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Chapter 6 - 東京大学学術機関リポジトリ

1. Nyy 231 Total thickness 0 425 mm 15 um solder resist 18 um Cu film pe ___ 12 um PTH m 100 um substrate 100 um substrate First conductor layer 35 um Cu film 100 um prepreg Second conductor layer 18 um Cu film 12 um PTH Third conductor layer 15 um solder resist PTH Through hole plating Through hole Fig B 3 Cross section view of triple layered printed circuit board LA oo Ww 80 mm Fig B 4 Structure of the first conductor layer Red and pink lines represent the two phase armature conductors for the x directional drive dark and light green lines represent the two phase armature conductors for the y directional drive and dark and light blue lines represent the two phase armature conductors for the a directional drive 233 80 mm 80 mm Fig B 5 Structure of the second conductor layer Red and pink lines represent the two phase armature conductors for the x directional drive dark and light green lines represent the two phase armature conductors for the directional drive and dark and light blue lines represent the two phase armature conductors for the a directional drive f sz Oo x S 80 mm 0 0 OQ 0 0 O iM e p x x 80 mm Fig B 6 Structure of the third conductor layer Dark and light blue lines represent the two phase armature conductors for the a directional drive 235 a Top view b Bottom view F
2. a B PU based on rotations around the z y and x axes Vectors of the y and x axes with respect to the laser coordinate xyz da and Ay are represented as follows 0 1 V2 Ay R 1 TN OD TTT ERR IRR UR TTT C 25 0 0 1 v42 T osi etant honda ibat Re tt LI C 26 0 0 From Eqs 6 2 2 1 6 2 2 3 and C 25 C 26 the orientation Rm can also be represented by utilizing the Euler angle d as follows ID M MO e T C 27 where Rim Rim and Rim can be represented as follows sina sin sin y cos cos y cosa sin sin y cos f cos y Rint 5 sina sin f sin y cos f cos y cosa sin f sin y cos f cos y J2 sine sin cosy sin y cosa 7 sin B cos y sin y 243 sin a sin 8 sin y cos cosy cosa sin sin y cos f cos y sin sin B sin y cos f cos y cosa sin sin y cos f cos y M2 sin a sin B cos y sin y cosa sin B cosy sin y Rim p sin f cos sin y Rm3 sin J cos f siny l e C 30 2 5 2 cos B cosy From Eqs C 21 and C 27 C 30 the Euler angle can be represented by the different Euler angle d as follows pee sin cosa Xsin Z sin y cos sina cosa cos y C 3 2csB Jj TT f sin nacen TREE NO RR IPTE C 32 V2 qa 2280 B sing C 33 S KO As mentioned above the 6 DOF mover position can be detected by using the six laser displac
3. 20 IB BRBABBOF HIZA YY RY OS 21B1 1 pp 133 138 SAT 2008 5 H T Yano Development of a High Torque Spherical Motor Proposal of a Hexahedron Tetrahedron Based Spherical Stepping Motor Journal of the Japan Society of Applied Electromagnetics and Mechanics Vol 16 No 2 pp 108 113 June 2008 in Japanese RS E kL me A OSE ENA L EM MAIC OK lt RH MAT ye YTt FORR HA AEM 2356 Vol 16 No 2 pp 108 113 2008 A 6 A T Yano and M Kaneko Basic Consideration of Actuators with Multi Degrees of Freedom Having an Identical Center of Rotation Journal of the Robotics Society of Japan Vol 11 No 6 pp 107 114 June 1993 in Japanese RRS amp TRE ePbth tt ZB BETZ Fary DE RREI AAU Ay SH Vol 11 No 6 pp 107 114 1993 4F 6 A H Li C Xia P Song and T Shi Magnetic Field Analysis of A Halbach Array PM Spherical Motor IEEE International Conference on Automation and Logistics pp 2019 2023 Jinan China August 2007 260 Publications Journal Papers P1 P2 P3 P4 P5 Y Ueda and H Ohsaki A Long Stroke Planar Actuator with Multiple Degrees of Freedom by Minimum Number of Polyphase Currents Motion Control IN TECH Book ISBN 978 953 7619 X X September 2009 to be submitted Y Ueda and H Ohsaki Compact Three Degree of Freedom Planar Actuator with Only Six Currents Capable of Driving over Large displacements in Yaw Direction ZEEJ Transaction on Industry A
4. Fig 6 3 2 I Analysis result of torque 7 due to the armature currents for the x directional drive for the Euler angle a 206 10 pus 2 7 2 0 2 2 Cn Ks1 mN mm A e 2 1 5 1 0 5 0 0 5 1 5 Euler angle D deg tO a Ks 7 1 14 at a 0 0 2 0 0 2 and 2 2 15 10 Nn Ks2 mN mm A e 5 10 15 2 1 5 1 0 5 0 0 5 1 1 5 2 Euler angle D deg b Ke 7 1 1 at a 0 0 2 0 0 2 and 2 2 Fig 6 3 2 2 Analysis result of torque T due to the armature currents for the x directional drive for the Euler angle 207 2 0 0 0 2 P 2 0 2 2 Kai mN mm A 2 1 5 1 05 0 0 5 1 5 Euler angle y deg w a Ky T 14 at a 0 0 2 0 0 2 and 2 2 K42 mN mm A 2 15 1 05 0 0 5 l 1 5 2 Euler angle y deg b Ko Ty I 1 at a A 0 0 2 0 0 2 and 2 2 Fig 6 3 2 3 Analysis result of torque 7 due to the armature currents for the x directional drive for the Euler angle y 208 From these results when rotational motions with more than 2 DOF occur K is almost in agreement with Kr in Eq 6 1 2 3 Therefore negative d axis currents L lay that control the suspension forces F generate stable restoring torques T T However the q axis currents that control the translational forces F F generate torques 7 Ty T which a
5. Torque 7x Ty mN mm tO e Translational force Fy mN 90 60 30 0 30 60 90 Yawangle 7 deg b Driving forces from the q axis current for the y directional drive Igy 1A Fig 6 1 2 4 Driving forces for yaw angle lt at pitch and roll angles B y 0 deg when the armature currents for the y directional drive are supplied 179 T FTI Mutually opposite poles n RH for the y direction BN LLL NI r1 4 Opposite driving lt L f rs are offset LII LINN LTR dU RIS ESSA duo ENSE HELLE EL T SN Lo ara Kk mim f A LL LET dL ADI TTT LETRA ET TUI Ill M dH Hit MO Wl HH EH E IH 1 e A a 111 ERE I P 51 e F ILL RII Ix PEN J 111 AREN a oU j Same currents C Fig 6 1 2 5 Relation between pitch lengths of the meander shape and magnetic pole when the yaw angle 23 6 deg LI HOH Zee zHoHzHHo 37r SON a nas o Hzpr o LETS ILI aS Cc Rea Not lati ea Bete Tode 5555 o translationa io HzHo Hz force generation nui Fig 6 1 2 6 Integration of flux density B along a line l in armature conductors when the yaw angle 45 deg 180 Tx Ty T mN mm tO 2 1 5 1 0 5 0 0 5 1 5 Pitch angle 2 deg a Driving forces due to the d axis current for the x directional drive Ir 1A 15 fy pee MM AST AL Tx Ty T mN mm
6. ru Lo Ks6 Ty Lo and Ka6 y d Tol at LH 0 0 Fig 6 3 2 4 Analysis result of the torques from the armature conductors for the a directional drive for the Euler angle at 5 0 0 UJ B 7 2 2 i Kss T f Las Mar aru Ncc sis E C lt C Z e Q o m Q Q o n K 45 gt T ifs E PoF ai Les K 65 p ls l faa T adds PT ds odi m E Kas Kss Kos mN mm A 20 b 2 1 5 1 05 0 0 5 1 5 Euler angle deg NW a Kis Ln lag Kass T lig and Kes i TL Lig at B ZU S UJ ce K 46 Ty j tTa t iS C e 10 Ub ET Aae Kao Kso Koo mN mm A 2 1 5 1 05 0 0 5 l 1 5 Euler angle deg tO b K 46 da La Ks6 Ty je and Keo T m at B 2 20 Fig 6 3 2 5 Analysis result of the torques from the armature conductors for the a directional drive for the Euler angle at 2 2 6 4 Numerical Analysis of Mover Motion This section presents the analytical conditions of the 6 DOF motions of the mover and the analysis results 6 4 1 Analytical Model and Conditions Motion characteristics with 6 DOF can be obtained by solving Eqs 6 2 3 1 6 2 3 4 using the Runge Kutta method In order to numerically solve the equations it is necessary to calculate the driving forces F and Tsm at each time step The calculation at each time st
7. x x 7 0 Displaced in 7 y axis Current for x drive 1 gt 0 Yy I 0 No magnetization Stator No Torque generation b Generated torques T due to the q axis current for the x directional drive Displaced in 7 s d axis current fory drive l gt 0 Stator Positive torque generation c Generated torques 7 due to the d axis current for the y directional drive Displaced in y q axis current y forjy drive7 O Stator Positive torque generation d Generated torques 7 due to the q axis current for the y directional drive Fig 6 1 2 12 Schematic views of generation of torques 7 186 As the analysis results above show the driving forces F Fy Fa Tey Ty Te ean be expressed from the d and q axis currents i lyx lay la as follows F F Ia F _ KL c p y Ls 6 1 2 7 T Gard Hatin A a 1 253 Ty I i T where K is a 6 x 4 matrix and all elements of the matrix nonlinearly depend on the yaw angle a pitch angle J and roll angle y In this study the pitch and roll displacements of the mover are assumed to be very small f 0 deg and y 0 deg because of small air gap less than 1 mm between the mover and stator and in the range all elements of K almost linearly depend on the pitch and roll displacements Furthermore if the yaw displacements are assumed also to be very small 0 deg all elements of Krr almost linearly depend on the yaw displacemen
8. NO 2 1 5 I 0 5 U 0 5 l LS Pitch angle D deg b Driving forces due to the q axis current for the x directional drive 1 A Fig 6 1 2 7 Driving forces for pitch angle 2 at yaw and roll angles a y 0 deg when the armature currents for the x directional drive are supplied 181 CA 10 A H 3 Z LET 0 E G 5 ES 10 15 2 15 1 0 5 0 0 5 1 3 Pitch angle D deg i a Driving forces due to the d axis current for the y directional drive I 1A tO 2 15 1 0 5 0 0 5 1 1 5 Pitch angle 2 deg b Driving forces due to the q axis current for the y directional drive Igy 1A Fig 6 1 2 8 Driving forces for pitch angle 2 at yaw and roll angles y 0 deg when the armature currents for the y directional drive are supplied 182 y Displaced in 0 i Attractior gt Z d axis current action force B for x drive gt 0 Stator Positive torque generation a Generated torques T from the d axis current for the x directional drive Attraction force yer Displaced in 2 q axis current zs Repulsion force p for x drive 1 gt O Stator Negative torque generation b Generated torques T from the g axis current for the x directional drive Displaced in Attraction force d axis current p for drive gt 0 Stator Positive torque generation c Generated torques 7 from the d axis current for the y direction
