controllers are shown.Chapter 5 presents the measured closed loop response, load capability, andregulation error of the stage. The step response for each axis is also shown as wellas the dynamic stiffness. This chapter also analyzes the power used by the actuator.Chapter 6 concludes with an overview of the project noting the challenges en-countered and the solutions chosen. Lastly, suggestions of future work are made.1.1 Micro-Machining OverviewMicro-machined components are generally only a few millimeters in size and havefeatures that are between 1µm to 500µm in size [9] [10] [11]. Examples of suchparts can be seen in bio-medical, automotive and integrated circuits applications[12]. Micro-machining requires the workpiece and cutting tool to be positionedrelative to each other with micron level accuracy [9]. The more rapidly this posi-tioning can be done the more desirable it is as it increases the throughput of themicro milling machine. This high precision positioning requirement creates manychallenges for the machine design.1.2 Current TechnologyTo produce complex shaped parts, the micro milling machines need to be ableto position the part relative to the work piece with multiple Degree of Freedom(DOF). Typically this is accomplished by stacking multiple single DOF stages inseries [13]. While this simplifies the inverse kinematics and allows for controllerdecoupling it also produces several difficulties such as increased mass, flexibilityand space. The increased mass means that the stages near the base of the kinematicchain have large inertia, creating difficulties for high speed precision positioning.Increasing the mass also increases the friction, especially the static friction, whichfurther increases the positioning challenge. For small movements static frictiontends to cause overshoot, therefore minimizing friction is important and in someapplications air bearings are used to achieve this [14]. Similar to static friction,2backlash in the drive can cause positioning errors. Therefore direct-drive motorsare often used to eliminate backlash errors and increase the speed of the drives [9].Stacked single DOF stages also increase the positioning error as the encodersfor each axis are generally mounted on that axis. This means that if there are anygeometric errors in the stages the errors are cumulative [15]. This same issue alsomeans that if there is flexibility in the stages the error is cumulative and will causeend effector positioning errors. Therefore, to avoid flexibilities errors the stagesneed to be as stiff as possible. This however, often requires making the stagesheavier, which increase the inertia and static friction.Typically, to keep the stages stiff ball bearings are used for out of axis con-straint. Any imperfections in the sphericity of the ball bearings will cause errors asthe ball bearings move. This limits the precision to the accuracy of the ball bear-ings, which can have errors similar to the required positioning accuracy [16]. Asmentioned previously, air bearings can be used to also alleviate this issue, howeverair bearings have their own set of difficulties. Another option is to use magneticbearings that are either passive or active. Passive permanent magnet bearings canbe used to eliminate friction [17] and can be easily miniaturized for micro machin-ing applications [18]. However similar to air bearings, passive magnetic bearingsare difficult to make stiff enough for micro machining which by its nature is con-stantly experiencing varying forces. However, active bearings can be used to botheliminate the friction and ball roundness errors while simultaneously having in-creased stiffness [19].1.3 Magnetically Levitated Rotary Table ArchitectureOne solution that overcomes most of the limitations the current technology has isto have a single moving mass that can be controlled to move in multiple DOF simul-taneously by having the actuation forces act directly on the table. This eliminatesthe challenges that stacked stages create while still allowing for decoupled con-troller design. Furthermore, this solution would use magnetic levitation to providea non-contact actuation force that allows for 6DOF movements. This is essentiallyan active bearing, however instead of only constraining it, can also provide theactuation forces for movement, reducing complexity and eliminating the issues as-3Figure 1.1: Proposed System Overviewsociated with ball and air bearings. An overview figure of the proposed system canbe seen in figure 1.1.This rotary table would allow for full rotation around one axis and limitedrotation in all other axes, for complete 6DOF. Benefits of such a design include acompact and lightweight table, when compared to traditional methods of achievingthis range of movement. Since it uses non-contact magnetic levitation there is nostatic friction making high precision positioning possible. To achieve high stiffnessthe positioning is accomplished using a closed loop control system which allowsfor high stiffness in all directions. The table has the permanent magnets mountedon the underside, creating a table that requires no cables or connections. The statorcoils can be manufactured using Printed Circuit Board (PCB) technology which isan established manufacturing process leading to an accurate coil layout at minimalcost. Using a PCB also creates a compact system with a high coil packing factor.1.4 Previous Non-contact Table WorkAn ideal stage for micro machining would allow for multiple DOF without usingmultiple stacked stages. It would also be stiff, have no friction, and be low massallowing for high precision and high speed positioning. Because this type of stageis desirable much research has been done in this area. The following sections willfirst discuss the previous research done for magnetically levitated planer motionmulti-degree of freedom actuators (none or limited rotation movement only). Next,magnetically levitated multi-degree of freedom rotary actuators will be discussed,which is most related to this project (limited or no translation with at least one axisof unlimited rotation).41.4.1 Multi-Degree of Freedom Planar ActuatorsTo keep the analysis relative, only planar motor actuators that are moving magnetconfiguration are discussed. If moving coil actuators are used they still suffer fromthe varying disturbance forces that the umbilical cord creates.In 1998 Kim and Trumper [1] developed a 6DOF ”high precision magneticlevitation stage for photolithography”. This stage allowed for movements of 50mmby 50mm in the planar directions and fine movement in the remaining axes. Itspositioning Root Mean Square (RMS) noise was 5nm. With this stage there werefour single dimension magnetic Halbach arrays mounted on the underside of themover. The stator was made by wire coils and had four parts, one under eachmagnet array. Each coil and magnet array can produce a levitation and translationforce, as shown in figure 1.2. To sense the location of the table three capacitiveprobes and three laser interferometers are used. This allows for non-contact highresolution position information.This stage was one of the first to demonstrate the advantages a 6DOF singlemass mover can offer. However this stage has limited applications because of thesize of the footprint. To achieve the 50mm by 50mm stroke the footprint needs tobe ∼300mm by ∼300mm [20] leading to a much larger footprint if a larger rangeof motion is required.Another magnetically levitated 6DOF motor design was presented in 2001 byHazelton et al. [2]. For this design the underside of the stage has a checkerboardstyle magnet array, as shown in figure 1.4. The circular stator coils are wound in thesame plane as the underside of the stage and are arranged in a grid, figure 1.3. Thisdesign allows for larger range of motion relative to the stator size when comparedto the Kim and Trumper design, however this suffers from other challenges suchas increased amplifier complexity due to the large number of coils. This designalso inherently has position dependent force variations leading to complex controlalgorithms to provide smooth motion.A similar design of an actuator was done by Jansen et al. [3] in 2007. Thisactuator is very similar to [2] however has a more complex 2-D Halbach magnetarray and uses racetrack coils setup in a chevron pattern. This can be seen in figure1.5. Very similar to the work done by [2], Wei et al. [21] modified the 2-D magnetic5Figure 1.2: ”Perspective view of the magnetically levitated stage; the motorforces acting on each magnet array are shown as arrows; the stators arelabeled I through IV” - Image and Caption from [1], [Precision Engi-neering, 22/2, Won-jong Kim, David L. Trumper, High-precision mag-netic levitation stage for photolithography, 66-77, Copyright (1998),with permission from Elsevier]Figure 1.3: Hazelton et al. 6DOF Stage Design Overview - Image from [2]6Figure 1.4: Hazelton et al. Stage Checkerboard Magnet Array - Image from[2]array to try and minimize the force ripple. This design, however, is complex, moreexpensive, and difficult to manufacture.Similar to the previous designs Compter et al. [4] patented a very similar designwhere the underside of the mover has a modified 2-D Halbach array and the coilsare racetrack shaped and are arranged with three side to side. Blocks of three coilsare then arranged in a checkerboard pattern, as seen in figure 1.6.All of these designs suffer from force ripple and position dependent forces asthe coils are discrete underneath the magnet arrays. The coils also have end turnsthat are always underneath the magnetic field, causing unwanted force couplingbetween axes and force ripple.7Figure 1.5: Overview Image of Jansen et al. Actuator Design - Image takenfrom [3], c©2007 IEEEFigure 1.6: Compter et al. Coil Arrangement Overview - Image taken from[4]8More recently in 2012 Lu and Irfan-ur rab [22] [5] developed a new 6DOF pla-nar stage that also is a moving magnet configuration. This stage, similar to the onedone by [1] uses four 1-D Halbach arrays. The difference is that the stator coilsare arranged so that each layer runs the whole length of the movable area. Orthog-onal layers, for planer motion, are stacked on top of each other in an every-otherconfiguration. An overview figure can be seen in figure 1.7. The main benefitsof this design are that it is easily scalable to large moving ranges. Other key ben-efits are that it eliminates force coupling and ripple from coil end effects as thecoils do not end or turn within the active area. Because of the coil and magnetarrangement there is essentially no coupling between the axes. However, since theHalbach arrays are made using discrete magnets (as is commonly done) there isstill some force ripple from the magnetics field’s higher order spacial harmonics.They have however come up with an elegant method of essentially eliminating thisripple which can found in [23]. Another key benefit to this design is that the statorcoils can be manufactured using a PCB allowing for high precision manufacturingat a reasonable cost. Using a PCB also creates a very compact and high packingfactor stator design.1.4.2 Multi-Degree of Freedom Rotary ActuatorsThe previous section focused only on moving magnet 6DOF magnetically actuatedstages which is similar to what we would like to achieve for a rotary stage. How-ever, very little work has been done in creating a magnetically actuated 6DOF rotarytable that has unlimited rotation in one axis. Therefore, this section will focus onthe work that has been done on projects that have some similarity to this objective.In 1991 a magnetically levitated 6DOF wrist joint was developed by Holliset al. [6]. This motor, however, does not have a free axis (i.e. unlimited rotationabout one axis). Another important difference is that this motor is a moving coilconfiguration. However, this motor could conceivably be made to have movingmagnets instead of moving coil by simply inverting it. A diagram of the motorcan be seen in figure 1.8. This now meets our 6DOF and non-contact criteria but itcannot rotate freely in any axis.Similar to the above stage Verma et al. [24] developed a magnetically levitated9Figure 1.7: Lu and Irfan-ur rab Planer Motor Overview - Taken from [5],[CIRP Annals - Manufacturing Technology, 61/1, Xiaodong Lu, Irfan-ur-rab Usman, 6D direct-drive technology for planar motion stages,359-362, Copyright (2012), with permission from Elsevier]6DOF stage in 2004. This stage uses six single degree of freedom Lorentz forceactuators to achieve 6DOF which allows for fine positioning in all axes, but over alimited stroke. Its range of rotation is limited to 3.5mrad, therefore eliminating thisas a possibility for a non-contact rotary table.In 2001 Liebman [25] developed a rotary-linear stage for high speed machin-ing. This stage provided both an unlimited rotation axis and a limited translationaxis with only one moving part. The other DOF were constrained with an air bear-ing. This project is similar, but still uses air bearings, however Liebman alongwith Trumper made an online public disclosure regarding a 6DOF ”MagneticallySuspended Artificial Heart Pump Impeller” [7]. This idea uses a magnetic arraymounted circumferentially on the underside of the actuator. The stator is made10Figure 1.8: Hollis et al. 6DOF Magnetically Actuated Wrist Join - TakenFrom [6], c©1991 IEEEwith three to six coil sets which can each provide both a levitation and rotationforce. They suggest that its position could be sensed using the back ElectroMotiveForce (EMF). However, no proof of concept prototype