9. Kidz DXEXcEUROZBBEFZ4733IBOb SIM TEX 4 SB BARES T RII TARAS TER 08 19 LD 08 19 pp 35 40 HELE 2008 7 B Y Ueda and H Ohsaki Survey of Development of Multi degree of freedom Drive for Optical Memories ZEEJ Joint Tech Meeting on Transportation and Electric Railway and Linear Drives Kagoshima TER 08 19 LD 08 19 pp 35 40 July 2008 LEHA KIB Z 33HO 2 THEE GR T kL Ga ERI T 77 2 20 WERD B 20 E DERLZBDEEOZ4TRZA YY RYU 21B2 2 pp 165 170 BAF 2008 5 A Y Ueda and H Ohsaki Positioning of a Maglev Planar Actuator by Controlling Three Sets of Two Phase Currents The 20 Symposium on Electromagnetics and Dynamics sead20 21B2 2 pp 165 170 Beppu May 2008 263 P21 P22 P23 P24 P25 P26 LARA KAZ EET Fary OA 3 B 09 IOI L TT D EKNE tE BRFSS WK 5 213 p 321 W 2008 4E 3 A Y Ueda and H Ohsaki Electromagnetic Force Characteristics of a Planar Actuator for Three Degree of Freedom IEEJ Annual Meeting 5 213 p 321 Fukuoka March 2008 LEWA Ai A AMICKA CE DEET 772 204 804r eR SS UTK SHES LD 07 34 pp 11 16 Hm 2007 10 A Y Ueda and H Ohsaki Position Detection of a Mover of a Planar Actuator Capable of Traveling over Large Displacements in Yaw Direction IEEJ Tech Meeting on Linear Drives LD 07 34 pp 11 16 Tokyo October 2007 LA A Xl a AloM a EET 7Fart FOMBRORE F RE 19F SL LEAMA XS II pp 137 138 Xl 2007 8H Y Ueda and
10. No 2 pp 171 180 April 2004 J C Compter Towards Planar Drives for Lithography The International Symposium on Linear Drives for Industry Applications LDIA2007 KS2 1 Lille France September 2007 Cybernet Systems MATLAB User s Manual K Kahlen and R W De Doncker Current Regulators for Multi Phase Permanent Magnet Spherical Machines The 354 IEEE IAS Annual Meeting Vol 3 pp 2011 2016 Rome Italy October 2000 K Kahlen I Voss and R W De Doncker Control of Multi Dimensional Drives with Variable Pole Pitch The 37 IEEE IAS Annual Meeting Vol 4 pp 2366 2370 Pennsylvania USA October 2002 A Tanaka M Watada S Torii and D Ebihara Proposal and Design of Multi Degree of Freedom Spherical Actuator Magnetodynamics Conference MAGDA 11D pp 169 172 Tokyo March 2002 in Japanese H EE MMR BER BERK TEBET ZI Fary OBE LRH 6 11IBIMAGDA 2 77 7 V V ARE pp 169 172 RR 2002 F 3 A S Torii H Nakano T Yamaguchi D Ebihara Y Hasegawa and K Hirata Characteristics of the Two Dimensional Oscillatory Actuator with Attractive Force of Driving Source The International Symposium on Linear Drives for Industry Applications LDIA2003 pp 101 104 Birmingham UK September 2003 Y Honda S Torii D Ebihara Y Hasegawa and K Hirata Development of Cylindrical Two Dimensional Linear Oscillatory Actuator The International Symposium on Linear Drives for Industry Appl
11. pp 19 24 Sapporo July 2006 LEWA Tei Z IKARA Y 7 AREY REL DELY IAA X A 0B S IZ RBT SSH 25 18 B IR DRE D ZW TIZZA VYR 717 h A2PO1 pp 489 494 F 2006 5 B Y Ueda and H Ohsaki Discussion about Drive Control of a Coreless Surface Motor based on Permanent Magnet Type Linear Synchronous Motor The 18th Symposium on Electromagnetics and Dynamics sead18 A2P01 pp 489 494 Kobe May 2006 LAHA IFRA KERZ TLS X BAAO EDE 7 ze At 4 330 5 ET oi SEDI 5 1718 Ta HRS OS TT 7A YURYY dL pp 249 252 fn 2005 4F 6 B Y Ueda and H Ohsaki Control of Mover Yawing Motion in a Coreless Surface Motor using Halbach Permanent Magnet The 17 Symposium on Electromagnetics and Dynamics sead17 2AMO6 pp 249 252 Kochi June 2005 HERA LMA KZ DA 7dWUBxRHwIeEy 7zr4e 3 DEERE BRASS VAT KIAT RRSBARRAAMAS LD 04 98 SPC 04 170 pp 7 12 mai 2004 F 12 H Y Kawamoto Y Ueda and H Ohsaki Drive Characteristics of a Coreless Type Surface Motor Using Halbach Permanent Magnets JEEJ Joint Tech Meeting on Linear Drives and Semiconductor Power Converter LD 04 98 SPC 04 170 pp 7 12 Suwa December 2004 LSA KITS gt EBT BRR LAGE LO IR D y 4 HECHA BA S BVH CREWSOB U TFEZ4781l889 2 2 TER 04 31 LD 04 52 pp 1 6 4 E 2004 F 7 B Y Ueda H Ohsaki and E Masada Application of Fuzzy Control to Suspension System of Electromagnetic Suspension Type Magnetically Levitated Vehicle IEEJ Joint Tech Mee
12. rotational motions with more than 2 DOF occur in the range within 2 deg lt a f and y 2 deg Figure 6 3 2 1 shows the system constants Kg T I and Ko Tz I 1 2 which are dominant on the a motion for the Euler angle a The system constant Ks is independent on the Euler angles J and y and the system constant Kg is almost independent on the Euler angles and f Figure 6 3 2 2 shows the system constants Ks T I4 and Ks2 T 1 2 which are dominant on the motion for the Euler angle The system constant Ks is independent on the Euler angle y and the differential OK Of is independent on the Euler angles a and y The system constant Ks is almost independent on the Euler angles a 2 and y Figure 6 3 2 3 shows the system constants Ky T Ix and Ky 5 7 12 which are dominant on the 7 motion for the Euler angle y The system constant Ka is independent on the Euler angles and and the system constant Ky is almost independent on the Euler angles 2 and 205 10 T 5 Bg E Z G 0 gt t spth B 7 0 2 Q 2 15 2 1 5 l 0 5 0 0 5 1 5 2 Euler angle deg a Kar TT I4 at B 0 0 0 2 0 0 2 and 2 2 15 10 Cn Ko2 mN mm A o E BU z 5 Di 1 lt E ee B 7 0 0 2 0 10 F i i C 15 2 1 5 l 0 5 0 0 5 l 1 5 2 Euler angle deg b Ke amp T 1 2 at B 0 0 2 0 0 2 and 2 2
13. 0 0 5 1 5 2 2 5 3 3 5 4 Time s a Planar motions x y 0 18 0 16 0 14 mm e ro Displacement S oot e Ss o E c 00 t2 e 0 02 uU L3 Un A 0 0 5 l 1 5 2 25 Time s b Vertical motion z 0 5 0 4 0 3 0 2 0 1 0 1 0 2 0 3 0 4 0 5 Euler angle f y deg Un 4 0 0 5 1 1 5 2 2 5 3 3 Time 7 s c Rotational motions g f y Fig 6 4 2 3 Analytically obtained mover motions under analysis condition ID 218 0 05 i 0 15 ly A 1 e N 0 25 0 3 0 35 0 4 0 45 0 5 Current Lc 0 0 5 l I3 2 25 Time s 35 4 bo a d axis currents and la used to generate the suspension forces F 0 06 0 05 0 04 0 03 0 02 0 01 e Current lyx lay lda loa A 0 01 0 02 2 Time 7 s 0 0 5 l l Un Un L v Un 4A 2 b d and g axis currents l la lda and lya used to control planar motions Fig 6 4 2 4 Analytically obtained armature currents under analysis condition II 219 6 5 Summary of Chapter 6 This chapter presents a feasibility verification of a planar actuator with both 3 DOF planar motions and magnetic suspension of the mover in order to further improve performance Then based on a numerical analysis of the 6 DOF driving forces a planar actuator having a mover positioned above a plane and magnetically levitated by only six currents and the six cu
14. 3 are elements of the position vector r and 6 is Kronecker delta An inertia tensor Jo of a rectangular prism which has uniform mass density p with respect to the coordinate axes xyz with the origin at O can be represented as follows M 1 0 0 Jo 0 lt M U 2 MEE rH 6 2 1 3 0 0 MU 1 where and are the lengths of the edges of the prism as shown in Fig 6 2 1 2 Next we can easily calculate the inertia tensor Jo of the same prism with respect to the coordinate axes x y z with the origin at O parallel to the coordinate X35z With each other as follows b e ab ac Jo Jg M ba Dg DO us epe ee c E etc 6 2 1 4 ca cb amp b where d la b c is the displacement vector from the origin O to the origin O The inertia tensor J of the mover with respect to the coordinate axes x y z J can be calculated from Eqs 6 2 1 3 and 6 2 1 4 as follows 0 1828 0 0 J 0 0 828 0 K107 kg M2 6 2 1 5 0 0 0 3543 As we can see the inertia tensor J is a diagonal matrix The diagonal elements of the inertia tensor J and the coordinate axes x y z are referred to the principal moments of inertia and the principal axes respectively Once the principal moments and their axes of the mover are known the inertia tensor Jm with respect to any other axes passing through the center of mass can be found by a similarity transformation defined by the Euler angles relating the two coord
15. R m sina cosy cosa sin J siny cosa cosy sina sin f siny cos siny sina sin y cosa sin B cosy cosa siny Sin d sin D cosy cosf cosy A position vector of an arbitrary point on a surface i with respect to the sensor coordinate xyz ri U 1 2 3 4 5 or 6 satisfy the following equation nus Lp p l TTT C 22 where r expresses the mover position with respect to the laser coordinate xyz The mover position rj can be calculated from the Euler angle by Eqs C 17 C 22 with respect to the three Surfaces 1 3 or 2 6 or 4 or 5 239 Sensor 4 Sensor 5 Sensor 3 Sensor Cross section at B B b Case in which the mover is displaced from the base position Fig C 1 Position relation among the six laser beams and mover 240 Sensor 4 Sensor 5 Sensor 6 0 v3 6 Displaced A tee OB Not displace Not displace a Measurement point of Sensor 4 b Measurement points of Sensors 5 and 6 Fig C 2 Definition of displacements in the measurement points of Sensors 4 5 and 6 from the base positions AS ASs and AS a Cross section view in the x y plane b Cross section view at B B Fig C 3 Displacements in the measurement points of Sensors 4 5 and 6 from the base positions AS ASs and AS P ais n O CC MC m Ns n Bea ge nnn l T ms3 H VE O LT n ms H wia a Case i
16. T are almost constant and the torques T and T are proportional to the yaw angle when the yaw angle 0 deg Because of the symmetric magnetization of the mover the same driving forces can be generated every 180 deg In the same way the driving forces resulting from the d and q axis currents for the y directional drive Z Iy can be numerically analyzed and are shown in Fig 6 1 2 4 From these results the d axis currents for the x and y directional drives Z and Ly generate nearly equal translational forces F and torques T and therefore cannot be uniquely determined from the total translational forces F and torques 7 In other 175 words with only the d axis currents for the x and y directional drives Jz and ly 2 DOF driving forces cannot be controlled The torques resulting from the q axis currents for the x and y directional drives J and J are similar because of the symmetry of the actuator When the yaw angle a 24 7 deg and 45 deg 3 DOF translational forces cannot be generated regardless of the magnitudes of the d and q axis currents las L This is presumed to be caused by the magnetic field resulting from magnet mover which is tilted an angle of 24 7 deg or 45 deg The mover generates opposite magnetic poles every pitch length r in the J direction and so the magnetic poles at a position and 5rdistant position along the J direction are mutually opposite as shown in Fig 6 1 2 5 When tilted by
17. between the mover and ball bearings aimed at incremental improvement of the drive performance Based on a numerical analysis of the 6 DOF driving forces I designed a planar actuator that has spatially superimposed magnetic circuits formed by only six currents and a 223 permanent magnet mover so that the mover motions could be independently controlled in the 3 DOF translations and 1 DOF rotations above a plane The drive characteristics were validated by a numerical analysis of the 6 DOF motions This thesis demonstrated the following significant accomplishments of a novel study gt experimental verification of the design and control of a long stroke 3 DOF planar actuator numerical verification of design and control of a planar actuator with a stably and magnetically levitated mover capable of 3 DOF planar motions 7 2 Future Work This section discusses future works aimed at incremental improvements in the performance of the planar actuator as follows Improvements to the drive system realization of decoupled 6 DOF motion controls by redesigning the mover or stator structure improvements to the specifications of the controller boards input output range resolution sampling time and so on that would improve drive characteristics such as positioning precision and response investigation of a movable area out of plane consideration of payloads mounted on the mover gt Improvements to the position sensin
18. defined to be rotated from the coordinate xyoz by y around the x axis Next the orientation of the mover coordinate x y z with respect to the stationary coordinate x yz Rsm is introduced from the Euler angle When a body is rotated counterclockwise by w around an arbitrary vector A 41 42 As the rotation matrix KE can be represented as follows R Ecosy 4M 44M 44M siny AA 1 COSY cesscsssseseessessnsees 6 2 2 1 where E is a 3 x 3 unit matrix and M i 1 2 or 3 is an infinitesimal rotation generator which can be represented by the following equations 1 0 0 L0 0 OO tt 6 2 2 2 00 1 00 0 0 0 1 0 0 M 0 0 1 My 0 0 0 M O 0 J e 6 2 2 3 01 0 1 0 0 0 0 0 Zn a y y gt Y E Jm x Xn Stationary coordinate x Mover coordinate Fig 6 2 2 1 Definition of Euler angle o f PU At first a rotation matrix to rotate counterclockwise by g around the z axis R can be calculated from Eqs 6 2 2 1 6 2 2 3 Because the unit vector of the z axis with respect to the stationary coordinate x y z is represented as As 0 0 17 the rotation matrix R can be represented as follows cosa sing 0 Raps PCOS OY uos co heen es M he Dem hale we Bg hh a 6 2 2 4 0 0 1 Then the unit vector of the y axis with respect to the coordinate xjyiz Azs is represented as follows 0 sinc T E EA I2 MERERI 6 2 2 5 0 0 The
19. flux densities B B B with respect to the y direction is nearly equal to zero that is translational force F 176 shown in Eq 3 3 1 3 is expressed as follows B d 0 B d 0 TRE RE 6 1 2 5 Jk Jk jk F D f E Bd 0 6 1 2 6 Figures 6 1 2 3 and 6 1 2 4 also indicate that a magnitude of torque 7 resulting from the mover tiled by 24 7 deg is larger than that by 45 deg Magnitudes of torques 7 and T resulting from the mover tiled by 45 deg are equal because flux density resulting from the magnet mover is symmetrically distributed in the x and y directions On the other hand magnitudes of torques 7 and T resulting from the mover tiled by 24 7 deg are not equal because of asymmetric distribution of the flux density in the x and directions Figures 6 1 2 7 and 6 1 2 8 show the analysis results of the torques T T T for the pitch angle 2 when the d and g axis currents are supplied Ix 1 A lx 1A ly 1A or Jy 1 A the yaw and roll positions are not displaced a y 0 deg From these results it can be seen that the d axis currents generate the torques T proportional to the pitch angle 5 and the q axis currents generates the almost constant torques 7 Figure 6 1 2 9 shows schematic views of the generation of the torques T The g axis current for the y directional drive also generates the torques T proportional to the pitch angle f Figures 6 1 2 10 and 6 1 2 11 show the analysis results of th
20. of the permanent magnets So in other words I fabricated a Halbach permanent magnet array using only LOCTITE However the adhesive strength was not high enough and the bonded permanent magnet array often became unglued when the electromagnetic forces for the MDOF drive acted upon the permanent magnet array Next in order to strengthen the adhesion I coated the Halbach permanent magnet array bonded with LOCTITE with Araldite which bonds slowly more than 12 hours but has greater shear strength Araldite is viscous and keeping a flat coating using Araldite is difficult So after the Araldite hardened completely I removed the unwanted Araldite using sandpaper to flatten the surface of the permanent magnet array Figure A 1 shows the fabrication procedure for the smallest 2 D Halbach permanent magnet array 227 1 2 mm thick Bonding surface Bonding surface 2 0 mm thick 2 0 mm thick iron plate iron plate Ec E D PM 1 2 mm thick iron plate x _ S lt 2B Permanent e magnets S v3 Nonmagnetic materials 2 0 mm thick iron plate C m e a m ooo n e e e a a A ELLE loco e e e e e Epoxy adhesive Coating the permanent magnet array with epoxy adhesive m m m we we wm ee oo ooo Fig A 1 Fabrication procedure for the smalles
21. pp 2935 2940 Nagoya Japan May 1995 258 Toy96 Tsu07 Ueh05 Uet03a Uet03b Van06 Van07a Van07b Van07c S Toyama G Zhang and O Miyoshi Development of New Generation Spherical Ultrasonic Motor The IEEE International Conference on Robotics and Automation pp 2871 2876 Minnesota USA April 1996 J Tsuchiya and K Yasuda The Positional Detection System for the Surface Motor Using Halbech Type Permanent Magnets The International Symposium on Linear Drives for Industry Applications LDIA2007 094 2 Lille France September 2007 H Kawano H Ando T Hirahara C Yun and S Ueha Application of a Multi DOF Ultrasonic Servomotor in an Auditory Tele Existence Robot IEEE Transaction on Robotics Vol 21 No 5 pp 790 800 October 2005 T Ueta and B Yuan Moving Coil Type Planar Motor Control U S Patent Application Publication US 2003 0102721 A1 June 5 2003 T Ueta B Yuan and T C Teng Moving Magnet Type Planar Motor Control U S Patent Application Publication US 2003 0102722 A1 June 5 2003 A Lebedev E Lomonova D Laro and A J A Vandenput Optimal Design Strategy for a Novel Linear Electromechanical Actuator IEEJ Transactions on Industry Applications Vol 126 No 10 pp 1330 1335 October 2006 J W Jansen C M M van Lierop E A Lomonova and AJ A Vandenput Magnetically Levitated Planar Actuator with Moving Magnets The International E
22. so the vertical motions are stable Therefore in this study the mover of the magnetically levitated planar actuator is positioned on the stator Figure 6 1 2 1 shows the analytical model for the driving forces In this figure the mover and polyphase armature conductors for the x or y directions only are shown A moving 2 D Halbach permanent magnet array has the same structure as shown in Fig 3 2 1 1 and four pole and seven segment magnetization with pole pitch length rwu 3 mm along the x and y directions Its dimensions are 11 mm x 11 mm x 2 mm which are almost two fifths the size of the magnet array dimension shown in Fig 3 2 1 1 The ultimate miniaturization of the permanent magnet mover enables higher accelerations to be generated using the same armature currents and flux density as given in Subsection 3 3 1 Figure 6 1 2 2 shows an analytically obtained flux density distribution on the plane 0 5 mm below the mover bottom for the x and y directions Figure 6 1 2 2 indicates that the permanent magnet mover also generates a quasi sinusoidal flux density with a pitch length of r 2 1 mm in the x and y directions On the other hand pitch lengths of the meander shaped armature conductors are equal to the pitch 7 2 1 mm In the mover motions there are 3 DOF rotations However this analysis deals with the rotations around only one axis Gm Ym or Zm The rotational angles around the x Ym and z axes are referred to as roll ang