has been demonstrated butthe actuator configuration is a solid idea and one that can be built upon.More recently in 2010 LaunchPoint Technologies developed a lightweight highefficiency electric motor [8]. While this motor has only one DOF there are somesimilarities that should be mentioned. The motor uses a set of two circular axialHalbach arrays mounted circumferentially on the moving part of the motor aboveand below the stationary coils which can be seen in figure 1.10. This motor is11Figure 1.9: Trumper and Liebman Online Public Disclosure of 6DOF Mag-netically levitated rotary stage - Image from [7]capable of 5 hp/lb with an efficiency of ∼95% [26]. The magnetic field and forcegeneration is similar to that proposed by Trumper and Liebman in [7]. This motor,however only utilizes the driving force, not the levitation force that Trumper andLiebman proposed using. It does show, however, that such a design is capable ofhigh efficiency and power output.In conclusion, this project will build upon the work done previously to design,manufacture and test a 6DOF magnetically levitated rotary stage that has one free-axis.12Figure 1.10: LaunchPoint Technologies High Power Density Halbach ArrayMotor - Taken from [8]13Chapter 2Working Principle andElectro-Mechanical DesignIn this chapter the analysis of the force generation theory and force ripple attenu-ation considerations is presented. The electro mechanical design of the Magneti-cally Levitated 6DOF Table (MAGTABLE) is presented and the features and designdecisions are discussed.The force generation is produced from the Lorentz force which arises from theinteraction between charges (current) flowing through a magnetic field. A totalof eight forces are generated using four linear three-phase power amplifiers. Tooptimize the force generation for this application the magnetic field, coil designand configuration were iteratively designed in parallel.2.1 Working PrincipleControl of the MAGTABLE requires a minimum of six forces to completely con-strain it. However for this project we chose to use eight forces as it creates re-dundancy and allows for straight forward control. As mentioned above, the forcearises from the Lorentz force. The Lorentz force is represented by the followingequation:F = l(~B×~I) (2.1)14Figure 2.1: Halbach and Coils Cross Section ViewWhere l is the length of the current carrying wire, B is the magnetic field and Iis the current.The magnetic field is generated by 24 Halbach arrays mounted circumferen-tially under the Table while the current is carried by a stator that has coils alsoarranged circumferentially under the table, but mounted to the base. To producethe eight forces the stator coils are divided into quarters, each with their own am-plifier. The following analysis will be for one quarter, as they all are identical. Toaid in understanding, a cross section of one Halbach array is used to analyze theforce generation as shown in figure 2.1.The magnetic field on the underside of the Halbach array can be approximatedwith the following two equations which have previously been derived in [5].Bθe(θe,Z) =−Brsin(θe)eZNar (2.2)15BZ(θe,Z) = Brcos(θe)eZNar (2.3)Where Br is the magnetic field magnitude, r is the radius from the center of themover, Z is the distance from the base of the magnet (below magnet is negative)and NH is the number of Halbach arrays around the circumference. The electricalangle of rotation, θe, is related to the mechanical angle of rotation (θm) by thenumber of Halbach arrays used (NH).θe = NHθm (2.4)Looking just at coil ’A’ the Lorentz force in the Z and θe directions are givenby 2.5 and 2.6 respectively, with the total force from coil ’A’ represented by 2.7.FA,Z(θe,Z) = lBθeIA =−lBrsin(θe)eZNar IA (2.5)FA,θe(θe,Z) = lBZIA = lBrcos(θe)eZNar IA (2.6)~FA(θe,Z) =−lBrsin(θe)eZNar IAzˆ+ lBrcos(θe)eZNar IAθˆe (2.7)These forces have a mean of zero because of the sine and cosine functions.To create a mean force the current can be modulated at the same frequency andphase, however there is still the exponential term in the force which is non-idealas it creates a varying force that changes as the height of the table changes. It isdesirable to eliminate this non-linear behavior so that the control of the table canbe completed using simple classic controllers. This leads to the current throughcoil ’A’ looking like:IA =−IZsin(θe)e−ZNar + Iθecos(θe)e−ZNar (2.8)Therefore the force generation for coil ’A’ now looks like this:~FA(θe) = lBr{[IZsin(θe)2− Iθesin(θe)cos(θe)]zˆ+[−IZsin(θe)cos(θe)+ Iθecos(θe)2]θˆe}(2.9)16Using the following three trig identities the total can be re-written, shown in 2.11.sin(θ)2 = 1− cos(2θ)2; sin(θ)cos(θ) = sin(2θ)2; cos(θ)2 = 1+ cos(2θ)2(2.10)~FA(θe) = lBr[IZ1− cos(2θe)2− Iθesin(2θe)2]zˆ+lBr[−IZsin(2θe)2+ Iθe1+ cos(2θe)2]θˆe(2.11)The remaining coils produce a similar force, however the magnetic field isshifted by pi/3 for each coil due to its spacial location. This means the current forthose coils also needs to be shifted. This leads to the current for the remaining coilslooking like this:IB =−IZsin(θe−1pi3)e−ZNar + Iθecos(θe−1pi3)e−ZNar (2.12)IC =−IZsin(θe−2pi3)e−ZNar + Iθecos(θe−2pi3)e−ZNar (2.13)I′A =−IZsin(θe−3pi3)e−ZNar + Iθecos(θe−3pi3)e−ZNar (2.14)I′B =−IZsin(θe−4pi3)e−ZNar + Iθecos(θe−4pi3)e−ZNar (2.15)I′C =−IZsin(θe−5pi3)e−ZNar + Iθecos(θe−5pi3)e−ZNar (2.16)Which conveniently means that the following is also true:I′A =−IA; I′B =−IB; I′C =−IC (2.17)Using the same force derivation above, the forces from the remaining coils canbe found.17~FB(θe) = lBr[IZ1− cos(2θe− 2pi3 )2− Iθesin(2θe− 2pi3 ))2]zˆ+lBr[−IZsin(2θe− 2pi3 ))2+ Iθe1+ cos(2θe− 2pi3 ))2]θˆe(2.18)~FC(θe) = lBr[IZ1− cos(2θe− 4pi3 )2− Iθesin(2θe− 4pi3 ))2]zˆ+lBr[−IZsin(2θe− 4pi3 ))2+ Iθe1+ cos(2θe− 4pi3 ))2]θˆe(2.19)~FA′(θe) = lBr[IZ1− cos(2θe− 6pi3 )2− Iθesin(2θe− 6pi3 ))2]zˆ+lBr[−IZsin(2θe− 6pi3 ))2+ Iθe1+ cos(2θe− 6pi3 ))2]θˆe(2.20)~FB′(θe) = lBr[IZ1− cos(2θe− 8pi3 )2− Iθesin(2θe− 8pi3 ))2]zˆ+lBr[−IZsin(2θe− 8pi3 ))2+ Iθe1+ cos(2θe− 8pi3 ))2]θˆe(2.21)~FC′(θe) = lBr[IZ1− cos(2θe− 10pi3 )2− Iθesin(2θe− 10pi3 ))2]zˆ+lBr[−IZsin(2θe− 10pi3 ))2+ Iθe1+ cos(2θe− 10pi3 ))2]θˆe(2.22)The total force acting on the Halbach array is found by summing together theforces from all the coils. To simplify the force derivation Z and θe direction forceswill be done independently from each other.18Fzˆ(θe) = lBr[IZ12[6− cos(2θe)− cos(2θe−2pi3)− cos(2θe−4pi3)−cos(2θe−6pi3)− cos(2θe−8pi3)− cos(2θe−10pi3)]−Iθe12[sin(2θe)+ sin(2θe−2pi3)+ sin(2θe−4pi3)+sin(2θe−6pi3)+ sin(2θe−8pi3)+ sin(2θe−10pi3)]](2.23)However, this can be further simplified by using trig identities:cos(u− v) = cos(u)cos(v)+ sin(u)sin(v)sin(u− v) = sin(u)cos(u)− cos(u)sin(v)(2.24)Fzˆ(θe) = lBr[IZ12[6−6cos(2θe)[cos(0)+ cos(−2pi3)+ cos(−4pi3)+cos(−6pi3)+ cos(−8pi3)+ cos(−10pi3)]−6sin(2θe)[sin(0)+ sin(−2pi3)+ sin(−4pi3)+sin(−6pi3)+ sin(−8pi3)+ sin(−10pi3)]]−Iθe12[6sin(2θe)[cos(0)+ cos(−2pi3)+ cos(−4pi3)+cos(−6pi3)+ cos(−8pi3)+ cos(−10pi3)]−6cos(2θe)[sin(0)+ sin(−2pi3)+ sin(−4pi3)+sin(−6pi3)+ sin(−8pi3)+ sin(−10pi3)]]](2.25)Which can be simplified to:Fzˆ(θe) = lBr[IZ12[6−6cos(2θe)[0]−6sin(2θe)[0]]−Iθe12[sin(2θe)[0]− cos(2θe)[0]]](2.26)19Leading toFzˆ(θe) = lBrIZ3 (2.27)Which is a force in the zˆ direction that is only dependent on IZ and has no couplingwith Iθe . The same simplifications can be applied to the θˆe direction which leadsto:Fθˆe(θe) = lBrIθe3 (2.28)Which also is a force in the θˆe that is only dependent on Iθe and has no couplingwith Iθe . Summing these forces back together we get:~F(θe) = KIZ zˆ+KIθe θˆe (2.29)Where K = 3lBr, which is the motor constant. This means that with one set ofcoils and Halbach arrays two forces can be independently generated and controlled.It is also important to mention that the force is produced at the coil, not the magnet.2.1.1 Force Ripple CancellationThe above force analysis assumed a perfect Halbach array, in reality since we areonly using four discrete magnets to produce the magnetic field there are other har-monics. The main harmonics seen on the underside of the Halbach array are the1,5,9 and 13 cycles per 2pi electrical angle [27]. The 9th harmonic is canceled outby the multi-coil configuration and the 13th harmonic is really small, leaving the5th harmonic to be dealt with. As the distance from the bottom of the Halbacharray increases the harmonics magnitudes decrease quickly. Furthermore, becausethe coils being used are quite wide an averaging effect occurs which helps to mini-mize the harmonics as well. This is because the force is from the integration of thecurrent density with the magnetic flux density through-out the volume of the coil.Another method to help reduce the undesired harmonics is to use a split magnetarray configuration, however this has its own set of challenges, which is discussed20more in chapter 6.2.2 Electro Mechanical DesignThe magnetic field is created by using a Halbach array, which produces 1.4 timesthe force compared to using a simpler vertical only magnet configuration [28].However, the number and size of the magnets used can be changed. To build thestator coils a PCB was utilized as it allows for a compact design with a high copperfill factor. Due to many different manufacturing options for PCBs the design can beoptimized for the electro-mechanical system.2.2.1 Magnetic Array DesignAs mentioned above, Halbach arrays are desirable because they create a magneticfield that is 1.4 times stronger compared to using only vertically arranged magnets[28]. Another benefit of using a Halbach array is that the magnetic field on the topside is very small which is very desirable in this application as the workpiece willbe mounted on the top side of the table. On the underside of a Halbach array themagnetic field shape approximates a sinusoidal function.To have an intuitive understanding of the magnetic field a Halbach array pro-duces, two simple magnet configurations can be used to better visualize the field,which are shown in figure 2.2. In figure 2.2(a) the horizontal magnets are shownwith the simplified magnetic field shown in red. In figure 2.2(b) the vertical mag-nets are shown with the simplified magnetic field shown in blue. When they arecombined in figure 2.2(c) it is clear that on the top side of the Halbach array themagnetic fields oppose and cancel each other out while on the underside the mag-netic fields are in the same direction and combine to create a stronger field.When designing the magnetic array there are many factors to consider such as:Height to Width ratio, Spacial Wavelength, Shape of Magnets and Magnet material.This process was done iteratively to achieve a working solution that was both costeffective and had good performance.To fully optimize the magnetic field strength trapezoidal or wedge shaped mag-nets should be used. However, this requires having two custom magnets manufac-tured which increases the cost for two reasons. One reason is that the quantity for21Figure 2.2: Halbach Array Simplistic Magnetic Field22each type of magnet is half as much as if they are all the same, which increases thecost as there is a setup cost involved. Another factor is that during manufacturing,the magnets would be made in blocks, magnetized and then ground into the cor-rect shape, which adds additional cost. Therefore, since this prototype’s purpose isto demonstrate the working principle, the performance gains are small when com-pared to the increased cost. The main performance gain that trapezoidal shapedmagnets could produce is increased load capacity for the same size table. There-fore, for this project rare earth magnets with a square cross section were chosen.Within the rare-earth magnet family there are many different types and grades ofmagnets. Generally the Neodymimum Iron Boron rare earth magnets are labeledby their class and BHmax [MGOe] value. For this project N44SH magnet materialwas chosen as it has a relatively high magnetization (44 BHmax) capability withthermal properties that meet the requirements for this project. This leads to a rema-nence of 1.325T and the maximum operating temperature for the SH grade magnetis 150C [29].To optimize the magnet thickness or ’H’ a paper by Lu and Usman [30] sug-gest that the following equation can be used to optimize the system for maximumacceleration.a =JBrρmfM fH fC fG fW fT fS (2.30)Where J is the current density, Br is the magnet remanence and ρm is the mag-net density. The remaining factors are dimensionless factors that can be indepen-dently maximized. However, the only factor that contributes to the magnet designis the fH or height factor. From [30]:fH =λCH(1− e−H/λC) (2.31)However we do not only want to maximize acceleration we also want to maxi-mize the load capacity. Using the above information the equation for the maximumforce can be found as:F = wlJBr[λC(1− e−H/λC)] (2.32)Where w is the width of the individual magnet used in the four magnet Halbach230 5 10 15 20 25 30 3500.10.20.30.40.50.60.7 X: 1.258Y: 0.6397H/λCF*aOptimal Acceleration Force RatioFigure 2.3: F*a Optimization Plotarray and l is the length of the magnets. Therefore if no weighting factors are usedthe optimization function is F ∗a which is:F ∗a =wlJ2B2rH[λC(1− e−H/λC)]2 (2.33)The constants can be replaced with:K = wlJ2B2r ; (2.34)Leading to:F ∗a = K[λC(1− e−H/λC)]2H(2.35)If K and w is set to one, and λC = 4w2pi the relationship can be plotted, shownin figure 2.3, showing that the optimal thickness of the magnets is approximatelyslightly larger than λC.The number of arrays to use was partially determined by the size of the floatingtable. This was partially constrained by the area