23. 23 6 deg close to 24 7 deg in the a direction the mover generates opposite magnetic poles every 2r along the x direction as shown in Fig 6 1 2 5 because of geometry relation as shown in the following equation a 7 sin B FOO TT 6 1 2 1 Then the same armature currents flow every 27 along the x direction Therefore if the magnet mover generates a completely sinusoidal magnetic field distribution in the Xm and y directions each phase current generates opposite translational forces every 27 in the x direction during the yaw angle a 23 6 deg Consequently these opposite translational forces can be mutually offset The error between the theoretically 23 6 deg and analytically 24 7 deg obtained yaw angle is presumed to be caused by an incomplete sinusoidal magnetic field generated by the magnet mover As mentioned in Subsection 3 2 1 the miniaturized mover also generates a quasi sinusoidal flux density in the vr and y directions When the mover is tilted by 45 deg in the a direction as shown in Fig 6 1 2 6 the flux densities B By B below the mover are approximately expressed as follows B xn 91525 Bem Z a Z Jeo TT 6 1 2 2 T pM TPM B xi yj 2 7 Bnl Je Zala T EE EEE A ERI 6 1 2 3 PM PM B x AP Zs Bim z a Z Z U 6 1 2 4 T pM TPM So armature currents flowing through a line J U x or y k u v or w in armature conductors i generate no translational force because average of the
24. 4 and 6 2 2 15 as follows x e an o EE E E 6 2 2 16 Rl Qc est stein ial Reais ane tae e tota Dh 6 2 2 17 199 jl l Pa cos 2a sin amp sin y cosg sin f cosy cosg siny L Sin G sin cosy cos D cosy x sin cosy cosa sin siny cosa cosy sing sin siny cos D siny cos amp cos fg sin a cos f sin m NR 6 2 2 18 Equation 6 2 2 18 indicates that the matrix R4 cannot be defined and therefore the Euler angle d cannot be uniquely determined from this equation when the Euler angle a 45 or 135 deg The orientation of the mover is often called a singular posture However in this study it is assumed that the mover is driven in the range within the Euler angle a 0 deg Therefore a singular posture cannot occur and the differential of the Euler angle d d can be calculated from Eqs 6 2 2 17 and 6 2 2 18 Fig 6 2 2 2 Angular velocity Om le o oJ and Euler angle g a B H 6 2 3 Equation of Motion The equation of the motion of the mover can be represented by the translational forces acting on the mover F F Fy EI and torques around the mover center O Tom T T TT as follows dv M Se a Pre ree ee nc eT ASE qum xau MU YE e Ed 2 3 1 m A 6 2 3 1 1 do 1 1 1 1 Ju n Ta 0 CF EN DDR 6 2 3 2 where Vem v v vl and F z 0 0 Mgl are velocity of the mover and the force of gravity acting on the mover respectively Equati
25. BERBZBCE OBIBZIEOSHI TETIBUIGSXS XT BAR Vol 103 No 340 pp 49 54 2003 9 A M Aoyagi T Nakajima Y Tomikawa and T Takano Examination of Disk Type Multi Degree of Freedom Ultrasonic Motor Japanese Journal of Applied Physics Vol 43 No 5B pp 2884 2890 May 2004 T Asakawa Two Dimensional Precise Positioning Device for Use in a Semiconductor Manufacturing Apparatus U S Patent 4 535 278 August 13 1985 M Binnard System and Method to Control Planar Motors U S Patent 6 650 079 November 18 2003 M Binnard Six Degree of Freedom Control of Planar Motors U S Patent Application Publication 2003 0085676 May 8 2003 J D Buckley D N Galburt and C Karatzas Step and Scan Lithography Using Reduction Optics Journal of Vacuum Science and Technology B Vol 7 No 6 pp 1607 1612 November 1989 G S Chirikjian and D Stein Kinematic Design and Commutation of a Spherical Stepper Motor JEEE ASME Transactions on Mechatronics Vol 4 No 4 pp 342 353 December 1999 247 Com03 Com04 Com07 Cyb01 Don00 Don02 Ebi02 Ebi03 Ebi05 Ebi89 J C Compter A Planar Motor with Electro Dynamic Propulsion and Levitation under 6 DOF Control The International Symposium on Linear Drives for Industry Applications LDIA2003 MA 01 pp 149 152 Birmingham UK September 2003 J C Compter Electro Dynamic Planar Motor Precision Engineering Vol 28
26. Chapter 6 Feasibility Study on Magnetically Levitated Planar Actuator This chapter proposes a conceptual design for a planar actuator having the same configuration for the magnetic circuits as for the planar motion control so that the mover can be magnetically suspended In addition it presents a feasibility verification of motion control characteristics by numerical analysis 171 6 Feasibility Study on Magnetically Levitated Planar Actuator This chapter presents a feasibility verification as to whether a planar actuator can magnetically suspend a mover capable of 3 DOF motions on a plane so as to further improve the drive performance of a planar actuator First the planar actuator is redesigned so it can both suspend the mover and control the planar motions Then the planar motion and magnetic suspension characteristics of the planar actuator are verified by numerical analysis 6 1 Conceptual Design of Magnetically Levitated Planar Actuator This section presents a compatibility verification of planar motion and magnetic suspension and then introduces a conceptual design for a planar actuator with a magnetically suspended mover 6 1 1 Design Considerations The proposed planar actuator has spatially superimposed magnetic circuits for the x y and a directions which are its most important feature and enable the mover to travel over a wide movable area on a plane by exciting only two polyphase armature conductors The
27. E 7 PLANESERV LZE But Vol 45 No 2 pp 83 86 2001 4F A Yamamoto K Mori H Yoshioka and T Higuchi 2 DOF Electrostatic Surface Actuator Using Mesh Type Printed Electrodes The 2004 JSPE Autumn Technical Meeting B19 pp 117 118 shimane September 2004 in Japanese LIERE MEA FEDAS BOER 2 o Yo ET X Ae 2 BB EXE TAL 2004FE R T KEKR TIR mALS B19 pp 117 118 Bik 2004 4F 9 A T Higuchi Electrostatic Motors Symposium materials on Motor Technologies in TECHNO FRONTIER 2006 Makuhari April 2006 in Japanese HOGER ERHEE Z7 TECHNO FRONTIER 2006 7 ixi z VY RYO LSR EE 2006 F 4 A T Ueno E Summers M Wun Fogle and T Higuchi Micro Magnetostrictive Vibrator using Iron Gallium Alloy Galfenol Journal of Magnetics Society of Japan Vol 31 No 4 pp 372 375 July 2007 in Japanese ERE U UU VY AIL PROBE Fe Ga Galfen HL YE lt 7 OBERT RAIA RRS 43 Vol 31 No 4 pp 372 375 2007 7 A 250 Hig08a Hig08b Hig89 Hig90 Hin87 Hir04 Hir05 T Ueno E Summers and T Higuchi Machining of Iron Gallium Alloy for Microactuator Sensors and Actuators A Physical Vol 137 No 1 pp 134 140 June 2007 T Ueno T Higuchi C Saito and N Imaizumi Micro Spherical Motor using Iron Gallium Alloy Galfenol The 20 Symposium on Electromagnetics and Dynamics sead20 2342 4 pp 597 600 Beppu May 2008 in Japanese tS HORE
28. FRETS ARER Fe Ga amp amp Galfenol RHv kv 7o0Rmt F 20E ERJEN T3272 Yum SY h 23A2 4 pp 597 600 BIAS 2008 F 5 A T Higuchi and H Kawakatsu Development of a Magnetically Suspended Stepping Motor for Clean Room Transportation and Sample Handling Zhe International Conference on Magnetically Levitated Systems and Linear Drives Maglev 8 pp 363 368 Yokohama Japan July 1989 T Higuchi A Horikoshi and T Komori Development of an Actuator for Super Clean Rooms and Ultra High Vacua The 24 International Symposium on Magnetic Bearings pp 115 122 Tokyo Japan July 1990 W E Hinds Single Plane Orthogonally Movable Drive System U S Patent 4 654 571 March 31 1987 Y Kawase T Yamaguchi H Naito M Tanaka K Hirata and Y Hasegawa 3D FEM Coupled with the Rotation and Linear Motion Equation IEEJ Tech Meeting on Static Apparatus and Rotating Machinery SA 04 24 RM 04 24 pp 63 66 Chiba January 2004 Gn Japanese IIE WS ARES PER FARS RAH 2 BB ERT 7 Fary ORE L IB ERROR RE EAFA Hubs BEES FITZ SA 04 24 RM 04 24 pp 63 66 T 2004 1 B Y Hasegawa and K Hirata A Study on Electromagnetic Actuator with Two Degree of Freedom IEEJ Transactions on Industry Applications Vol 125 No 5 pp 519 523 May 2005 in Japanese EAJ Ht EE BSL T2 AREBRT IF I 208 95 BR 340k D Vol 125 No 5 pp 519 523 2005 4E 5 A 251 Hir08 HNa04 HOh07 Hol98 H
29. Figure 6 4 2 1 indicates that the mover can be positioned at these reference positions in the x y z and directions with less suppressed and displacements Therefore the mover can be magnetically suspended with stability Figure 6 4 2 2 shows the analysis result of the armature currents under analysis condition I The d axis currents I and Jz used to generate the suspension forces are absolutely less than 0 36 A and 0 45 A respectively The q axis currents J and I used to generate the translational forces F and F are absolutely less than 3 mA therefore high resolution current controls are necessary to control the mover motions The armature currents for the a directional drive are absolutely less than 0 04 A Planar motion control with magnetic suspension Figure 6 4 2 3 shows the analysis result of the mover motions under analysis condition II Figure 6 4 2 3 indicates that the mover can track the reference positions in the x and y directions and be positioned in the z and a directions with suppression of the and displacements Therefore mover motions can be controlled with stable magnetic levitation Figure 6 4 2 4 shows the analysis result of the armature currents under analysis condition II The g axis currents Ix and Jy are absolutely less than 7 mA but slightly larger than those in analysis I The g axis currents I and Jz used to control the translational forces F and F also generate simultane
30. H Ohsaki Positioning characteristics of a planar actuator for yaw angle IEEJ Annual Meeting on Industry Applications IIl pp 137 138 Osaka August 2007 LRA AME LEEBE ORAJ 9 19 8 anm DRM HOFFA TS DAI VY RY SD A812 pp 363 365 RR 2007 5H Y Ueda and H Ohsaki Magnetic suspension force characteristics of a small planar motor The 1 4 Symposium on Electromagnetics and Dynamics sead19 A312 pp 363 365 Tokyo May 2007 LEA KAZ LIRSHZEBBEZZTc 209 887JRME EAFA F F34 THES LD 06 63 pp 79 84 RI 2006 F 10 H Y Ueda and H Ohsaki Electromagnetic characteristics of a small actuator for multi degrees of freedom IEEJ Tech Meeting on Linear Drives LD 06 63 pp 79 84 Tokyo October 2006 LEA KARZ ABA 7 IR BLY 7 ze AE FOR EDE ER 18 F EAZ BRISA BAKS II pp 155 158 4 E 2006 4F 8 H Y Ueda and H Ohsaki Electromagnetic Characteristics of a Coreless Surface Motor based on Permanent Magnet Type Synchronous Motor IEEJ Annual Meeting on Industry Applications III pp 155 158 Nagoya August 2006 264 P27 P28 P29 P30 P31 HA KAZ DIRJETZBSBETZZTL ZO0BBBI2S51x5N8 BA e Qi BARB VAT FIA TSAMAS TER 06 51 LD 06 29 pp 19 24 tL 2006 7 B Y Ueda and H Ohsaki Investigation about drive of a small actuator for multi degrees of freedom ZEEJ Joint Tech Meeting on Transportation and Electric Railway and Linear Drives TER 06 51 LD 06 29
31. S 6 2 2 12 The rotation matrix of the stationary coordinate x y z with respect to the mover coordinate XmYmZm Rms can be calculated as follows Rys Roy Rem COS G 005 D sina cosy cosa sinf siny sina siny cosa sin f cosy sina cosf cosa cosy sina sin siny cosa siny sina sin B cosy sin J cos f siny cos J cosy renin 6 2 2 13 We can convert positions with respect to the mover coordinate x y z into those with respect to the stationary coordinate x j z as follows from Eq 6 2 2 13 The angular velocity of the mover with respect to the mover coordinate x y z as shown in Fig 6 2 2 2 m o Oy 0X can be calculated as follows 1 l l U i t 1 Osm Rom Rp Oa Rim 0505 ao 7t 1 A O T rene 6 2 2 14 Royl sin g sin y cosg sin J cosy sina cosy cosg sinf siny cosa cosf Ryg cos siny sina sinB cosy cosa cosy sina sin J siny sina cos D cos B cosy cos B siny sin D EE E 6 2 2 15 where dli 2 and co are angular velocities of the mover about the z axis with respect to the immediate coordinate xjyizi the y axis with respect to the immediate coordinate x y 2 and the x axis with respect to the mover coordinate xjy z respectively The angular velocities 2 and can be calculated from the unit vectors Ais As Ams and Euler angle d lt Lo as follows Qa A An Z Then we can calculate the differential of the Euler angle d dt from Eqs 6 2 2 1
32. X Y LIM IEEJ Transaction on Industry Applications Vol 118 No 1 pp 105 110 January 1998 in Japanese KEM SAF TEMS X Y LIM STR L BL vT ESE AWRY ATF ADEA EAZA us D Vol 118 No 1 pp 105 110 1998 F 1 H K Ozaki Rare earth magnets without heavy rare earth elements AIST TODAY Vol 8 No 5 pp 12 13 May 2008 in Japanese Ra avi XH Ep 7s AMA ERI TODAY Vol 8 No 5 pp 12 18 2008 5 H Philips Applied Technologies Magnetic Levitation Planar Technology Backgrounder Press Center October 2006 http www apptech philips com html press center planar maglev bac kgrounder htm 256 Rau02 Rau06 Sag07 Sag84 Sas96 Saw68 Shi01 Taj06 Taw05 Tex01 B Dehez D Grenier and B Raucent Two Degree of Freedom Spherical Actuator for Omnimobile Robot ZEEE International Conference on Robotics and Automation Washington DC Vol 3 pp 2381 2386 May 2002 B Dehez G Galary D Grenier and B Raucent Development of a Spherical Induction Motor With Two Degrees of Freedom IEEE Transaction on Magnetics Vol 42 No 8 pp 2077 2089 August 2006 M Sagawa M Hamano and M Hirabayashi Permanent Magnet Material Science and Application Agne Gijutsu Center September 2007 in Japanese Pe PLA EE EAA KARA BEE E AS TT eile v 2007 449 A M Sagawa S Fujimura N Togawa H Yamamoto and Y Matsuura New Material for Permane
33. al drive T 0 Y X y ay Mover Displaced in OTN q axis current 3 for y drive gt 0 X N 0 No magnetization Stator No Torque generation d Generated torques 7 from the g axis current for the y directional drive Fig 6 1 2 9 Schematic views of generation of torques T 183 2 15 1 05 0 0 5 1 LS Roll angle y deg NW a Driving forces due to the d axis current for the x directional drive Ls LA 15 mN mm I c Tx Ty 2 1 5 1 05 0 0 5 l L Roll angle deg Un L2 b Driving forces due to the q axis current for the x directional drive lx 1A Fig 6 1 2 10 Driving forces for roll angle y at yaw and pitch angles a B 0 deg when the armature currents for the x directional drive are supplied 184 N 2 1 5 1 0 5 0 0 5 1 1 5 Roll angle y deg a Driving forces due to the d axis current for the y directional drive Ii 1A Tx Ty Tz mN mm in i 2 1 5 1 05 0 0 5 Roll angle deg b Driving forces due to the q axis current for the y directional drive 1 A Fig 6 1 2 11 Driving forces for roll angle y at yaw and pitch angles a B 0 deg when the armature currents for the y directional drive are supplied 185 Displaced in 7 Z d axis current y forx drive gt 0 Stator Positive torque generation a Generated torques T due to the d axis current for the x directional drive
34. also shows that the g axis currents IJ ly generate the translational forces F F on a plane without vertical forces F Therefore the d and q axis currents lax lgx Lay Igy gt independently control the translational forces F F Fz gt stabilize the pitch and roll motions However the d axis currents utilized to control the suspension forces F generate yaw directional torques proportional to the yaw angle a that is they generate instable yaw motions Therefore in order to realize both 3 DOF motion controls on a plane and magnetic suspension a stabilization mechanism for the yaw motions is needed Then we can consider the following two methods toward addition of the stabilization mechanism redesign of structures of the permanent magnet mover or stationary armature conductors Fabricating the permanent magnet mover is difficult in bonding each permanent magnet component On the other hand the armature conductors can be flexibly and easily manufactured by means of multilayered printed circuits In this study the armature conductors are redesigned to offer stable yaw motion with less interference to the translational pitch and roll motions The torques acting on the mover depend on the relative yaw pitch and roll distances between the mover and the armature conductors but relative pitch and roll distances should be always nearly equal to 0 deg in order to maintain a small air gap The torques also depend on pitch lengths of
35. anslational forces Fy F and torques 7 T when the pitch and roll positions are not displaced 8 y 0 deg So at least four kinds of the g axis currents that is four pairs of polyphase currents are needed to actively control 6 DOF motions Furthermore Figs 6 1 2 3 and 6 1 2 4 indicate that the d and qg axis currents generate only torques without translational forces when the relative yaw distance is 24 7 deg or 45 deg As mentioned in Subsection 6 1 2 a magnitude of torque T resulting from the mover tiled by 24 7 deg is larger than that by 45 deg Therefore in this study the armature conductors are tilted by 24 7 deg in the yaw direction from the armature conductors for the x directional drive I term this arrangement armature conductors for the a directional drive When the yaw angle of the mover a 0 deg the d axis currents for the a directional drive L gt generate only torques T7 gt without vertical forces F Therefore the d axis currents Jj can separate the generation of the vertical forces F and torques 7 and stabilize the yaw motion To date the d and g axis currents are generated by three phase currents but they can be also be generated by two phase currents In this study a magnetically levitated planar actuator with three pairs of two phase armature conductors is organized as shown in Fig 6 1 3 4 Tables 6 1 3 1 and 6 1 3 2 show the specifications of the miniaturized permanent magnet mover and a tri
36. ators with which this study deals have especially good controllability of the driving forces in planar actuators With these technical details in mind I then summarized the specifications of synchronous planar actuators that had been developed In synchronous planar actuators planar actuators with a permanent magnet mover realize 222 sophisticated motion controls but have insufficiently wide movable area unless the planar actuators have a large number of armature conductors The planar actuator that I proposed in this study is aimed at achieving compatibility of both sophisticated motion controls and a wide movable area using just a small number of armature conductors In Chapter 2 I clarified the orientation of my proposed planar actuator in relation to previous planar actuators Chapter 3 presented the fundamental conceptual design of my proposed planar actuator which aims to resolve the technical issues of previous planar actuators The drive principle of the planar actuator is based on two orthogonal linear synchronous motors The planar actuator form spatially superimposed magnetic circuits corresponding to the magnetic circuits of the two orthogonal linear synchronous motors There are two polyphase armature conductors and exciting these armature conductors generates twordirectional multipole magnetic field over the stators Therefore increasing the length of all the armature conductors easily expands the movable area Based on the nu