needed to mount workpieces, butalso by the amount of force required to hold the workpiece. The larger the diameter24the larger the operating forces can be. Therefore a size with a 280mm outsidediameter and 200mm inside diameter was chosen as it worked well with the sizeof magnet (figure 2.4). It also has 24 Halbach arrays which is divisible by four andwould be able to produce a large enough force to work well for micro machining.One main limiting constraint to the overall size was the working envelope of theThree Axis Micro Milling Machine that the Manufacturing Automation Laboratoryat UBC has made. This table needs to fit on top of the X-Y stage to allow for largertranslations while micro machining.With this diameter of Halbach arrays the average λC is:λC =λ2pi =2pi24 120mm2pi = 5mm (2.36)This works well as the magnet width to achieve this is 6.4mm and is near theoptimal thickness of 5∗1.258 = 6.29. Therefore the magnets can be made with asquare cross section which is the most cost effective configuration as only one typeof magnet is required.Having chosen the magnetic array configuration a simulation of the array wasrequired to predict the achievable forces and harmonics that would be produced.This magnetic field simulation also was required to simulate the force capabilitieswith different PCB designs. The simulation was completed using Comsol [31] asthe FEM engine and then Matlab to visualize the results. To display the field adirection and height below the magnet were chosen and then the intensity of themagnetic field was plotted. For the Z-direction two heights were chosen to showthe field: -0.5mm and -2.0mm below the magnets. These are shown in figure 2.5and figure 2.6, respectively. Similarly for the tangential or θ direction the same twoheights were chosen and are shown in figure 2.7 and figure 2.8. Both the tangentialand Z direction fields are quite similar but shifted by 90◦ electrical angle, fromeach other.Closer to the magnets the fields have more harmonics due to the discrete Hal-bach array, which is visible particularly near the highest and lowest point on thefield. A Fourier analysis of the harmonics was done at both heights. However, de-pending on the location along the radius the magnitude of the harmonics change.An analysis of the strength of the fundamental frequency was done along the ra-25Figure 2.4: Magnet Array Configuration (280mm OD, 200mm ID)Figure 2.5: Magnetic Field Simulation - Z-direction at -0.5mm below mag-nets26Figure 2.6: Magnetic Field Simulation - Z-direction at -2.0mm below mag-netsFigure 2.7: Magnetic Field Simulation - Tangential direction at -0.5mm be-low magnets27Figure 2.8: Magnetic Field Simulation - Tangential direction at -2.0mm be-low magnetsdius and the strength versus the radius can be seen in figure 2.9. Similarly for the5th, 9th and 13th harmonic the magnitude of the field along the radius is shown infigures 2.10, 2.11, and 2.12, respectively.An interesting discovery is that at certain radii each harmonic goes to zero.This occurs at approximately 122.5mm, 110mm, and 106mm for the 5th, 9th and13th harmonic, respectively. The fundamental spacial wavelength (λ ) at differentradii (r) can be found using:λ = 15◦ ∗pi180◦r (2.37)Therefore the spacial wavelength for a harmonic is simply the λ divided by theharmonic number. It appears that if the spacing between the magnets is a quarterof the harmonics’ wavelength, the harmonic goes to zero. An example of this canbe seen in 2.38.28100 105 110 115 120 125 130 135 1400.10.20.30.40.50.60.70.8Radius [mm]Magnitude [T]  Z = −0.5Z = −1Z = −2Z = −3Figure 2.9: Fundamental Frequency of Halbach Array Along Radius100 105 110 115 120 125 130 135 14000.020.040.060.080.10.12Radius [mm]Magnitude [T]  Z = −0.5Z = −1Z = −2Z = −3Figure 2.10: 5th Harmonic Frequency of Halbach Arrays Along Radius29100 105 110 115 120 125 130 135 14000.010.020.030.040.050.060.07Radius [mm]Magnitude [T]  Z = −0.5Z = −1Z = −2Z = −3Figure 2.11: 9th Harmonic Frequency of Halbach Arrays Along Radius100 105 110 115 120 125 130 135 14000.0050.010.0150.020.025Radius [mm]Magnitude [T]  Z = −0.5Z = −1Z = −2Z = −3Figure 2.12: 13th Harmonic Frequency of Halbach Arrays Along Radius30λ5 = 6.414mmλ9 = 3.200mmλ13 = 2.135mm(2.38)The spacing (S) between the magnets, which are 6.4mm wide, can be foundusing the following equation:S =3.75◦ ∗pi180◦r−6.4mm (2.39)This leads to the following spacings:S5 = 1.618mmS9 = 0.800mmS13 = 0.538mm(2.40)This leads to the ratio of S/λ to be:S5/λ5 = 0.25S9/λ9 = 0.25S13λ13 = 0.25(2.41)This ratio is interesting and may be useful in minimizing specific harmonicswhich cause force ripple, however due to lack of time, further research into thisarea has not been carried out.2.2.2 Stator DesignAs shown in figure 2.1 and in the force derivation this design uses a six coil config-uration as it increases the force capabilities and cancels out some of the non-idealharmonics. One way of driving this current is to use a six phase amplifier, howeverthe scope of this project did not include design and manufacture of our own ampli-fiers. Commercially there are many three phase linear and switching amplifiers tochoose from. Therefore, it is ideal if a three phase amplifier is used to power this31Figure 2.13: 6 Phase Commutation Diagramtable. As mentioned previously the following is true:I′A =−IAI′B =−IBI′C =−IC(2.42)This configuration can be hard wired ensuring that this relationship is alwaystrue. Looking at a vector diagram of the currents, shown in figure 2.13 the anglescan be seen. For a three phase system the current between each phase is offset by120◦ relative to the other two phases, while in six phase it is 60◦. Therefore a threephase amplifier can be used if it is wired to A, C and B’ as they are 120◦ apart.Knowing this, the star center can be designed to make this work: A’, C’ and B areall connected in the center. This allows any three phase amplifier to be used.The main objectives while designing the stator was to achieve a high copperfill factor and to keep the stator footprint as small as possible. However, the statoralso needs to work well with the amplifiers chosen and needs to take into account32the amount of heat it generates and its ability to dissipate the heat. Manufacturingoptions considered for the stator were PCB, Solid Copper cut to shape (water jet)and coil windings (wound using wire). Quite quickly coil winding was disqualifiedas an option due to the complexity of achieving high precision in this particularform factor. The Solid Copper was also disqualified because to achieve the benefitsof a high fill factor very few coil windings could be used, requiring large currentand very low voltage. Large currents require a large amplifier which drives thecost of the project up. Having large currents also increases the resistive heatingbecause the force is linearly proportional to the current while the power is a squaredfunction of the current.Power = RI2 (2.43)Therefore a PCB was chosen to be used for the stator. To achieve the currentcapacity and number of coils required a Heavy Copper PCB was required. Gen-erally, when talking about PCBs the units used are thousands of an inch [mil] andounces [oz] of copper.1oz = 1.38mil1mil = 0.0254mm(2.44)The manufacturer that we worked with had the capability to produce a heavycopper layer up to 20oz thick. The number of layers was limited by an overall boardthickness limit of 190mil (4.8mm). The minimum thickness of the insulatingfiberglass layers that go between the copper layers was 3mil. One other factorrequired to choose the layout was the minimum trace to trace spacing, which varieswith the copper thickness used. Each layer was put in series with the other layers.This means that the total current through each ’phase’ is the current through onelayer times the number of layers. Therefore by having thinner but more layers thedriving current required is less. However, by having thicker layers the fill factor(the amount of conductor to insulator) increases slightly. By considering all ofthese parameters and by communicating with the PCB supplier a design that utilized6oz copper layers with 16 layers was chosen. This is a cost effective design and33Figure 2.14: PCB Stackup Usedhas enough layers that a relatively low power current amplifier can be used. Thefinal stack-up used for the PCB is shown in figure 2.14 and has a total theoreticalthickness of 188mil (4.78mm).When designing the layout of the PCB the main goal was to maximize the min-imum cross sectional area of each trace. This is because the maximum current thatcan be passed through the board is limited by the current density, which was cho-sen as 20A/mm2. For standard copper wire that is wrapped in insulating materialand is not open to free airflow the standard maximum current density is 10A/mm2,however for PCBs the heat dissipation is better than an insulated wire so a highercurrent density is permissible. Therefore, with the final design the minimum crosssectional area achieved was 0.5mm2 which allows for up to ∼10A continuouscurrent. For this particular layout using buried vias between layer pairs (layers 2-3,4-5,6-7,8-9,10-11,12-13,14-15,16-17) helped optimize the cross sectional area.Because the buried vias are just between layer pairs the cost of manufacturing doesnot increase substantially. To make the vias have the same cross sectional area as34Figure 2.15: Manufactured PCBthe traces the barrel plating in the via needed to be 4oz thick. For the through holevias (they pass completely through the PCB) the plating could only be 1oz thick soa larger via was required. However due to space limitations a large enough via wasnot possible so a multi-via design was used. It was found that four vias fit and metthe cross sectional area requirements. The final manufactured PCB can be seen infigure 2.15. A sample of a layer pair layout can also be seen in figures 2.16 and2.17. The average packing factor for the stator coils is 64.4%.2.2.3 Mechanical Structure DesignThis subsection covers the mechanical design and layout of the MAGTABLE. Thefirst section explains the design of the moving table and its attributes while the sec-ond part discusses the design of the stator and method of mounting the senors. Thefinal section shows how the force is transmitted from the actuator to the mountingframe and discuses the effects of this force transmission. In figure 2.18 the overallsystem setup is shown mounted on a granite table for testing.35Figure 2.16: Layer 1 PCB LayoutMoverOnce the size of the Halbach array was determined the size of the table was quiteeasy to design. The table needs to be slightly larger than the magnet array to allowfor alignment and a particle intrusion seal, therefore a 10mm spacing around themagnets was given leading to a table diameter of 300mm. There are four maindesign criteria for the table:• It needs to provide a surface to mount the magnets to36Figure 2.17: Layer 2 PCB Layout• It needs to allow for the sensing metrology mounting• It must allow for workpieces to be attached to the top surface• It needs to be lightweight and stiffThese objectives were met by utilizing an aluminum honeycomb structure for thetable frame. A picture of the honeycomb used can be seen in figure 2.19 with themagnet assembly spacer already attached to the underside. This single piece ofhoneycomb weights only ∼741grams but has a very high bending stiffness. To37Figure 2.18: Assembled System Overview Testing Setupallow for mounting of the workpiece, holes were put in a grid pattern on the topside of the table. These holes allow rivet nuts to be installed which have an internalM4 thread, allowing for a workpiece to be mounted.On the underside of the table a plate is mounted which allows for the opticalencoder and a truncated spherical ball to be mounted. This plate also provides aflat surface for the capacitive probes to measure from. This plate is bolted to thebottom of the table with 16 M3 bolts. The Halbach arrays are mounted aroundthe outside perimeter of this plate. An aluminum spacer was used to help hold themagnets in place during assembly. Drawings for the honeycomb panel and centerplate are in A.1.The truncated spherical ball in the center allows for the table to be mechanicallycentered before takeoff and after landing. This is used to find the starting locationas the optical encoders are incremental and therefore lose their position when theyare powered down.38Figure 2.19: Honey Comb Panel with Magnet Spacer Mounted to BottomFigure 2.20: Bottom View of Table39Figure 2.21: Magnet Assembly JigAssembly of the magnets required a special jig and procedure. The forcesbetween the magnets are ∼100N leading to challenges in assembly. The assemblyjig shown in figure 2.21 was used in conjunction with the magnet spacer to hold themagnets in place while the epoxy cured. The jig was made out of a 3/8” aluminumplate. Each magnet had two M5 bolts used to hold it in place leading to a totalof 192 M5 threaded holes in the plate. The bolts had nylon acorn nuts placed ontheir heads to eliminate excess epoxy from bonding to the bolts. This works asthe epoxy used (Loctite E-121HP) does not bond to nylon strongly. To ensure thatthe magnets had some epoxy underneath them two shallow ’grooves’ were madearound the circumference of the bottom of the mover, which are visible in figure2.20.Each magnet was coated with a thin layer of epoxy on the three sides that arein contact. The following procedure was followed to assemble the magnets:1. One of the horizontal magnets and then every fourth magnet was placed.These magnets all face the same