37. d Dr Diy Dy Dy are proportional and differential parameters respectively In this study references of the armature currents L and i are calculated from those of the translational forces F as follows Driving Currents forces Translational force control F O 00001714 F 0 Ka lil Fy 000 00 1 fz gt F 2 Ka 0 g T 1 os LE 0 000 E F Hl 0 rj L E 3x4 3x2 F12 K33 9 ll A matrix matrix bi Kai Kas lt 0 r va in ly lt 0 gt F0 K r 6 x 6 matrix M Torque control 1 lac Ty p uex2 e 3x4 l la atrix lye matrix lav lau Fig 6 3 1 3 Control method for driving forces Ta x ud zs 6 3 1 9 LO Ks Kar pip mmm 3 1 ly J S Fy 6 3 1 10 lle ku eal mme 3 Supplying the armature currents i and i equal to the references i and i generates the translational forces F equal to the references Fun 6 3 2 Torque Characteristics and Rotational Motion Control The armature currents i and i generate not only the translational forces F but also the torques Tsm Therefore it is extremely important to investigate how the torques Tsm resulting from the armature currents i and i influence the rotational motions of the mover When the Euler angle 0 the torques 7 7 and T are dominant on the Euler angle o f and y respectively Next I performed a numerical analysis of the torque characteristics due to the armature currents for the x directional drive when
38. e number of armature conductors However there is a disadvantage to magnetic circuits that needs to be solved which is that realizing decoupled controls among the driving forces in each degree of freedom is difficult The most important assertion and technical contribution of this thesis is the design of the planar actuators so as to achieve independently control more degree of freedom mover motions by using spatially superimposed magnetic circuits Chapter 1 presented an introduction to and applications for MDOF drive systems Multiple moving part actuators consisting of multiple 1 DOF actuators have been most utilized in MDOF drive systems However there are several disadvantages with multiple moving part actuators that make it difficult to improve the accuracy and response of the mover drive In order to solve these disadvantages single moving part actuators capable of direct drive with MDOF have been studied Chapter 1 then introduced important element technologies including magnetic materials and circuits position sensing and suspension and guide mechanisms With this in mind the purpose and technical contributions of this study were detailed Finally the structure of this thesis was outlined Chapter 2 presented classification of MDOF drive systems and remarks about their features and technical issues MDOF drive systems can be classified by the number of moving parts form of driving forces and drive principle Synchronous planar actu
39. e Euler angle a can be calculated from Eqs C 11 C 15 and represented as follows 238 a Vas cos 8 Y Y sin sin y Y 3 Y cos y e C 16 L X3 COS B r Y sin 8 Sin y a sin Next in order to obtain the mover positions a normal vector of each surface mms and a position vector of each surface center rms U 1 2 3 4 5 or 6 with respect to the sensor coordinate xyz are introduced as shown in Fig C 4 In Fig C 4 O and O express origins at the sensor and mover coordinates respectively and O expresses center of surface i i 1 2 3 4 5 or 6 When the mover is not displaced from the base position the normal vector msio and position vector Fat can be represented as follows Has 0 ol A ms2 0 1 0 of nasi O Us Ol es Eos OO anite tereti eom C 17 A ms5 0 o 0 1P Nins6 0 o 0 il m Esso A120 Poy g Sle SU 0 kite e Eee C 18 Fass 0 0 h 2J Tns6 0 10 0 h2 rio 7 w 2 0 OF ras w 2 0 of The normal vector Hav and position vector rms can be calculated by the normal vector Amsio and position vector Fras i 1 2 3 4 5 or 6 as follows TTE d eri S C 19 Eg REL ev ea ee ee I luus iue ME C 20 where R m expresses the orientation of the mover with respect to the laser coordinate xyz and can be represented by the Euler angle as follows cosa cos D sina cos f sin f
40. e torques 7 T T for the roll angle y when the d and q axis currents are supplied U 1 A Ign 1A I 1A or ly 1 A the yaw and pitch positions are not displaced 0 deg From these results it can be seen that the d axis currents generates the torques T proportional to the roll angle y and the g axis currents generates the almost constant torques T Figure 6 1 2 12 shows schematic views of the generation of the torques 7 The g axis current for the x directional drive also generates the torques 7 proportional to the roll angle y 177 20 ren 40 T 24 3 gt I Ja asl _ 15 pi 30 K 10 20 z 5 10 S amp 0 0 id C E S 5 102 G S S 10 208 E 15 30 20 40 90 60 30 0 30 60 90 Yaw angle deg a Driving forces from the d axis current for the x directional drive Ls LA 15 Uu O a Cn Translational force Fx mN oS Kus Ur tO 90 60 30 0 30 60 90 Yaw angle deg b Driving forces from the y axis current for the x directional drive L 1 A Fig 6 1 2 3 Driving forces for yaw angle c at pitch and roll angles y 0 deg when the armature currents for the x directional drive are supplied 178 30 Z E 20 p 10 z 2 E G 0 E E 9 103 S E 5 204 a 30 40 90 60 30 0 30 60 90 Yaw angle deg a Driving forces from the d axis current for the y directional drive Zy 1 A Ww e oO oc o
41. ement sensors Figure C 5 shows the calculation procedure of the 6 DOF position from the output signals of the six laser displacement sensors Next I fabricated the position sensing system shown in Fig C 6 and then investigated the characteristics The specifications of the fabricated position sensing system are shown as follows gt Sensors 1 2 and 3 LK 080 Key01 gt Sensors 4 5 and 6 LK G080 Key02 gt tilted angles of laser beams from Sensors 4 5 and 6 to z axis 0 25 deg 6 15 deg and amp 15 deg gt distances between sensor head and measurement point in Sensors 4 5 and 6 db 70 mm db 68 mm and db 68 mm The results show there are important problems to be resolved the detected positions include errors caused by dimension and placement errors of each piece of experimental apparatuses property variations of the sensors and power amplifiers due to temperature variations electrical noise and so on Furthermore these errors can induce identification errors in the system constant matrix K in the motion control algorithm and deteriorate the motion control characteristics Therefore calibrating the position sensing system is an extremely important issue 244 Sensor E osition Mine Vine lm gt Euler angle a gt Euler angle 2 Euler angle c gt Euler angle 7 gt Euler angle f gt Sensor 1 Sensor 2 gt Euler angle 7 gt Sensor 3 or 2 S
42. ems ICEMS2006 Nagasaki Japan November 2006 H Ohsaki and Y Ueda Numerical Simulation of Mover Motion of a Surface Motor using Halbach Permanent Magnets The 8th International Symposium on Power Electronics Electrical Drives Automation and Motion SPEEDAM2006 pp 364 367 Taormina Italy May 2006 262 P15 P16 P17 Y Ueda and H Ohsaki Two dimensional Drive by a Coreless Surface Motor using Halbach Permanent Magnet Array The 7th University of Tokyo Seoul National University Joint Seminar on Electrical Engineering pp 157 161 Tokyo Japan November 2005 Y Ueda and H Ohsaki Positioning Characteristics of a Coreless Surface Motor using Halbach Permanent Magnet Array The 5th International Symposium on Linear Drives for Industrial Applications LDIA2005 pp 270 273 Awaji Japan September 2005 Y Ueda Y Kawamoto and H Ohsaki Dynamic Characteristics of a Coreless Surface Motor using Halbach Permanent Magnets The 5th International Power Electronics Conference IPEC Niigata2005 84 1 Niigata Japan April 2005 Domestic Conference Proceedings in Japanese P18 P19 P20 ELBA KREZ 6 DBAS ALHOKARH EMT 7 Fany nE Reali 2205 BASS BREA BAAS II pp 135 136 in 2007 t 8 B Y Ueda and H Ohsaki Planar Motion Control of a Maglev Planar Actuator with Six Armature Conductors IEEJ Annual Meeting on Industry Applications III pp 135 136 Kochi August 2008 LHR
43. ensor 2 Sensor 3 5 or 6 l um wy T rM i Sensor 5 Euler angle gt Sensor 6 or 4 or 5 SensorJ3 Euler ang Euler gt Sensi Sens Sensor 4 Rotation matrix R Position Nuus DP Tun gt Position x gt Position y gt Position z Euler angle a p y gt Euler angle a Sensor 5 gt Euler angle 2 udi gt Sensor 6 E gt Euler angle y F p Fig C 5 Calculation procedure for the 6 DOF position from the output signals of the six laser displacement sensors 245 F der Ca T S Top plate a ME Sensor 2 P Base plate M gt mca Emo 4 C P Em Sensor ES Mover and Stator Base plate b Side view c Mover and stator Fig C 6 Fabrication of position sensing system with 6 DOF 246 Bibliography ACh98 Act04 Aoy03 Aoy04 Asa85 Bin03al Bin03b Buc89 Chi99 A Chitayat Two Axis Motor with High Density Magnetic Platen U S Patent 5 777 402 July 7 1998 Technical Committee on Actuator Systems Actuator Engineering Yokendo December 2004 in Japanese TZaiI ALATA WBER 7772a 271 R S 2004 12 A T Nakajima M Aoyagi Y Tomikawa and T Takano Examination of High Power Disk Type Multi Degree of Freedom Ultrasonic Motor IEICE Technical Report Ultrasonics Vol 103 No 340 pp 49 54 September 2003 in Japanese Paes GS BRA Swe TPIERUSASB
44. ep consists of an integration of Lorentz force acting on the line segments as shown in Eqs 3 3 1 3 and 3 3 1 4 and so requires a lot of computation time The flux density B acting on the armature conductors greatly depends on the mover position Fsm and Euler angle d Therefore the driving forces F and Tsm are functions of the mover position r and Euler angle d In this study the system constant matrix K was calculated and the data table of K was made before the motion analysis Then the system constant matrix K is calculated from the mover position Fsm and Euler angle d by interpolating it with the data table at each time step Figure 6 4 1 1 shows a flow chart of the motion analysis The analysis conditions are shown as follows gt time step di 0 2 ms gt control period t 2 ms gt initial position r 0 gt initial Euler angle 4 0 When the z position is zero the mover is assumed to be on the stator The proportional and differential parameters are determined so that the settling times in the x y z and a motions are less than 1 s In this analysis to investigate the planar motion control and magnetic levitation the following two position references are given D Magnetic suspension at specific positions In this analysis the position references are given as follows the mover position Fem 0 0 0 15 and Euler angle a 0 deg Therefore the large q axis currents lx and 15 to generate the translatio
45. epresented by the Euler angle y and displacement of the measurement points AS AS AS as follows Sl RARE E c 9 Therefore the Euler angle fj can be obtained by Eqs C 8 and C 9 as shown in the following equation AS cos AS cos tan y AS sin 6 AS sin X45 B za x cos ERE OPERE C 10 Next in order to obtain the Euler angle oj output signals of Sensors 2 and 3 are necessary The y directional positions of the points measured by Sensors 2 and 3 Y and Y as shown in Fig C 3 can be calculated from the output signals The y directional distance between the two measurement points Y Y2 depends on only the Euler angle d lt L A nl and can be represented by the Euler angle as follows Y Y yu JYnp aeecc020900909909909900909009009990009000909099090090999990900099099990990909999999999999904999995990900990999990909909 C 1D y e EE tasin Y Tal aco te de ree oisisel vss dose u tens Hav ipae ea eaa tue PM nea C 12 Y12 X53 tana eecccsss000000222090090909000009909999999009990995995092229090909909090090000900929990990900909909902009022299922 92 C 13 where a and y express tilt angles about the z axis in x y plane and about the xr axis in cross section B B respectively and can be represented as follows i i 1 cosa sin zc Sen eur teasa siny C 14 sin a sin f sin y cosa cos y a an nem ia C 15 cosa cos y sin a sin D sin y Th
46. g 6 3 1 1 A cross section view of the triple layered printed circuit board is shown in Fig B 3 The total thickness of the printed circuit board is 0 425 mm The first second and third conductor layers have two phase armature conductors for the x y and a directional drives as shown in Figs B 4 B 5 and B 6 respectively The first and third conductor layers consist of 18 um thick copper film and 12 um thick through hole plating and the second conductor layer consists of 35 um thick copper film The width of all the conductors is 0 8 mm In the printed circuit board there are a lot of 0 3 mm diameter through holes including 12 um thick through hole plating in order to form mutually insulated three pairs of two phase printed circuits There are 15 um thick solder resist layers and 5 mm diameter lands with 1 4 mm diameter through holes on the top and bottom surfaces Figure B 7 shows the manufactured triple layered printed circuit board 229 PT H PEE TTET emet Z Z EO rf SHH A gt reperar H geseesss nM Z HAA nn SE QA EUT L4 H gt gt i 4444 AAA AA AAA H Ii Mepit 3 tese Hi i i i BL BU I Xr s D Z LIII M gt Xe G Z Structure of the double layered printed circuit board The solid lines Fig B 1 represent the copper film and the dashed lines represent external circuits 230 9 L t e L BH N a illi
47. g system realization of 6 DOF position sensing system preferably integrated with the mover or stator lt calibration of sensor signals against the experimental environment such as temperature and thermal expansion 224 In conclusion this thesis presents high performance MDOF planar actuators with a permanent magnet mover capable of traveling over a wide movable area on a plane with just a small number of stationary armature conductors The combination of the mover and stator can generate spatially superimposed magnetic fields for the MDOF drive and therefore increasing the length of the armature conductors can easily expand the movable area regardless of the number of armature conductors A planar actuator was conceptually designed and fabricated The fabricated planar actuator can independently control the 3 DOF motions of the mover Furthermore in order to eliminate deterioration of the drive characteristics due to friction forces the planar actuator was redesigned so that the mover could be stably levitated and the 3 DOF motions on a plane could be controlled Then the mover motion characteristics were successfully verified by means of a numerical analysis Next a small fabrication size was realized by integrating the permanent magnet array and armature conductors for the MDOF drive The planar actuator has the first millimeter sized mover and would provide a significant starting point when used with small electromechanical com
48. h nnn C 4 ra db sin 3 db cos Os 4 enp sind cosb C 5 n db sings 7 db sngt 06 sinOg cosby F C 6 where w and h are width length and height of the mover respectively x and y i j 1 2 3 4 5 or 6 are relative positions between Sensors 1 2 3 4 5 or 6 and N is a positive number Laser beams from Sensors 4 5 and 6 are tilted by amp 6 and amp to the zr axis respectively When the mover position with respect to the stationary coordinate XJsZ Fsm 0 0 0 and the Euler angle g 0 0 Ol distances between the sensor head and measurement point in Sensors 4 5 and 6 are db dbs and dbs respectively 237 The orientation of the mover can be calculated relatively easily by using a new Euler angle d lt La f yl that is defined by counterclockwise first o rotation around the z axis second j rotation around the y axis and third rotation around the x axis The Euler angle 5 can be represented by the amount of a displacement in the measurement points of Sensor 5 and 6 ASs and AS respectively as shown in Fig C 2 as follows AS cos AS cos 6 y tan 7 AS sin 0 AS sin Ys6 E PEE NT c7 Next the Euler angle can be represented by which is a tilt angle of the mover to the x y plane about the y axis as follows tan S tan P COS Sede mice Eee ELO o i LE EE C 8 Then the tilt angle can be r
49. ications LDIA2005 pp 266 269 Awaji Japan September 2005 D Ebihara and M Watada Study of a Basic Structure of Surface Actuator IEEE Transaction on Magnetics Vol 25 No 5 pp 3916 3918 September 1989 248 Ebi91 Edw01 Fit90 Fon03 Fuj02 Fuj99 Fuk04 Ga185 GKi01 D Ebihara M Watada and H Higashino Basic Structure of Four Phase PM Type Stepping Surface Motor and the Driving Method IEEJ Transaction on Industry Applications Vol 111 No 8 pp 654 660 August 1991 in Japanese HERAK MS Hk RE WPM HAT C 7 a ZE y NERE L TORBIA BRFSS amos D Vol 111 No 8 pp 654 660 1991 4F 8 B E P Furlani Permanent magnet and electromechanical devices materials analysis and applications San Diego Academic Press 2001 A E Fitzgerald C Kingsley Jr and S Umans Electric Machinery Mc Graw Hill Inc Sixth Edition 2003 Antoine Ferreira and Jean Guy Fontaine Dynamic Modeling and Control of a Conveyance Microrobotic System Using Active Friction Drive JEEE ASME Transactions on Mechatronics Vol 8 No 2 pp 188 202 June 2003 N Fujii and K Okinaga X Y Linear Synchronous Motors without Force Ripple and Core Loss for Precision Two Dimensional Drives IEEE Transaction on Magnetics Vol 38 No 5 pp 3273 3275 September 2002 N Fujii and M Fujitake Two Dimensional Drive Characteristics by Circular Shaped Motor IEEE Transaction on Industry App
50. ig B 7 Photographs of the manufactured triple layered printed circuit board C 6 DOF Position Sensing Utilizing Laser Displacement Sensors In order to suspend the mover without mechanical contact it is extremely important to detect the 6 DOF positions of the mover In this study a position sensing method utilizing six laser displacement sensors was investigated to precisely detect the position of the extremely small mover the dimension of which are approximately 11 mm x 11 mm x 2 mm The six laser displacement sensors are arranged as shown in Fig C 1 As mentioned in Chapter 4 we measure the distance from the sensor head to the surface of an object using the sensors and the principle of laser triangulation The sensors output a voltage proportional to the magnitude of the displacements from reference distance D Sensors 1 2 and 3 irradiate different lateral sides of the mover and Sensors 4 5 and 6 irradiate the same top surface of the mover In this study a sensor coordinate xz is defined to be tilted by 45 deg around the z axis to the stationary coordinate x y z Six laser displacement sensors are aligned so that path of the laser beam from Sensor i with respect to the sensor coordinate xyz r i 1 2 3 4 5 or 6 can be represented as follows n 2 5 0 o ed OO csetedus tatis eae pL Ee DM IE C D m 22 D 4 0 ons ene E EE EL EA A C 2 l pL o oe Sb T C 3 Tj 4 sin 9 75 ES db cost 2 Ning 0 cos
51. inates If the transformation matrix is given as R the inertia tensor J can be represented as follows The transformation matrix R from the stationary coordinate axes x y z to the mover coordinate axes XmVmZm shown in Fig 6 2 1 1 is given as follows cos z 4 sin z 4 0 R sin z 4 cos z 4 0 0 0 l Therefore we can calculate the inertia tensor J of the mover with respect to the mover coordinate axes Xn VmZm as follows 0 1828 0 0 Ja 0 04828 0 x107 kemi 6 2 1 8 0 0 0 3543 195 x SS O Q Q SOs OA OSA L c p S rs 2m Q Fig 6 2 1 1 Mover with mover coordinate axes x y z and stationary coordinate axes YMZ Fig 6 2 1 2 Rectangular prism with two mutually parallel coordinate axes 196 6 2 2 Euler Angle and Angular Velocity In order to define the 3 DOF rotational orientation of the mover the Euler angle needs to be defined Gol01 Taj06 In this study Euler angle d lt z f A is defined from a D and yas orderly counterclockwise rotations around the stationary z y and x axes passing through the center of mass of the mover respectively as shown in Fig 6 2 2 1 At first an immediate coordinate xjy z is defined to be rotated from the stationary coordinate x y z by around the z axis Then an immediate coordinate x ysz is defined to be rotated from the coordinate xiy zj by around the y axis Finally the mover coordinate x y z is