direction. Each magnet was clamped inplace by lightly tightening the two bolts above it.2. The other horizontal magnets were then placed between the previously mountedmagnets. These were also clamped in place by lightly tightening the two40Figure 2.22: Horizontal Magnet Assemblybolts above each magnet. (The magnets are now in a ’neutral’ position withvery little force acting between them) This can be seen in figure 2.22.3. The first vertical magnet was placed with the north pole facing away from thebottom of the mover and between two vertical magnets that each had theirnorth poles facing towards each other. These magnets where not clampeddown firmly yet as the field held them half way up (figure 2.23) and drewthem in so caution was required when placing them. Similar to before everyfourth magnet was placed in the same way.4. The remaining magnets were placed with their north pole facing the honey-comb.5. Now all the jig bolts were tightened in a circular pattern until they all had thesame torque and the magnets all appeared flush on the bottom surface, seenin figure 2.24.While this method of assembly worked quite well if it was repeated two thingsshould be changed:• The jig should be made out of thicker aluminum as it deflected too muchwhen all the bolts were tightened.41Figure 2.23: Third Magnet AssemblyFigure 2.24: Completed Magnet Assembly42Figure 2.25: Cross Section of Rotary Table Assembly• The bolts used should have a longer threaded section, which for this projectwere actually ordered, but due to time constraints were not used.Mechanical Stator MountThe stator is made from a PCB, as outlined in section 2.2.2, however it still needs tobe mounted to the base and held relative to the metrology system. A cross sectionview can be seen in figure 2.25. The underside of the PCB is epoxied to an engi-neered quartz circular slab which has a circular section cut out of the center. Engi-neered quartz was chosen as a support for the PCB because of its thermal stabilityand electrical conductivity properties. Because it is electrically non-conductive itwill not produce damping through the eddy current effects.Mounting of the PCB and engineered quartz base is accomplished by a mechan-ical clamp. This is discussed further in section 2.2.3. Within the center of the PCBthe metrology hub is mounted. The metrology hub has three main purposes whichare to:• Mount the sensors• Hold a fine thread adjusting screw• Provide protection to the sensors in the event of an uncontrolled landingOn the underside of the table there is a truncated spherical ball, this ball, whenthe table is not floating, rests in the cone on the top of a fine thread screw. This43Figure 2.26: Assembled Stator Assemblyallows for the screw to be adjusted so that it just touches the truncated ball whenit lands but does not interfere once it is levitating. Figure 2.26 shows the statorassembly. In the center metrology hub a groove near the perimeter of it can beseen. This groove protects the sensors in the event of an uncontrolled landing andfrom particle ingression. The four capacitive probes and four optical encoders canbe seen as well.Mounting of the capacitive sensor is completed by four aluminum clamps thatwere designed specifically for this project. These clamps have three points thatclamp onto the capacitive probe by one screw mounted on the side of the clamp.Once they are attached to the capacitive probe they are installed into the metrologyhub by two mounting screws. The optical encoders are bolted directly to the insideof the metrology hub which can be seen in figure 2.27. The metrology hub consistsof two pieces, the top plate, where all the sensors and components are mountedto and the bottom support spider which supports the top when the table rests onit. The bottom spider support can be seen in figure 2.28 and is bolted to the topsection with eight bolts.44Figure 2.27: Metrology Hub Bottom ViewFigure 2.28: Side View of Metrology Hub45Figure 2.29: Non-Desirable Force PathForce TransmissionWhen designing a high precision system the path of the force transmission must beconsidered. If the force path goes through the metrology frame then varying forceswill affect the location of the sensors leading to errors in the stage position. Anexample of a non-ideal setup can be seen in figure 2.29. Here, the red line illus-trates where the force path is located. Since the engineered quartz stator supportis mechanically clamped between the base and the metrology hub the force pathgoes through the metrology hub. With this setup when the applied force varies, theforce through the metrology hub also varies causing small, but measurable deflec-tions in the metrology hub. If the metrology hub deflects, the sensors move relativeto the ground, resulting in the table moving relative to the ground. Since this is aprecision application this effect is undesirable.To alleviate this issue the engineered quartz support can be epoxied to the basering and a small spacer can be inserted underneath the metrology hub to ensurethere is a gap between it and the engineered quartz support. This can be seen infigure 2.30. The force path now does not pass through the metrology hub providinga more stable and precise measurement.2.2.4 Force to motion system overviewSo far the force generation principle, magnetic field analysis, stator design andmechanical overview have been discussed. The purpose of all of these systems46Figure 2.30: Desirable Force Pathis to work together to produce a magnetically levitated stage with 6DOF. Thisis achieved, as mentioned earlier, by creating eight individually controlled forces.These eight forces act on the floating table allowing for full 6DOF with some re-dundancy. The location of these eight forces can be seen in figure 2.31 where thegreen circles indicate the four levitation forces and the orange arrows indicate thelocation of the four translation forces.47Figure 2.31: Acting Location of Actuation Forces48Chapter 3Metrology DesignOne of the main benefits of the 6DOF MAGTABLE are its frictionless attributes. Tomaintain this attribute the sensing method also needs to be non-contact. Similar tothe force, to achieve 6DOF position measurements the table requires a minimumof six sensors to measure its position. However, to simplify the control and buildin redundancy a total of eight sensors were used: four optical encoders and fourcapacitive probes. To measure the Z, A and B axes four capacitive probes wereused and positioned as shown in figure 3.1. Position feedback for the remainingthree axes, X,Y and C is achieved using four optical sensors mounted underneath anoptical grating disk also shown in figure 3.1. The optical encoders are not typicallyused in applications where the optical grating can move relative to the encoder readhead with 6DOF. Therefore, the alignment tolerances of the optical encoders areutilized to allow for small movements in 6DOF. Due to the metrology setup and theoptical encoder’s alignment tolerances the range of motion for the Mover is shownin table 3.1.Axis X Y Z A B CRange ±200µm ±200µm ±150µm ±0.54deg ±0.54deg UnlimitedTable 3.1: Range of Motion49Figure 3.1: Non-Contact Sensor Overview3.1 Capacitive SensorsThe four capacitive sensors work by creating an alternating voltage which causescharges between the probe and the target to continually reverse their direction. Thiscreates an alternating current which can be measured by the amount of capacitancebetween the sensor and target. As the distance to the target changes the amount ofcurrent also changes which is detected by a change in the capacitance. However,since there is an alternating electric field produced by each capacitive sensor theyall need to be synchronized so that they do not interfere with each other. This isdone automatically within the capacitive probe module [32]. For the sensing towork properly the target needs to be grounded, or have at least 100 times morecapacitance than the probe does [33]. Since the target or stage is floating, there isno direct connection to ground. However, the underside of the stage was designedto create a large flat conductive surface that is close to the sensing hub and thetop surface of the PCB. The PCB was designed with a large ground plane on thetop layer to help increase the capacitance of the stage. Because the stage has alarge surface that is parallel and close to a ground plane the estimated capacitanceof the stage, relative to the ground, is well over 100 times the capacitance of oneprobe. This allows for accurate position measurement despite not having a physicalconnection to the electrical ground. Measuring the tilt on axes A and B requiresusing two of the capacitance probes while measuring the Z height averages the four50capacitive sensors leading to the following equations:θA = tan−1 (P2−P4d) (3.1)θB = tan−1 (P3−P1d) (3.2)Z =P1+P2+P3+P44(3.3)3.2 Optical Encoder SetupThe three remaining degrees of freedom are measured using the optical encodersas follows:X =k1(E2−E4)2(3.4)Y =k1(E3−E1)2(3.5)θC =k2(E1+E2+E3+E4)4(3.6)Where k1 is a mm per count constant and k2 is a radians per count constant ofthe encoders. Since the optical encoders have a limited range that can be exceededif the table is tilted too much a more robust algorithm was developed to detectwhen a sensor stopped working and automatically switch to using the remainingthree optical encoders. To detect when a sensor has stopped working the followingequation is analyzed in real time:CheckSum = |E1+E3− (E2+E4)| (3.7)As long as all the encoders are reading correctly the CheckSum signal shouldalways be near zero, within the four times resolution of the encoders. However,when one encoder goes out of range and loses its position then the error signaljumps quickly. If the error is detected fast enough the other three sensors canseamlessly be used, with reduced resolution. Therefore, when the CheckSum value51rises above a set threshold the following equations are analyzed to determine whichencoder has given the fault. The equation with the highest value is assumed to havethe fault:Encoder1 : |E1−θ |Encoder2 : |E2−θ |Encoder3 : |E3−θ |Encoder4 : |E4−θ |(3.8)Whereθ = E1+E2+E3+E44(3.9)Then, based on which encoder has failed, one of the following equation sets areused for the position feedback.Encoder 1 FailsθC =k2(E2+E4)2X =k1(E4−E2)2Y = k1(Ck2−E3)(3.10)Encoder 2 FailsθC =k2(E1+E3)2X = k1(E4−Ck2)Y =k1(E1−E3)2(3.11)Encoder 3 FailsθC =k2(E2+E4)2X =k1(E4−E2)2Y = k1(E1−Ck2)(3.12)Encoder 4 FailsθC =k2(E1+E3)2X = k1(Ck2−E2)Y =k1(E1−E3)2(3.13)Once the encoder comes back online and is passed by index on the grating,the system can switch back to using all four encoders. An illustration of this isshown in figure 3.2. In this example encoder two was disconnected while the tablewas rotating at 20 Revolutions Per Minute (RPM). As can be seen in figure 3.2 theencoder was disconnected just after one second, at this point the system automat-52Figure 3.2: Optical Encoder Monitoringically switched to using only the other three encoders for position feedback. Justpast two seconds the encoder was reconnected, but its position was still unknownas the optical grating’s index mark had not yet passed that encoder. Once the indexpassed the encoder five and a half seconds the position feedback was switched backto using all four encoders.A similar algorithm could be implemented for the capacitive probes where thefour probes could be used to ensure they are all working properly. This could beaccomplished using the following equation.CapacitanceProbeCheckSum =P1+P32−P2+P42(3.14)Once an error is detected however, there is no elegant way to detect which sen-sor has failed. This is because the capacitive sensors are basically measuring theangle and location of a plane in space. When they no longer equate to a flat planean error has occurred, however which capacitive probe failed is unknown. The ca-pacitive sensors are more robust than the optical encoders and have a large enoughrange that it is impossible for them to go out of range while still having the opticalencoder within range. Therefore, such an algorithm has not been implemented forthe capacitive sensors.533.3 Initialization ProcedureTo operate the table in a known, repeatable location, the absolute position of thetable relative to the base needs to be known. However, the optical encoders areincremental therefore their position is lost when they are powered down. To over-come this limitation a startup method was developed that utilizes the index mark onthe optical grating (which is absolute). Initially before the index mark has passedan encoder a position is assumed. This position was measured using the truncatedball to center the table and then counting the number of counts between the en-coders. Therefore to start the table, encoder two needs the index mark passed overit before power is applied. This gets the measured position close enough to theactual position to commutate the current commands correctly. The table can thenbe powered and levitated. At this point the remaining three axes are assuming aposition. To update the encoder’s positions the table needs to be commanded torotate slowly. As the index mark passes each encoder the system updates the ac-tual position. Once the index mark is passed by all three encoders, the system willretain this position until the next power down.3.4 Geometric Distortion EffectsTypically for a rotary optical encoder the optical grating’s rotation axis, relative tothe optical encoder does not change. However, for this application this is not thecase. Because of this some geometric errors are introduced. As the grating is tiltedaround the A and B axes the location above the encoder shifts. This can be seen infigure 3.3.In figure 3.3(a) the blue line represents the table tilted only around the Y axiswhile figure 3.3(b) shows the table tilted around both Y and X axes. The value ’Q’shown in the figure is the error the encoders see, which is perfectly canceled outfor X and Y translations, however this error is seen in the rotation around the Zaxis measurement.V = tan(θB)r (3.15)54Figure 3.3: Geometric Encoder Error DiagramQ = tan(θA)V (3.16)Q = tan(θA) tan(θB)r (3.17)This causes a measurement error in the rotation around the Z axis by:θQ =Qr= tan(θA) tan(θB) (3.18)Since this error is seen on both encoders the resultant equation for the C axisis:θC =k2((E1−θQ)+E2+(E3−θQ)+E4)4(3.19)This error will cause the whole table to rotate to compensate, leading to thefollowing equation:θCcompensated =k2((E1+φ)+(E2+φ))+(E3+φ)+(E4+φ)4(3.20)Where φ is the compensation for the error. This leads to an offset on each55encoder such that:4φ =−2θQφ = −θQ2(3.21)This means that as it is tilted around any combination of the two tilt axes (Aand B) each encoder has an error associated with that. This can be compensatedwithin the feedback decoupling algorithm.These errors however, do not affect the translation axes, which are now:Y =k1((E3−θQ)− (E1−θQ))2=k1(E3−E1)2(3.22)Similarly encoders E2 and E4 see the same error when tilted:X =k1((E2−θQ)− (E4−θQ))2=k1(E2−E4)2(3.23)This is the same as before, leading to no error from this effect.56Chapter 4Controller DesignTo aid in controller design, two assumptions were initially made:• The plant can be modeled as a simple mass• Each axis is decoupled from the other axesThese assumptions proved to hold true well enough for a stable system the firstattempt. Once the system was stable and operating, closed loop frequency responsemeasurements were made for each axis to get a more accurate plant measurement.4.1 Axis DecouplingTo initially design the controllers the plant model had to be developed. The mass ofthe table and the rotational inertia around the rotary axes was initially estimated us-ing the 3D solid model used for manufacturing the components. This proved to bequite accurate. Next, the eight forces needed to be decoupled to produce decoupledmotion in only the desired axis. This was accomplished using a geometric analysis.For rotation around the X and Y axis (A and B) the location where the levitationforce acts is important to get the correct force to torque conversion. Therefore,figure 4.1 shows the geometric force location of the system. In the diagram Ractis the radius that the average force per Halbach array acts on while FZdist is the Zforce distribution along that arc. FZ is the sum of FZdist and RZ is the radius whereit acts.57Figure 4.1: Z Force Acting LocationTherefore the following equations can solve for RZ:FZdist =2FZpiRact(4.1)Using the sum of the moments around the center:FZRZ = Ractpi/4∫−pi/42FZpiRactcos(θ)Ractdθ (4.2)RZ =2√2Ractpi (4.3)Similarly for the forces that act in the translation directions (X and Y) themagnitude is found as follows (4.2):Fθ =TorqueRact(4.4)58Figure 4.2: Translation Force MagnitudeFθdist =2FθpiRact(4.5)FY =pi/4∫−pi/4FθdistRactcos(θ)dθpi (4.6)FY =2√2Fθpi (4.7)Therefore the dynamic equations can be found, as shown in 4.8.59FXFYFZTATBTC=MX¨MY¨MZ¨JxA¨JyB¨JzC¨=0 0 −2√2pi 0 0 02√2pi 02√2pi 0 0 0−2√2pi 0 0 00 1 0 1 0 1 0 10 0 0 2√2Ractpi 0 0 0 −2√2Ractpi0 −2√2Ractpi 0 0 02√2Ractpi 0 0Ract 0 Ract 0 Ract 0 Ract 0Fθ1FZ1Fθ2FZ2Fθ3FZ3Fθ4FZ4(4.8)This dynamic equation was used in the decoupling and commutation block,shown in figure 4.3 allowing the controllers to only output a single force or torque.The commutation block takes the force or torque commands and based on thepresent position, (rotation angle and height) correctly commutates and applies thecorrect currents to produce that force or torque in the desired axis. The derivationfor the commutation method can be seen in Chapter 2.4.2 Initial Controller DesignThe initial controller design used a simple lead lag compensator with an integrator,as seen in 4.9.C(s) = Kαll√αllWc s+11√αWcs+1s+ Wc10s(4.9)Where Wc is the desired crossover frequency of the Negative Loop TransferFunction (NLT), K is the gain to achieve the crossover frequency and φ is the phaseshift required to meet the desired phase margin at the crossover frequency, leadingto:αll =1+ sin(φ)1− sin(φ) (4.10)Based on only the plant model, the above controllers were used with a ’de-signed’ bandwidth of 200Hz. The actual bandwidth varied as the plant model was60Figure 4.3: Closed Loop Control Overviewnot perfect. This was stable, but not robust (initial levitation was done with con-servative 40Hz bandwidth controllers). The plant of each axis was then measuredusing a frequency response method. This is completed by inputing a sinusoidalsignal over a range of different frequencies and amplitudes. The input and outputare recorded and the gain and phase can be measured from the results.4.3 Plant ResponseThe actual Plant Frequency Response Function (FRF) compared with the modeledPlant FRF can be seen in figures 4.4, 4.5, 4.6, and 4.7.4.4 Classic High Performance Controller DesignTo achieve a higher bandwidth and more robust system a loop shaping controldesign method was used. Achieving the desired phase margin and crossover fre-quency required using two controllers in series which are shown in 4.11 and 4.12.C1(s) = Kc,1sWc,1/α1 +1sWc,1α1 +1(4.11)C2(s) = Kc,2sWc,2/α2 +1sWc,2α2 +1(4.12)Where Kc is a gain constant, Wc is the desired crossover frequency of the NLTand α is a design constant, which is different than the αll used in the lead-lag61controller. To eliminate steady state error an integrator was added to the controller.I(s) =s+ Wc,110s(4.13)To attenuate higher frequency responses a low pass filter was implemented,shown below.FLP(s) =11+ sWLP(4.14)In the low pass filterWLP is the break frequency. Because the table is not purelya floating mass there are resonance frequencies. To combat this effect two notchfilters were implemented in the control design.N1(s) =s2 +2sσ1W1 +W 21s2 +2sσ2W2 +W 22(4.15)N2(s) =s2 +2sσ3W3 +W 23s2 +2sσ4W4 +W 24(4.16)In the notch filter W1 and W2 are the break frequencies and σ1 and σ2 are thecorresponding damping ratios for the notch filter.By combining all of these loop shaping functions together, the final controltransfer function is represented in 4.17. The parameters were tuned to manipu-late the NLT into having a shape that had the desired crossover frequency with thecorrect phase. It was also important to ensure that if there is more than one cross-ing each crossing also had the minimum phase margin required. Since some ofthe axes had resonance frequencies that were lower than the desired bandwidth thenotch filters were used to help mitigate the effect of the resonance frequencies. Thecontroller parameters used for the final tests are shown in table 4.1.C f inal(s) =C1(s)C2(s)I(s)FLP(s)N1(s)N2(s) (4.17)62XXXXXXXXXXXParametersAxisA B C X Y ZKc,1 2352.8 2384.4 12668 1669900 1729000 365900Kc,2 0.2542 0.2566 0.1252 0.2870 0.28579 0.3248α1 8 8 8 8 8 8α2 4 4 8 4 4 4Wc,1[Hz] 150 150 300 300 300 150Wc,2[Hz] 150 150 300 300 300 180WLP [Hz] 120 150 360 450 420 3000σ1 0.06 0.05 0.3 0.06 0.06 0.1σ2 1 1 0.5 1 1 1σ3 1 1 0.3 1 1 0.3σ4 0.08 0.07 0.5 0.08 0.08 1W1 [Hz] 206 295 1000 885 1200 405W2 [Hz] 210 299 800 889 1280 395W3 [Hz] 184 267 1000 832 1040 1850W4 [Hz] 180 263 800 820 1000 1820Table 4.1: Controller Parameters4.5 Controller ResultsAfter an iterative loop shaping procedure, where the measured plant was used topredict the new NLTs, the final NLTs were measured from the system using a sinesweep method. The results can be seen in figures 4.8, 4.9, 4.10, and 4.11. Duringthe sine sweep test it was observed that the table created a very audible noise. Thisled to a realization that this table may be able to play music, like a speaker. Totest this, one of the spare Analog to Digital Converters (ADC)s was implementedto convert an audio signal into a position command for either the X,Y, or Z axisin real time. Remarkably this actually plays music fairly well with fairly goodfidelity. The X and Y axes reproduce the sound with better clarity, due to theirhigher bandwidth; however, because of their limited surface area in the directionof motion the sound is not as loud as the Z axis direction.63100 101 102 10310−1010−5100105Frequency [Hz]Magnitude [rad/Nm]100 101 102 103−400−300−200−1000Frequency [Hz]Phase [deg]  A,B Modeled PlantA Measured PlantB Measured PlantFigure 4.4: A and B Axis Plant Frequency Response100 101 102 10310−1010−5100105Frequency [Hz]Magnitude [rad/Nm]100 101 102 103−350−300−250−200−150−100−50Frequency [Hz]Phase [deg]  C Modeled PlantC Measured PlantFigure 4.5: C Axis Plant Frequency Response64100 101 102 10310−1010−5100Frequency [Hz]Magnitude [m/N]100 101 102 103−350−300−250−200−150−100Frequency [Hz]Phase [deg]  X,Y Modeled PlantX Measured PlantY Measured PlantFigure 4.6: X and Y Axis Plant Frequency Response100 101 102 10310−1010−5100Frequency [Hz]Magnitude [m/N]100 101 102 103−600−500−400−300−200−100Frequency [Hz]Phase [deg]  Z Modeled PlantZ Measured PlantFigure 4.7: Z Axis Plant Frequency Response65100 101 102 10310−410−2100102104Frequency [Hz]Magnitude [rad/rad]100 101 102 103−500−400−300−200−1000Frequency [Hz]Phase [deg]  A Measured NLTB Measured NLTFigure 4.8: A and B Axis Measured NLT FRFs100 101 102 10310−2100102104106Frequency [Hz]Magnitude [rad/rad]100 101 102 103−500−400−300−200−1000Frequency [Hz]Phase [deg]  C Measured NLTFigure 4.9: C Axis Measured NLT FRF66100 101 102 10310−2100102104Frequency [Hz]Magnitude [m/m]100 101 102 103−500−400−300−200−1000Frequency [Hz]Phase [deg]  X Measured NLTY Measured NLTFigure 4.10: X and Y Axis Measured NLT FRFs100 101 102 10310−2100102104106Frequency [Hz]Magnitude [m/m]100 101 102 103−500−400−300−200−1000Frequency [Hz]Phase [deg]  Z Measured NLTFigure 4.11: Z Axis Measured NLT FRF67Chapter 5Experimental Results5.1 Control MeasurementsMeasurements of the system’s FRFs was accomplished by providing a disturbancesignal ’S’, as shown in figure 5.1. Two measurement points were used to capturethe results for each axis, labeled as ’In’ and ’Out’. In figure 5.1 the connections areshown only for the X axis, however the connections were setup similarly for the re-maining axes. The disturbance signal was a sine signal with a range of frequenciesfrom 1Hz to 2000Hz. The disturbance signal was sent for multiple cycles so thatan accurate measurement of the phase and magnitude could be achieved. From thismeasurement the NLT can be found as follows:NLT =CP =OutIn(5.1)Where ’C’ represents the controller and ’P’ the plant.From this one measurement both the plant and closed loop response can beextracted. Because the controller was designed the FRF of it is known. Thereforethe plant can be found as shown in 5.2.P =NLTC(5.2)Using Black’s Law the closed loop response can be found from the NLT usingequation 5.3.68Figure 5.1: FRF Measurement MethodAxis A B C X Y ZCL Bandwidth ∼ 300Hz ∼ 300Hz ∼ 400Hz ∼ 550Hz ∼ 550Hz ∼ 250HzTable 5.1: Closed Loop Bandwidth ResultsClosed Loop =NLT1+NLT(5.3)5.1.1 Plant Frequency ResponseUsing the above equations the plant response for each axis was measured and canbe seen in figures 5.2, 5.3, 5.4, 5.5, 5.6, and 5.7.5.1.2 Closed Loop ResponseFrom the same measurement used to find the NLT the closed loop response for eachaxis can be found using equation 5.3. The closed loop bandwidth for each axis canbe seen in table 5.1.The closed loop FRF results can be seen in figures 5.8, 5.9, 5.10, and 5.11.5.2 Static StiffnessStatic Stiffness of the MAGTABLE is ’infinite’ until the maximum current capacityis reached, at which time the table can no longer hold its position. This ’infinite’69100 101 102 10310−1010−5100A Axis Plant Frequency ResponseFrequency [Hz]Magnitude [rad/N]100 101 102 103−400−300−200−1000Frequency [Hz]Phase [deg]Figure 5.2: A-Axis Plant FRF100 101 102 10310−1010−5100B Axis Plant Frequency ResponseFrequency [Hz]Magnitude [rad/N]100 101 102 103−400−300−200−1000Frequency [Hz]Phase [deg]Figure 5.3: B-Axis Plant FRF Result70100 101 102 10310−1010−5100105C Axis Plant Frequency ResponseFrequency [Hz]Magnitude [rad/Nm]100 101 102 103−300−250−200−150−100Frequency [Hz]Phase [deg]Figure 5.4: C-Axis Plant FRF Result100 101 102 10310−1010−5100X Axis Plant Frequency ResponseFrequency [Hz]Magnitude [rad/N]100 101 102 103−400−300−200−100Frequency [Hz]Phase [deg]Figure 5.5: X-Axis Plant FRF Result71100 101 102 10310−1010−5100Y Axis Plant Frequency ResponseFrequency [Hz]Magnitude [rad/N]100 101 102 103−350−300−250−200−150Frequency [Hz]Phase [deg]Figure 5.6: Y-Axis Plant FRF Result100 101 102 10310−1010−5100Z Axis Plant Frequency ResponseFrequency [Hz]Magnitude [m/N]100 101 102 103−600−400−2000Frequency [Hz]Phase [deg]Figure 5.7: Z-Axis Plant FRF Result72100 101 102 10310−1100101A,B Axes Closed Loop − Frequency [Hz]Gain [rad/rad]  A AxisB Axis−3dB100 101 102 103−250−200−150−100−500A,B Axes Closed Loop − Frequency [Hz]Phase [deg]Figure 5.8: A and B Axes Closed Loop FRF Results100 101 102 10310−1100101C Closed Loop − Frequency [Hz]Gain [rad/rad]  C Axis−3dB100 101 102 103−250−200−150−100−500C Axis Closed Loop − Frequency [Hz]Phase [deg]Figure 5.9: C Axis Closed Loop FRF Result73100 101 102 10310−1100101X,Y Axes Closed Loop − Frequency [Hz]Gain [mm/mm]  X AxisY Axis−3dB100 101 102 103−250−200−150−100−500X,Y Axes Closed Loop − Frequency [Hz]Phase [deg]Figure 5.10: X and Y Axes Closed Loop FRF Results100 101 102 10310−1100101Z Axis Closed Loop − Frequency [Hz]Gain [mm/mm]  Z Axis−3dB100 101 102 103−250−200−150−100−500Z Axis Closed Loop − Frequency [Hz]Phase [deg]Figure 5.11: Z Axis Closed Loop FRF Result740 1 2 3 4 501020304050607080Total Force [N]Current per Amplifier [A]  Measured PointsBest Fit LineSimulated ForceFigure 5.12: Current vs. Force Resultsstiffness comes from the integrator in the closed loop control. To demonstrate theload capacity known weights were placed on the table, and the current output forone amplifier was recorded. The position of the table was also monitored and itbehaved as expected and did not move. Maximum current capacity of the tablewas designed to be 10A continuous current with a peak current that could be twiceas high. The results shown in figure 5.12 demonstrate a load of ∼70N, includingthe table’s mass of ∼24N, using ∼ 4.7A through one amplifier, for a total currentthrough the PCB of 18.8A. This is at its nominal flying height of 1.6mm abovethe stator. The simulated force also matches very closely to the measured forceand is within ∼ 5% of one another. The differences could partially come frommeasurement errors as well as from variances in the actual magnetic field.5.3 Regulation ErrorDemonstration of the table’s positioning accuracy can be seen from the RMS regu-lation error in each axis while commanding the table to be stationary (but floating).The regulation error can be seen in table 5.2. It should be noted that the axes75Axis A B C X Y ZRMS Error 1.14µrad 1.14µrad 0.23µrad 12.5nm 10.8nm 55.2nmTable 5.2: RMS Regulation Errorthat use the capacitive probes for their position measurement (A, B, Z) have muchhigher regulation error. This is because even though the optical encoders and ca-pacitive probes have similar resolution, the ADCs used for the capacitive probeslimit the resolution. Measurement range of the capacitive probes is 2mm and thecontrol computer’s (dSpace) ADCs have 16 bits. Therefore the resolution can befound by:Resolution =2mm216= 30.5ηm (5.4)However this is an ideal resolution because any noise in the analog signal willincrease that value.To further show the table’s precise positioning capabilities a small staircasetrajectory was given to the table. Each staircase trajectory was given to only oneaxis at a time while recording all the axes positions. The size of the staircase stepwas made to be similar to the regulation error.5.4 Transient ResponseDemonstration of the transient response can be seen by looking at the step re-sponse. Each axis was given the step input individually. The results can be seen infigure 5.19.5.5 Dynamic StiffnessMeasurement of the dynamic stiffness was accomplished using an impact hammerconnected to a high speed ADC. Also connected to this ADC was a Laser DopplerVibrometer (LDV) which was used to measure the displacement of the table. ThisADC was connected to a computer running CutPro measurement and simulationsoftware [34]. Dynamic stiffness was measured by lightly tapping the table withthe impact hammer while recording the response of the table. This also serves to760 1 2 3 4 5 6 7 8 9 10−10010A Axis [urad]0 1 2 3 4 5 6 7 8 9 10−505B Axis [urad]0 1 2 3 4 5 6 7 8 9 10−101C Axis [urad]0 1 2 3 4 5 6 7 8 9 10−50050X Axis [ηm]0 1 2 3 4 5 6 7 8 9 10−50050Y Axis [ηm]0 1 2 3 4 5 6 7 8 9 10−2000200Z Axis [ηm]Time [s]Figure 5.13: A-Axis Staircase Trajectory (1µrad Step Size)770 1 2 3 4 5 6 7 8 9 10−505A Axis [urad]0 1 2 3 4 5 6 7 8 9 10−10010B Axis [urad]0 1 2 3 4 5 6 7 8 9 10−101C Axis [urad]0 1 2 3 4 5 6 7 8 9 10−50050X Axis [nm]0 1 2 3 4 5 6 7 8 9 10−50050Y Axis [nm]0 1 2 3 4 5 6 7 8 9 10−2000200Z Axis [nm]Time [s]Figure 5.14: B-Axis Staircase Trajectory (1µrad Step Size)780 1 2 3 4 5 6 7 8 9 10−505A Axis [urad]0 1 2 3 4 5 6 7 8 9 10−505B Axis [urad]0 1 2 3 4 5 6 7 8 9 10−202C Axis [urad]0 1 2 3 4 5 6 7 8 9 10−50050X Axis [nm]0 1 2 3 4 5 6 7 8 9 10−50050Y Axis [nm]0 1 2 3 4 5 6 7 8 9 10−2000200Z Axis [nm]Time [s]Figure 5.15: C-Axis Staircase Trajectory (0.5µrad Step Size)790 1 2 3 4 5 6 7 8 9 10−505A Axis [urad]0 1 2 3 4 5 6 7 8 9 10−505B Axis [urad]0 1 2 3 4 5 6 7 8 9 10−101C Axis [urad]0 1 2 3 4 5 6 7 8 9 10−1000100X Axis [nm]0 1 2 3 4 5 6 7 8 9 10−50050Y Axis [nm]0 1 2 3 4 5 6 7 8 9 10−2000200Z Axis [nm]Time [s]Figure 5.16: X-Axis Staircase Trajectory (20nm Step Size)800 1 2 3 4 5 6 7 8 9 10−505A Axis [urad]0 1 2 3 4 5 6 7 8 9 10−505B Axis [urad]0 1 2 3 4 5 6 7 8 9 10−202C Axis [urad]0 1 2 3 4 5 6 7 8 9 10−50050X Axis [nm]0 1 2 3 4 5 6 7 8 9 10−1000100Y Axis [nm]0 1 2 3 4 5 6 7 8 9 10−2000200Z Axis [nm]Time [s]Figure 5.17: Y-Axis Staircase Trajectory (20nm Step Size)810 1 2 3 4 5 6 7 8 9 10−505A Axis [urad]0 1 2 3 4 5 6 7 8 9 10−505B Axis [urad]0 1 2 3 4 5 6 7 8 9 10−202C Axis [urad]0 1 2 3 4 5 6 7 8 9 10−50050X Axis [nm]0 1 2 3 4 5 6 7 8 9 10−50050Y Axis [nm]0 1 2 3 4 5 6 7 8 9 10−5000500Z Axis [nm]Time [s]Figure 5.18: Z-Axis Staircase Trajectory (60nm Step Size)820 0.0500.511.522.5Displacement [um](a) X Axis − Time [s]0 0.0500.511.522.5Displacement [um](b) Y Axis − Time [s]0 0.0500.511.522.5Displacement [um](c) Z Axis − Time [s]0 0.0500.020.040.06Displacement [mrad](d) A Axis − Time [s]0 0.0500.020.040.06Displacement [mrad](e) B Axis − Time [s]0 0.0500.020.040.06Displacement [mrad](f) C Axis − Time [s]Figure 5.19: Step Response Resultsvalidate the magnitude of the built in metrology system as it is an external mea-surement. The experimental setup for measuring the Z-Axis can be seen in figure5.20.The dynamic stiffness from the experiment can be seen in figure 5.21. Themodel and experimental results agree quite well after ∼10Hz, as the LDV cannotmeasure lower than that. At higher frequencies there is also some variance whichcan be explained by noting that our model assumed a perfectly rigid body floatingin space while in reality the frame is not perfectly rigid and has its own resonancefrequencies. Another notable difference between our model and the actual systemis the damping that the actual system has due to eddy currents caused by a changingmagnetic field as the table moves/rotates.83Figure 5.20: Impact Hammer Experiment Setup5.5.1 Cross Dynamic StiffnessTo measure the coupling between axes the cross dynamic stiffness was found. Sim-ilar to the dynamic stiffness test setup, the cross dynamic stiffness between the Zand X axes was measured by impacting the table in the Z direction and measuringthe movement in the X direction, using the LDV. Similarly the Z and Y axis crossdynamic stiffness was also found. The results can be seen in figure 5.22.5.5.2 Modal AnalysisThe dynamic stiffness results in the Z axis showed a low stiffness around 24Hzand also a little drop in stiffness around 200Hz. To determine if this was from thecontroller or honeycomb deflecting a modal analysis was carried out. This wasdone by using the LDV to measure the displacement in the center and using the im-pact hammer to hit at numerous points on the surface in a grid pattern. The values84100 101 102 10310−1100101102Stiffness (N/µm)(a) X Axis Stiffness − Frequency [Hz]  MeasuredModeled100 101 102 10310−1100101102Stiffness (N/µm)(b) Y Axis Stiffness − Frequency [Hz]  MeasuredModeled100 101 102 10310−1100101102Stiffness (N/µm)(c) Z Axis Stiffness − Frequency [Hz]  MeasuredModeledFigure 5.21: Dynamic Stiffness Results85101 102 103100101102Stiffness (N/µm)(a) X Axis Cross Stiffness with Z Axis − Frequency [Hz]101 102 103100101102Stiffness (N/µm)(b) Y Axis Cross Stiffness with Z Axis − Frequency [Hz]Figure 5.22: Cross Axes Dynamic Stiffnesswere captured and analyzed using [34]. The results show three main frequencies at∼24Hz, ∼200Hz, and ∼1827Hz. These values correspond well to the results cap-tured in the dynamic stiffness test. For the ∼24Hz modal shape the results can beseen in figure 5.23. Since the deflection is nearly equal across all points it appearsas if this is a controller mode, which is also the case for the ∼200Hz mode, shownin figure 5.24. The remaining modal shape can be seen in figure 5.25. This modeis a bending mode of the honeycomb structure. Therefore the two lower frequencymode shapes can potentially be minimized using a more advanced controller.86Figure 5.23: 24Hz Z Axis Modal ShapeFigure 5.24: 200Hz Z Axis Modal Shape5.6 Power AnalysisAn analysis of the power used by the table was conducted at various RPMs todetermine how much heat the PCB is dissipating and how much power goes tothe eddy current damping. This experiment was carried out by monitoring onephase of one of the quarters, therefore the results need to be multiplied by twelve(four quarters and three phases) to achieve the total power consumed by the stator.An electrical model of the motor can be seen in figure 5.26 where points P1 andP2 indicate the voltage measurement points. The actual setup on the PCB for thevoltage measurement can be seen in figure 5.27. The current was monitored usinga Tekatronix TCPA300 current probe, attached to quadrant three’s phase A input.The total power consumed by the stator can be found using the following for-mula:Figure 5.25: 1827Hz Z Axis Modal Shape87Figure 5.26: Electrical Model of MotorFigure 5.27: Power Analysis Experimental SetupPA,T =VA,RMSIA,RMS cos(φVA−IA) (5.5)Where φVA−IA is the phase between the voltage and current, the sign does not matter.We also know that the resistive power loss is:PA,R = RAI2A,RMS (5.6)880 1 2 3 4 5 6 7−5051015202530Revolutions per Second [Hz]Watts per Phase, per Quarter  Total PowerOhm lossEddy lossFigure 5.28: Power Analysis Results for One Phase of One Quarter (For totalpower multiply by 12)Knowing this the eddy current power can be found as:PA,eddy = PA,T −PA,R (5.7)With that information the following results were obtained, shown in figures5.28, 5.29, and 5.30.The results seem reasonable, showing that the eddy current power loss is quitehigh even at relatively low speeds. However, a closer inspection of the phase be-tween the current and voltage reveals that the voltage is actually lagging the currentwhich can be confirmed in figure 5.30. At first glance this seems counter intuitiveas an inductor should make the current lag the voltage, not the other way around.However, if the model is analyzed with both the levitation and rotation currents thisdoes in-fact agree with the electrical model. An analysis of the system is carriedout as follows (all of the equations are done from the perspective of the stationarycoil):In figure 5.31 the stationary coil for phase A can be seen with the current goinginto the page. The BZ and Bθ magnetic fields can be seen. The co-ordinate systemis set up as if the coil is moving, to aid in the understanding, however the magnetic890 1 2 3 4 5 6 7051015202530354045Revolutions per Second [Hz]Phase Lag of Voltage Relative to Current [deg]Figure 5.29: Power Analysis Phase Measurement Results0 0.05 0.1 0.15 0.2−3−2−10123Time [s]Voltage [V], Current [A]  VoltageCurrentFigure 5.30: Raw current and voltage measurement at 1 revolution per second[Hz] rotation rate90Figure 5.31: Phase A Coil with Z and θ Magnetic fieldsfield is actually moving.BZ,Coil =−Bmax sin(θ) (5.8)Bθ ,Coil = Bmax cos(θ) (5.9)From Chapter 2 the current through coil A is:IA = Iθ sin(θ)+ IZcos(θ) (5.10)Knowing this the phase of the resistive voltage is the same as IA and can befound as:VR = IAR (5.11)We also know that the voltage from the inductor will be lagging IA by 90◦VL = LdIAdt(5.12)Therefore the only unknown voltage is the back EMF voltage (VBEMF ). Thiscan be found by using Faraday’s law:EMF = υBl (5.13)Where υ is the velocity, B is the magnetic field and l is the length of the wirein the magnetic field. The velocity direction must be perpendicular to the magnetic91Figure 5.32: Voltage - Current Phase Vector Diagramsfield, leading to:VBEMF = θ˙BZl (5.14)Therefore since Iθ and BZ have the same phase VBEMF has the same phase asIθ .If the vectors of the voltages are drawn, a better understanding of what is hap-pening can be seen. Therefore three cases are considered:(a) When the stage is floating, but not rotating (Iθ = 0)(b) When both the force in the Z and θ directions are the same (IZ = Iθ )(c) At very high rotational velocity when the rotation force is much larger than thelevitation force (IZ = 0)In figure 5.32(a) case (a) can be seen. Here VL = 0 because the system isnot rotating, meaning the current is not changing. The phase between the mea-sured voltage and current should be zero which aligns with the experimental re-sults. Once the stage is rotating figure 5.32(b) is a better representation of whatis happening. From this diagram the voltage lags the current, which is also whatwas measured. During really high speeds (figure 5.32(c)), the system behaves aswe initially thought, just as an inductor and the current lags the voltage. Thereforethe measured results align with our model of the system. An important note is thatthe maximum speed is limited by the eddy current damping and is ∼ 400RPM as92the heat generation at that speed causes the stator’s temperature to rise quickly. Ifhigher speeds are required, a more effective method of heat removal is required.93Chapter 6ConclusionsA novel, six degrees of freedom (DOF) magnetically levitated high precision non-contact rotary stage has been developed for precision positioning of micro-machiningsystem. The design, fabrication and experimental validation have been completed.The stage has a maximum measured load capability of 50N (in addition to the ta-ble’s mass) with a predicted maximum load capacity of 120N. Positioning accuracyis better than 55nm in the translation axes and better than 1.2µrad in the rotationaxes. The range of motion is ±200µm in X and Y translation and ±150µm in thelevitation direction. The roll and pitch have a range of ±0.54◦ with unlimited yaw.The actuator design is based on the following principles. By utilizing a Halbacharray and a six coil configuration two independently controlled forces are applied atthe coils. Such a system allows for easy control and has very low force ripple. Thecurrent is supplied from four commercially available three phase linear amplifiers.By creating the stator with four quadrants that each have their own amplifier, eightindependent forces can be controlled; four in the levitation direction and four inthe tangential direction. This allows for full 6DOF control of the stage.To optimize the force generation, the magnet size and number of magnets wereoptimized with the stator to achieve good force generation that is still reasonable tomanufacture. This resulted in having a magnet size that has a square cross sectionwith a side length of 6.4mm. A total of 96 magnets are mounted on the undersideof the stage. The stator was made using heavy copper PCB technology. It has 18layers, the internal 16 layers are 6oz copper and form the coils of the stator.94The mechanical design for the metrology frame allows for standard sensors tobe used. A better design was proposed to help stabilize the sensors under varyingloads. This small change can easily be made to the current setup. To supportthe stator PCB a piece of engineered quartz was used due to its electrically non-conductive properties. This setup is designed to be mounted on top of UBC’sManufacturing Automation Laboratory’s Micro Milling machine’s X-Y table.The three translational and three angular positions of the stage are measured byfour capacitive sensors and four optical encoders, which are non-contact devices.The mechanical design created high capacitance between the stage and the statorto ensure that the capacitance was over 100 times greater than the capacitance of aprobe. This ensures that the measurement is accurate, even with no physical groundon the stator. To sense the translation a novel approach was taken which utilizedthe alignment tolerance of the optical encoders. This, however, is what limits therange of motion for the stage.Although the 6DOF stage has coupled motion, the system is decoupled into sixindependent motion systems with uncoupled, dedicated controllers. By utilizingdecoupled forces and position feedback the uncoupled controller design is allowed.This was further simplified by having only a moving mass as the dynamic equation.All controllers have a phase margin of at least ∼ 50◦ with a bandwidth between∼ 250Hz to ∼ 550Hz.The stage has been built and its capabilities have been experimentally demon-strated. Static stiffness was close to the predicted results, and tracking accuracywas better than 13nm in X and Y axes, 55nm in z axis, 1.14µrad in the A and Baxes and 0.23µrad in the C axis. The power analysis showed that the effect ofthe eddy current damping is quite significant at higher angular speeds. The impactmodal tests showed that the dynamic stiffness is quite low at ∼ 20Hz in the Z axisand ∼ 50Hz in the X and Y axes.6.1 Future ResearchTo further minimize the force ripple seen as the stage rotates a split magnet arraycould be utilized. This would be similar to the work done by Usman and Lu in[23]. However, since the magnet arrays are not linear along the radial direction the95array needs to be split in such a way that the average force on both sides of the splithave the same average force. This will, however, create a torque, therefore morework is required to optimize the magnet array to minimize the torque ripple.One of the known geometric errors is the capacitive probe angular measure-ment. Generally the capacitive probes take the average area above the probe andfind the distance to that location. However, when the target is angled relative to theprobe’s sensing face, there is a known distortion that occurs leading to measure-ment errors, as outlined in [35]. Verification and then compensation for this errorcould increase the accuracy of this stage.The optical encoders are not being used in their typical application as the readhead is moving relative to the optical grating with the 6DOF stage. While the opti-cal encoders automatically adjust the signal strength as the distance to the gratingchanges, the effects of angular tilt is unknown. Therefore, to ensure the accuracy ofthe optical encoders, a method for detecting the small errors associated with 6DOFmovements should be developed. If these errors are significant, compensation forthese errors should be implemented.Dynamic stiffness is low, especially between∼ 20Hz to∼ 50Hz due to the con-trollers used. More advanced controllers can be designed to increase the dampingat the low frequency range, while retaining the high bandwidth.96Bibliography[1] W Kim and D Trumper, L. High-precision magnetic levitation stage forphotolithography. Precision Engineering, 22/2:66–77, 1998. → pages viii,5, 6, 9[2] J Hazelton, A, B Binnard, M, and M Gery, J. Electric motors and positioningdevices having moving magnet arrays and six degrees of freedom, March 272001. URL http://www.google.ca/patents/US6208045. 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Rotary-Linear Axes for High Speed Machining. PhD thesis,MIT, Cambridge MA, USA, 2001. → pages 10[26] G Long. A high power density, high efficiency axial flux halbach arraymotor/generator, April 23 2010. URL http://www.launchpnt.com/portals/53140/docs/dual-halbach-motor-presentation.pdf. Website last accessed onOctober 9, 2014. → pages 12[27] U R Usman, I and X Lu. Force ripple attenuation in 6 dof levitated planarmotor. In 2nd International Conference on Virtual Machining Process,Technology (VMPT 2013), 2013. → pages 20[28] D Trumper, M Williams, and T Nguyen. Magnet arrays for synchronousmachines. Industry Applications Society Annual Meeting, pages 9–18, 1993.→ pages 21[29] Amazing Magnets. Magnet grade chart, September 2014. URLhttps://www.amazingmagnets.com/magnetgrades.aspx. → pages 23[30] X Lu and U R Usman, I. A novel long-stroke planar motor. In AmericanSociety for Precision Engineering (ASPE). → pages 23[31] COMSOL. Comsol muliphysics 4.3b, 2013. URL http://www.comsol.com.→ pages 25[32] Lion Precision. Capacitive sensor operation and optimization, 2014. URLhttp://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html. → pages 5099[33] Lion Precision. Capacitive sensor phasing and ungrounded targets, 2013.URL http://www.lionprecision.com/tech-library/technotes/cap-0022-ungrounded.html.→ pages 50[34] Manufacturing Automation Laboratories. Cutpro 9.3, 2013. URLhttp://www.malinc.com/products/cutpro/#overview. → pages 76, 86[35] Lion Precision. Error sources: Probe/target angle, March 2004. URLhttp://www.lionprecision.com/tech-library/technotes/tech-pdfs/cap-0010-probe-tilt.pdf. → pages 96100Appendix ASupporting MaterialsA.1 Mechanical DrawingsThe mechanical drawings for the key components are included here.10111223344A AB BC CD DSHEET\ 1\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMDMDMarkDyckMD10\/30\/201310\/30\/201310\/30\/201310\/30\/2013DWG\ NO2013-001TITLESensor\ Mount\ PlateSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04DRAWINGS\ ON\ THIS\ PAGE\ ARE\ FOR\ REFERENCE\ ONLY102SECTION\ A-ASCALE\ 1\ :\ 1A A11223344A AB BC CD DSHEET\ 2\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMDMDMarkDyckMD10\/30\/201310\/30\/201310\/30\/201310\/30\/2013DWG\ NO2013-001TITLESensor\ Mount\ PlateSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04AB.0008.0308.19213.76022.26029.34335.00040.7365.65710.47013.76022.26029.34335.00040.736.0005.6578.75010.4706.3208.0308.192.0006.3208.0308.19211.28013.76022.26024.73029.34335.00040.7365.6578.75010.47011.28013.76022.26024.73029.34335.00040.736.0005.6578.75010.4706.3208.0308.192.0006.32011.03011.28017.50024.73026.73011.03011.28017.50024.73026.730.0008.75011.03011.28017.50024.73026.73011.03011.28017.50024.73026.730.0002.0005.0005.3006.00016.000? .025? .050 A BUnless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .200 A B? .025 A? .050 A B? .025 A? .100 A B2\ X\ .750\ X\ 45.0?\ ChamferD? .050 DMATERIAL:\ 6061-T6\ ALUMINUMNOTE:\ HIDDEN\ LINES\ NOT\ SHOWN\ FOR\ CLARITY.0008.00025.0008.00025.000.0008.00025.0008.00025.0002\ X\ .750\ X\ 45.0?\ Chamfer103SECTION\ C-CSCALE\ 1\ :\ 1DETAIL\ \ DSCALE\ 3\ :\ 1CCD11223344A AB BC CD DSHEET\ 3\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMDMDMarkDyckMD10\/30\/201310\/30\/201310\/30\/201310\/30\/2013DWG\ NO2013-001TITLESensor\ Mount\ PlateSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04B8\ X\ ?3.400?0.100\ THRU?\ ?6.500?0.100\ ?\ 10.000- 0.0000.200+M2x0.4\ -\ 6HROLL\ TAP?8.8908.940\ THRU?\ ?10.414?0.100\ ?\ 4.000?0.100?109.000? .050 A B? .050 A B? .050 A B? .050 A BUnless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .200 A B4\ X\ ?9.750?0.100\ THRU? .100 A B? .10015.0?TYP\ 45.0?TYP\ R48.5004\ X\ R4.0008\ X\ \ MAXR4.0008\ X\ R4.0008\ X\ \ MAXR1.59016\ X\ \ MAXM3x0.5\ -\ 6H\ ?\ 8.000?0.20ROLL\ TAPR51.300R57.700?137.000?121.000R11.3004\ X\ R.2508\ X\ \ MAX? .050 A B? .100 A B? .050 A B? .100 A B? .025 A BNOTE:\ HIDDEN\ LINES\ NOT\ SHOWN\ FOR\ CLARITY15.0?TYP\ M3x0.5\ -\ 6HROLL\ TAP? .100 A BMATERIAL:\ 6061-T6\ ALUMINUM\ 10411223344A AB BC CD DSHEET\ 1\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/5\/2013DWG\ NO2013-002TITLESensor\ Mount\ SupportSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04DRAWINGS\ ON\ THIS\ PAGE\ ARE\ FOR\ REFERENCE\ ONLY105SECTION\ A-ASCALE\ 2\ :\ 1AA11223344A AB BC CD DSHEET\ 2\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/5\/2013DWG\ NO2013-002TITLESensor\ Mount\ SupportSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04BA.0008.0009.25511.29013.77025.0008.0009.25511.29013.77025.000.0008.0009.25511.29013.77025.0008.0009.25511.29013.77025.000? .050Unless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .200 A B.0007.50012.4994\ X\ ?3.400?.100\ THRU?\ ?6.500?.100\ ?\ 6.000- .000.200+4\ X\ ?2.500?.100\ THRU4\ X\ ?3.400?.100\ THRU?\ ?6.500?.100\ ?\ 6.000- .000.200+? .100 A B? .100 A B? .150 A BMATERIAL:\ 6061-T6\ ALUMINUM10611223344A AB BC CD DSHEET\ 3\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/5\/2013DWG\ NO2013-002TITLESensor\ Mount\ SupportSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04B22.0?TYP\ 22.0?TYP\ 15.0?TYP\ \ 8\ X\ ?3.400?.100\ THRU?\ ?6.500?.100\ ?\ 9.000- .000.200+8\ X\ ?3.600?.100\ THRU8\ X\ ?3.400?.100\ THRUR48.500TYP\ ?121.000?14.000R3.000TYP\ ? .100 A B? .100 A B? .100 A BUnless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .200 A B?109.00015.0?TYP\ 15.0?TYP\ R48.500TYP\ MATERIAL:\ 6061-T6\ ALUMINUM10711223344A AB BC CD DSHEET\ 1\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/5\/2013DWG\ NO2013-003TITLEMoverSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04DRAWINGS\ ON\ THIS\ PAGE\ ARE\ FOR\ REFERENCE\ ONLY108SECTION\ C-CSCALE\ 1\ :\ 1DETAIL\ \ DSCALE\ 3\ :\ 1DETAIL\ \ ESCALE\ 3\ :\ 1CCDE11223344A AB BC CD DSHEET\ 2\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/5\/2013DWG\ NO2013-003TITLEMoverSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04?196.000?180.000 ?130.000R57.000TYP\ R32.000TYP\ 45.0?TYP\ 4.000TYP\ 3\ X\ ?2.438?.050\ THRU?\ ?4.763+.200.000+\ ?\ 2.184?.100SPACED\ 120?\ APART11.3?60.0?TYP\ 16\ X\ ?3.400?.075\ THRU?\ ?6.500?.080\ ?\ 3.000- .000.200+6\ X\ ?2.400?.10\ THRUB ? .025 A? .100 A B?186.000?122.000?49.000Unless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .200 A B? .100 A B? .050 A B?9.525NOTE:\ HIDDEN\ LINES\ NOT\ SHOWN\ FOR\ CLARITY112.700103.70056.50012.7006.350-.05.00+?3.264?.10\ THRU? .050 A BMATERIAL:\ 6061-T6\ ALUMINUM109SECTION\ F-FSCALE\ 2\ :\ 1FF11223344A AB BC CD DSHEET\ 3\ \ OF\ 3\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/5\/2013DWG\ NO2013-003TITLEMoverSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04A? .025 C BUnless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .200 A BMATERIAL:\ 6061-T6\ ALUMINUMC? .050 A B? .025? .025 A B? .050.0003.4004.4005.333.0003.73311.40011011223344A AB BSHEET\ 1\ \ OF\ 2\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/4\/2013DWG\ NO2013-004TITLECapacitive\ Sensor\ MountSIZEBSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04DRAWINGS\ ON\ THIS\ PAGE\ ARE\ FOR\ REFERENCE\ ONLY111SECTION\ A-ASCALE\ 3\ :\ 1AA11223344A AB BSHEET\ 2\ \ OF\ 2\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 11\/4\/2013DWG\ NO2013-004TITLECapacitive\ Sensor\ MountSIZEBSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04AB.0001.0005.0005.6578.0001.0005.7368.000.0003.0004.30812.50018.15721.58922.00025.000.0004.0008.000?3.400?.100\ ?\ 8.000?.100M3x0.5\ -\ 6HROLL\ TAP9.580? ?.05R2.5003\ X\ ? .200 A BUnless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .010 A2\ X\ ?2.400?.100\ THRU? .050 A B? .025? .100 A B? .100 A BMATERIAL:\ 6061-T6\ ALUMINUM60.0?60.0?11211223344A AB BC CD DSHEET\ 1\ \ OF\ 2\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 10\/11\/2013DWG\ NO2013-005TITLELanding\ PadSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04DRAWINGS\ ON\ THIS\ PAGE\ ARE\ FOR\ REFERENCE\ ONLY113SECTION\ A-ASCALE\ 3\ :\ 1DETAIL\ \ BSCALE\ 16:1A AB11223344A AB BC CD DSHEET\ 2\ \ OF\ 2\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck 10\/11\/2013DWG\ NO2013-005TITLELanding\ PadSIZECSCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04?56.000?52.000 ?46.000AB?49.00060.0?6\ X\ ? .050 A BUnless\ Otherwise\ Specified:1.\ All\ dimensions\ in\ mm2.\ All\ dimensions\ are\ Basic\ 2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .100 A BMATERIAL:\ 6061-T6\ ALUMINUMM2x0.4\ -\ 6HROLL\ TAP? .100 A B? .050.0003.0003.152114SHEET\ 1\ \ OF\ 1\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck10\/15\/2013DWG\ NOMagnetTITLEMagnet\ for\ Rotary\ MotorSIZEA4SCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV3\ 39.9840.00\ 6.406.38\ 6.406.38AN?SB? .02 A B CCTYP\ .25\ X\ 45.0?\ Chamfer? .05 A B CUnless\ Otherwise\ Specified:1.\ All\ dimsensions\ in\ mm2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ MaxNotes:1.\ Part\ fully\ magnetized\ to\ not\ less\ than\ 1.325T\ in\ direction\ shown\ by\ the\ S?N\ arrow.2.\ North\ side\ of\ magnet\ should\ be\ clearly\ marked3.\ Coated\ with\ 10-20\ micron\ VACCOAT\ 20011\ coating\ or\ similar4.\ All\ dimensions\ apply\ after\ coatingMATERIAL:\ N44SH115SHEET\ 1\ \ OF\ 1\ DRAWNCHECKEDQAMFGAPPROVEDMarkDyck10\/15\/2013DWG\ NOMoverHoneyCombTITLESIZEA4SCALEUBC\ Mechanical\ Engineering\ -\ Precision\ Mechatronics\ LabREV04?300.008\ X\ M3x0.5\ -\ 6H\ ?\ 8.006\ X\ ?5.00\ ?\ 5.00SPACED\ AT\ 60??4.65\ ?\ 5.0025.40Unless\ Otherwise\ Specified:1.\ All\ dimsensions\ in\ mm2.\ All\ tolerances\ to\ 3.\ All\ surfaces\ 63Ra\ (1.6\ um)\ or\ better4.\ Break\ all\ corners\ and\ edges\ 0.5\ Max? .1 A BABMaterial:Aluminum\ HoneycombFace\ Plates:\ 0.063"\ thickCore\ 1\/4"\ cell\ size.\ ?285.00.0012.5021.7535.2537.5062.5012.5021.7535.2537.5062.50.0012.5028.5037.5062.5012.5028.5037.5062.504\ X\ M2x0.4\ -\ 6H\ ?\ 6.008\ X\ M3x0.5\ -\ 6H\ ?\ 8.00 8\ X\ M2x0.4\ -\ 6H\ ?\ 6.0045.0?TYP\ 44\ X\ ?6.75\ ?\ 19.00HIDDEN\ LINES\ REMOVED\ FOR\ CLARITY\ 116UBC Precision Mechatronics Laboratory Mark Dyck, November 13, 2013 Layers Connected by Buried Vias2,3NOTES: LEGEND: 4,51) Material: FR-4 COPPER 6,72) Layers: 18 CORE 8,93) Silk Screen Colour: White PREPREG 10,114) Solder Mask Colour: Navy Blue 12,135) Clip silkscreen if covering exposed pads 14,156) All Burried and Blind Vias must have MINIMUM 5.0 mil copper plating (3.62 oz) 16,177) All through holes must have 2.07 mil copper plating [1.5 oz]8) Immersion Gold Finish(nominal 189 mil stack height)Layer# Type Gerber File Via Configuration Thickness [mil] Final Copper Weight [oz]Top Overlay .GTOTop Solder .GTS1 Top Copper .GTL 2.76 2PREPREG 32 Signal .G1 8.28 6CORE 3.03 Signal .G2 8.28 6PREPREG 34 Signal .G3 8.28 6CORE 3.05 Signal .G4 8.28 6PREPREG 36 Signal .G5 8.28 6CORE 3.07 Signal .G6 8.28 6PREPREG 38 Signal .G7 8.28 6CORE 3.09 Signal .G8 8.28 6PREPREG 310 Signal .G9 8.28 6CORE 3.011 Signal .G10 8.28 6PREPREG 312 Signal .G11 8.28 6CORE 3.013 Signal .G12 8.28 6PREPREG 314 Signal .G13 8.28 6CORE 3.015 Signal .G14 8.28 6PREPREG 316 Signal .G15 8.28 6CORE 3.017 Signal .G16 8.28 6PREPREG 318 Bottom Copper .GBL 2.76 2Bottom Solder .GBSBottom Overlay .GBOTOTAL BOARD THICKNESS (mils): 189117A.2 Setup MethodWhen setting up the capacitive probes the distance from the sensing surface to themounting surface of the aluminum clamp needs to be set at 5.9mm. This can beaccomplished by setting a jig up that has a known distance between a flat metalsurface and the front surface of the mounting clamp. If the capacitive probes areturned on and the position monitored, the depth can be accurately set. The offsetfor the capacitive probes is 250µm from the surface of the sensing face to the target.At this offset the capacitive probes read negative 10 volts. Therefore the distancewhere the probe measures -10V needs to be 6.150mm from the front face of themounting clamp.The optical encoders were set up using shims to space them on two sides withinthe pockets on the machined metrology hub. The location of the mounting positionrelative to the ’center’ can be seen on the datasheet drawing for the small rotarygrating.A.3 Suppliers Information118Capacitive Probe SupplierCompany Lion PrecisionContact Kent QueenslandAddress 563 Shoreview Park Road, Shorview, MN, 55126, USAOptical Sensor SupplierCompany MicroE SystemsContact David SmithAddress 125 Middlesex Turnpike, Bedford, MA, 01730, USAPCB SupplierCompany Saturn Electronics Corp.Contact Perry SutariyaAddress 28450 North Line Road, Romulus, MI, 48174, USALinear Amplifier SupplierCompany Varedan TechnologiesContact Bob DanekAddress 3870 Del Amo Blvd.,Suite 503, Torrance, CA, 90503, USAPower Supply SupplierCompany ACA TMetrix Inc.Contact Tyrene ShagolAddress 5805 Kennedy Road, Mississauga, ON, L4Z-2G3, CanadaMagnet SupplierCompany Adams Magnetic ProductsContact Patrick HannaAddress 88 Larch Avenue, Elmhurst, IL, 60126, USAMachined Parts SupplierCompany A One Machinery Ltd.Contact Rudi PankratzAddress 8002 Evans Parkway, Chilliwack, BC, V2R-5R8,Canada119A.4 Data Sheets120C LOPTICAL BC14.331.618.502.0522.6112.708.504X R0.82.104X R2.60 THRU.12.522X 4.14SENSOR MOUNTING SURFACESCALE PATTERNSURFACESCALE MOUNTING SURFACEA2.67±0.106.22.792.932.29HD C B AABCDSCALE:SIZEDWG.  NO.BSHEET    1  OF  2REV.DATEAPPROVALSDRAWNCHECKEDENGRG.MFG ENGUNLESS  OTHERWISE  SPECIFIEDALL DIMENSIONS ARE IN MILLIMETERSTOLERANCES  ARE:1234567887654323/28/113/28/11OF APPARATUS WITHOUT EXPRESS WRITTEN AUTHORIZATION FROM MicroE Systems Corp.REVISIONSLTRDESCRIPTIONDATEAPPROVEDDIM. APPLY AFTER PROCESSINGINTERPRET ALL GEOMETRIC TOLS.PER ANSI Y14.5M-1994DECIMALS:                      ANGULAR:NOT BE REPRODUCED OR COPIED OR USED AS THE BASIS FOR MANUFACTURE OR SALE.XX ± .1330 MIN.ECO.X ± .25PROJECTIONDESCRIPTION:CAD   FILE:   3rd ANGLEBedford, MA 01730Division of GSI GroupQA13/29/113/30/11         VBREVISED NOTES, RELEASE TO PRODUCTIONA       22978/11/10             VBCENTER TO EDGE OF SENSOR BODY DATUM C INCORRECT, WAS 11.192         22629/29/09              VB1          ----            INITIALDIRECTION "A"ROTARY SCALE w/INDEX and HUB,INTERFACE, ENCODER, 20 umMicroE Systems      THIS APPLIES TO QUADRATURE SENSOR ONLY.SUBJECT TO CHANGE WITHOUT NOTIFICATION9/21/09S.BUTURLIAUNITS: mm A125 Middlesex Tpk.THESE DRAWINGS AND SPECIFICATIONS ARE THE PROPERTY OF MicroE Systems Corp. AND SHALL      STATIONARY SENSOR, OUTPUT SIGNAL A+ (PIN 14) LEADSMERCURY II 6000 SENSOR5.SCALE/HUB IDENTIFICATION and SIZE      OUTPUT SIGNAL B+ (PIN 13).ID-00370  5. WHEN SCALE MOVES IN DIRECTION "A" WITH RESPECT TO ANOTES:  1. RECOMMENDED MOUNTING HARDWARE:      M2 x 6 mm SOCKET HEAD CAP SCREWS  2. IF BENCHING PINS ARE TO BE USED, PINS MUST BE PLACED      ALONG DATUM EDGES OF SENSOR FOR PROPER ALIGNMENT.      (REFERENCE DATUMS B1, B2 AND C1).  3. HEIGHT OF SENSOR BENCHING PINS MUST NOT EXCEED      HEIGHT OF SENSOR BODY (2.79 mm).  4. RECOMMENDED SENSOR MOUNTING PLATE THICKNESS:      MINIMUM: 4 SCREW THREADS      MAXIMUM: ALLOW FOR CLEARANCE TO SCALE AND SCALE                         MOUNTING HARDWARE (BENCHING SURFACE,                         TRENCHES, ETC).  A.GOLDMAND.McLOUGHLINA.VILLARROELMAIN PATTERNMOUNTING HOLE ANDCON A BOLT CIRCLE GTHREAD F. EQ. SPACEDBBCA12.52±0.08DEAC12.793.972X 2.03SENSOR MOUNTING PLATE RECOMMENDATION8.501.594X R18.50±0.08±0.0815.0713.452.47 1.712XM2 x 0.4 THRU.B2B1BC18.502.056.35Scale/HubCounts/Dim. AScale I.D.Dim. BDim. CDim D.Dim E.Thread FDim G.Dim. HIdentificationRevScale O.D.Optical Dia.Mounting Dim.Hub I.D.Mntg Hole Dia.Bolt CircleHub HeightR4513 / HI5,00044.4512.70+/-0.1331.8311.66+/-0.056.358+.013/-.0001.782-569.531.27R6425 / HJ8,19263.5025.40+/-0.1352.1521.82+/-0.0512.708+.013/-.0003.458-3219.051.52R12151 / HK16,384120.6550.80+/-0.13104.3047.90+/-0.0525.408+.013/-.0003.458-3238.102.03PIN 1PIN 8PIN 15PIN 9 SEE TABLES 2 AND 3 FORPIN FUNCTIONSDIAMETERLED4.2 CABLELED39.252.0CABLE LENGTH2X 24.5INTERPOLATOR SETTINGSIDENTIFICATION LABELIDENTIFICATION LABELMODEL#, SENSOR P/N,SERIAL#17.1 15.92.8TABLE 2.D C B AABCDSCALE:SIZEDWG.  NO.BSHEET    2  OF  2REV.1234567887654321MERCURY II 6000 SENSORTHESE DRAWINGS AND SPECIFICATIONS ARE THE PROPERTY OF MicroE Systems Corp. AND SHALLOF APPARATUS WITHOUT EXPRESS WRITTEN AUTHORIZATION FROM MicroE Systems Corp.CAD   FILE:   NOT BE REPRODUCED OR COPIED OR USED AS THE BASIS FOR MANUFACTURE OR SALEPROJECTIONDESCRIPTION:3rd ANGLEBedford, MA 01730Division of GSI GroupMicroE Systems AID-00370125 Middlesex Tpk.INTERFACE, ENCODER, 20 umROTARY SCALE w/INDEX and HUB,TABLE 3.5.6 Mercury II 6000  15-Plug       Quadrature OutputPinFunction1RL+3RL-2GND75V4I-12I+5B-13B+6A-14A+85V9GND10LL+11LL-15ALARM Mercury II 6000  15-Plug           Serial OutputPinFunction1nCS+3nCS-2GND75V4DIAG_IN_OUT-12DIAG_IN_OUT+5SCLOCK_OUT-13SCLOCK_OUT+6SDATA_OUT-14SDATA_OUT+85V9GND10SCLOCK_IN+11SCLOCK_IN-15ALARMCable Lengths1 Meter3 Meter5 MeterCustomD C B AABCDSCALE:SIZEDWG.  NO.BSHEET    1  OF  1REV.GRATING, RADIAL, R4513,20um w/INDEX, MERCURY IIOD. 1.750, ID. .500 x .090"DATEAPPROVALSDRAWNCHECKEDENGRG.MFG ENG MAKE FROM:UNLESS  OTHERWISE  SPECIFIEDALL DIMENSIONS  ARE  IN  INCHES [MILLIMETERS]TOLERANCES  ARE:MATERIAL:FINISH:SEE PS-001611234567887654321THESE DRAWINGS AND SPECIFICATIONS ARETHE PROPERTY OF MicroE Systems Corp. AND SHALLNOT BE REPRODUCED OR COPIED OR USEDAS THE BASIS FOR MANUFACTURE OR SALEOF APPARATUS WITHOUT EXPRESS WRITTENAUTHORIZATION FROM MicroE Systems Corp.REVISIONSLTRDESCRIPTIONDATEAPPROVED301-00133S.BUTURLIA7/6/06DIM. APPLY AFTER PROCESSINGINTERPRET ALL GEOMETRIC TOLS.PER ANSI Y14.5M-1994DECIMALS:                   ANGULAR:.XX [.X].01 [.25].XXX [.XX].005 [.13]30 MIN.ECOCAD   FILE:   3rd ANGLEPROJECTIONCDESCRIPTION:QA8 Erie DriveNatick, MA 01760Division of GSIMicroE SystemsSEE PS-00161NOTES:  1. MASTER TO BE GENERATED FROM PS-00161 (LATEST REV.) FOR GRATING MATERIAL,      INDEX, AND DESIGN REQUIREMENTS.  2. GRATING MODE OF OPERATION: TOP SURFACE REFLECTION.  3. ACCURACY: ±31 MICRORADIANS MAX. ERROR.  4. FLATNESS: 0.0001 INCH/INCH  5. CYCLES/REV. : 5000  6. CHARACTER HEIGHT: 1000 MICRONSDON GRIMES8/14/06L.. SALATE8/28/06A. VILLARROEL9/5/06SB9/6/06RELEASE TO PRODUCTION---A B        1719REMOVED BLACK CHROME FROM BACKSIDE OF GLASS.11/6/06              MFC       1862REV CHANGE DUE TO UPDATE TO PRODUCT SPEC06/13/07            MF.090±.0042.29±0.10GRATING PATTERNSURFACE1.750 O.D.44.45.500 I.D.12.701.25331.83OPTICAL DIAMETERGRATING FEATURES1.30033.03PATTERN O.D.1.20630.63PATTERN I.D..0872.20.287.1.328.11.422 I.D.36.13REFLECTIVE ZONE1.596 O.D.40.53REFLECTIVE ZONEINDEX.005 [.127]A.002 [.051]AA.310 RAD..375 RAD..001SECTION A-A SCALE 6 : 1.010/.015 x 45º CHAMFER2X R.010.0005A(OPTIONAL)AA+.004.007.850.0005.105.050 .2503-.0000.030.015+3X 2-56UNC-2B THRU..005.000EQ. SPACED ON A .491.375 B.C.-3X .060 THRU.EQ. SPACED ON A .685 B.C.A ABedford, MA 01730-1409ADD UNDERCUT OF .030 x .015 AND R.010; CHG MICROE ADDRESS8/21/08D C B AABCDSCALE:SIZEDWG.  NO.B   4. COMPLETION OF A MATERIAL DECLARATION IS REQUIRED FOR THIS ITEMB2030MERCURY II for R4513DATEAPPROVALSDRAWNCHECKEDENGRG.MFG ENG MAKE FROM:UNLESS  OTHERWISE  SPECIFIEDALL DIMENSIONS  ARE  IN  INCHESTOLERANCES  ARE:MATERIAL:FINISH:SEE NOTESSEE NOTES12345678876543SHEET    1  OF  1THE PROPERTY OF MicroE Systems Corp. AND SHALLA---Division of GSIMicroE SystemsAUTHORIZATION FROM MicroE Systems Corp.REVISIONSLTRDESCRIPTIONDATEAPPROVED403-00115S.BUTURLIASURFACE FINISH    32BREAK SHARP EDGES, REMOVE BURRS7/6/06DIM. APPLY AFTER PROCESSINGINTERPRET ALL GEOMETRIC TOLS.REV.CAD   FILE:   AS THE BASIS FOR MANUFACTURE OR SALE2OF APPARATUS WITHOUT EXPRESS WRITTEN1.01NOT BE REPRODUCED OR COPIED OR USED.00530 MIN.THESE DRAWINGS AND SPECIFICATIONS AREPROJECTIONBDESCRIPTION:QAECO.XXX 3rd ANGLEHUB, (HI) ROTARY GRATING,PER ANSI Y14.5M-1994DECIMALS:               ANGULAR:.XX        STATING THAT IT IS FULLY COMPLIANT WITH THE EU DIRECTIVE 2002/95/EC. (RoHS).7/14/06DON GRIMES7/28/06L. SALATE9/5/06A. VILLARROELSB9/6/06RELEASE TO PRODUCTIONNOTES:   1. MATERIAL: 303/304 STAINLESS STEEL.   2. CLEAR PASSIVATE PER QQ-P-35 (CURRENT REV.), TYPE II.   3. BREAK ALL CORNERS AND REMOVE ALL BURRS .002/.005.125 Middlesex Turnpike S.B.14/10/2014 Capacitive Sensor Probes: 3/8 inchhttp://www.lionprecision.com/capacitive-sensors/probes9-5mm.html#mech 1/2High-Performance Noncontact Sensorsand experts to help you use themH2 0( _ &2 N7$&7 _ &$5 ((5 S _ N(:S _ S,7( 0$P  Home > &apacitiY e Sensors 2 Y erY ieZ  > &apacitiY e Sensor ProE es > 9.5 mm (3/8") Diameter ProbesBookmark:      Follow:   Capacitive OverviewCapacitive Product SelectorElite Series Modular SystemCPL190/290 Sub-Nano SensorsCPL490 Picometer SensorsMM190 Meter Module7MP190 7emperature Mod.EnclosuresCompact DriverCPA100 Analog Pro[C8S7OM ElectronicsStandard Probes C3S, C3R C5, C5S, C5R C8, C8S, C8R C9.5, C9.5S, C9.5R C18 C25 R20 R452nd *eneration ProbesC8S7OM ProbesDiscontinued ProbesAir Bearing C-L9D7AccessoriesDiscontinued ProductsFA4CAPACITIVE SENSORS9.5 mm (3/8") Diameter Cylindrical Probes0echanical 'etails   _ 2 perating (nY ironment  Probes must be used with driver electronics.Probe Model = Body Style - Sensing Area Diameter1 mil = 0.001"SensingAreasDiametersmmProbe ModelNumbersMeasurement Ranges by DriverElectronicsCPL190CPL290µmmilsCompactDriverµmmilsCPA100µmmils5.6C9.5-5.6C9.5S-5.6C9.5R-5.650, 500, 20002, 20, 8050, 5002, 20500, 200020, 80?????????? ?????????? ??????C9.53D CAD FileC9.5S3D CAD FileC9.5R3D CAD FileProducts 0anuals 	 &atalogs 7echnical /iE rary &orporate &ontact14/10/2014 Capacitive Sensor Probes: 3/8 inchhttp://www.lionprecision.com/capacitive-sensors/probes9-5mm.html#mech 2/2Life-Cycle Status: ActiveProbe Operating Environment4ƒC-50ƒC 40ƒF-120ƒFProbes can be used at colder temperatures, including cryogenic temperatures, when condensation (frost) is prevented and thesystem is specially calibrated for the target temperature range.Probes can be ordered as vacuum compatible.© Lion Precision - All Rights Reserved • 563 Shoreview Park Road • St. Paul, MN 55126 • 800-250-9297 • 651-484-6544 • info@lionprecision.comCapacitive Sensors • Eddy-Current Sensors • Clear Label Sensors • Spindle Error Analysis

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