52. le y pitch angle J and yaw angle a respectively The driving forces acting on the mover can be calculated from the Lorentz force law with the same equations as Eqs 3 3 1 1 3 3 1 8 173 Armature conductors for x directional drive LET I I i f I i j 1 a Supplying three phase currents for the x directional drive Armature conductors S for y directional drive A a XX SA Xo SOL 2 BOX CO dado AA b Supplying three phase currents for the y directional drive Fig 6 1 2 1 Analytical model for 6 DOF driving forces Flux density B mT A Pa n 8 Siz 0 QUT 9 o ity a 0 V 4 per 4 my qo G 6 6 7 o0 Xm My an Fig 6 1 2 2 Flux density distribution on the plane 0 5 mm below the mover bottom Gi Analysis results for 6 DOF driving forces Figure 6 1 2 3 shows the analysis results of the driving forces F F T T T for the yaw angle when the d and q axis currents for the x directional drive are supplied U 1A or 1 A the air gap between the mover bottom and armature conductors is 0 5 mm and the pitch and roll positions are not displaced f y 0 deg Figure 6 1 2 3 indicates that the d axis current generates the translational forces F and torques T and the g axis current generates the translational forces F and torques Ty T The translational forces Fy F and torques
53. lectric Machines amp Drives Conference EMDC07 Vol 1 pp 272 278 Antalya Turkey May 2007 C M M van Lierop J W Jansen E Lomonova A A H Damen P P J van den Bosch and A J A Vandenput Commutation of a Magnetically Levitated Planar Actuator with Moving Magnets The International Symposium on Linear Drives for Industry Applications LDIA2007 OS6 2 Lille France September 2007 A Lebedev D Thakkar D Laro E Lomonova and AJ A Vandenput Contactless Linear Electromechanical Actuator Experimental Verification of the Improved Design The International Symposium on Linear Drives for Industry Applications LDIA2007 OS11 3 Lille France September 2007 259 Yan04 Yan07 Yan08a YanO8b Yan93 Xia07 T Yano Multi Dimensional Drive System The 14 International Symposium on Power Electronics Electrical Drives Automation and Motion SPEEDAM 2004 pp 457 462 Capri Italy June 2004 T Yano Y Kubota T Shikayama and T Suzuki Basic Characteristics of a Moultipole Spherical Synchronous Motor International Symposium on Micro Nano Mechatronics and Human Science MHS2007 pp 383 388 Nagoya Japan November 2007 T Yano Y Kubota T Shikayama and T Suzuki Development of a Spherical Synchronous Motor with Two Degrees of Freedom The 20th Symposium on Electromagnetics and Dynamics sead20 21B1 1 pp 133 138 Beppu May 2008 in Japanese RS MRA ELZ Mee 2 BHR OFF 36
54. lications Vol 35 No 4 pp 803 809 July 1999 H Fukunaga The Present State of High Performance Magnets IEEJ Journal Vol 124 No 11 p 694 November 2004 in Japanese BABE FESPEBEZK A REOR OBEN SE Vol 124 No 11 p 694 2004 11 B D Galburt Electro Magnetic Apparatus U S Patent 4 506 204 March 19 1985 J Tsuchiya and G Kimura Mover Structure and Thrust Characteristic of Moving Magnet Type Surface Motor The 27 Annual Conference of the IEEE Industrial Electronics Society ECON OLD pp 1469 1474 Colorado USA November 2001 249 GKi94 Go180 Ha186 Has01 Hig04 HigO6 Hig07 K Yamazaki T Shimizu and G Kimura The Motion Characteristics of a New Surface Actuator IEEJ Annual Meeting on Industry Applications pp 910 913 Matsuyama August 1994 in Japanese LR D KANE 13 BWR XA TAT TA 2 0158 Te TERUEL FR 6 F BASS BROEABA KS pp 910 913 1 1994 F 8 H H Goldstein Classical Mechanics Addison Wesley Publishing Co Inc Third Edition 2001 K Halbach Concepts for Insertion Devices that will Produce High Quality Synchrotron Radiation Nuclear Instruments and Methods in Physics Research Section A Vol 246 No 1 3 pp 77 81 May 1986 S Hashida F Kaiho Y Koizumi and T Tamura Surface Servo Motor PLANESERV Yokogawa Technical Report Vol 45 No 2 pp 83 86 2001 Gn Japanese fT WR Y E RB ANAS mY R
55. m Ultrasonic Motor The International Symposium on Linear Drives for Industry Applications LDIA2005 pp 258 261 Awaji Japan September 2005 254 MDD05 MDD07 MDD08 MTTO1 MTTO 2 MTTO3 Nis07 Investigating R amp D Committee on Multi dimensional Drive System Investigation of Possibility of Multi Dimensional Drive System IEEJ Technical Report No 1029 July 2005 Gn Japanese STT PJ TAT LRR BKM IAFYAT AON REIT ZEE 21 L nR No 1029 2005 4F 7 B Investigating R amp D Committee on Multi Degrees of Freedom Motors and Their Element Technologies Multi Degrees of Freedom Motors and Their Element Technologies ZEEJ Technical Report No 1081 March 2007 in Japanese SRREt LtOERRNMABMERS TGBmE t 27Lt 0 RRR ERFA Riv No 1081 2007 3 A Investigating R amp D Committee on Systematize Technology of Multi Degrees of Freedom Motors Systematize Technology of Multi Degrees of Freedom Motors IEEJ Technical Report No 1140 November 2008 in Japanese SBAHEE FOVAT LILI TSR SHH B ZE HRE D AF KJEE BRED Bess No 1140 2008 11 A MTT HERON DSP6067 hardware manual in Japanese MTT HERON DSP6067 F7zx7 27WwJ MTT HERON ADM16 4 hardware manual in Japanese MTT HERON ADM16 4 FUYUS7 v a77 MTT HERON DAM12 8 hardware manual in Japanese MTT HERON DAMI2 8 F7zxz7 Y 2o7M H Takahashi O Nishimura T Akita and H Tam
56. m of Global COE at University of Tokyo on Secure Life Electronics Tokyo Japan January 2009 Y Ueda and H Ohsaki A Planar Actuator with a Magnetically Levitated Mover Capable of Planar Motions by Only Six Current Control The 9th Seoul National University University of Tokyo Joint Seminar on Electrical Engineering Tokyo Japan January 2009 Y Ueda and H Ohsaki Six Degree of Freedom Motion Analysis of a Planar Actuator with a Magnetically Levitated Mover by Six Phase Current Controls The International magnetics conference Intermag2008 GH 09 Madrid Spain May 2008 Y Ueda and H Ohsaki Large Yaw Motion Control of a Planar Actuator for Two dimensional Drive The 6th International Symposium on Linear Drives for Industrial Applications LDIA2007 OS9 1 Lille France September 2007 Y Ueda and H Ohsaki Fundamental characteristics of a small actuator with a magnetically levitated mover The 4th Power Conversion Conference PCC Nagoya2007 pp 614 621 Nagoya Japan April 2007 Y Ueda and H Ohsaki Two dimensional Drive with Yawing motion by a Small Surface Motor The 8th Seoul National University University of Tokyo Joint Seminar on Electrical Engineering pp 79 82 Seoul Korea February 2007 Y Ueda and H Ohsaki Application of Vector Control to a Coreless Surface Motor based on a Permanent Magnet Type Linear Synchronous Motor The 2006 International Conference on Electrical Machines and Syst
57. magnetically levitated planar actuator is also designed so that all the magnetic circuits are mutually superimposed as in the following methodology i Compatibility verification of both 3 DOF planar motion and magnetic suspension controls of the planar actuator designed in Chapter 3 ii Redesign the planar actuator without increasing the number of the armature conductors so that planar motion and magnetic suspension are compatible if they are found not to be in i In order to design the planar actuator a numerical analysis of 6 DOF driving forces for 6 DOF mover positions is performed 172 6 1 2 6 DOF Force Analysis This section presents an analytical model of driving forces with 6 DOF and then presents the results of the analysis i Analytical model for 6 DOF driving forces The driving forces including the suspension forces greatly depend on the size of the gap between the mover and armature conductors and therefore this gap needs to be precisely controlled Generally reducing this gap increases the driving forces If the mover is located below the stator attraction forces to the stator are required to suspend the mover However the attraction forces are increased by reducing the gap which makes the vertical motions of the mover unstable Conversely if the mover is located above the stator repulsion forces from the stator are required to suspend the mover The repulsion forces are increased by reducing the gap and
58. merical analysis results of the driving forces I designed a decoupled control algorithm for 2 DOF translational and 1 DOF rotational motions Chapter 4 presented a design for an experimental system for an investigation into the drive characteristics of the planar actuator I implemented a control algorithm into a DSP connected to AD DA converter boards and designed a 3 DOF position sensing system using three laser displacement sensors as well as a suspension mechanism for the mover using ball bearings Then specifications of these experimental apparatuses were presented Chapter 5 presented an experimental verification of the 3 DOF motion controls of the mover on a plane and the results of the experiment From these experimental results I successfully demonstrated that 3 DOF motions could be independently controlled by two pairs of three phase currents The movable area in the translational motions can be infinitely extended and the rotational motions is in the range within the yaw angle 26 deg Furthermore the driving forces are periodic with a 90 deg period in the yaw direction and the mover can travel in multiple 90 deg steps in the yaw direction Therefore the planar actuator has a wider movable area than previous planar actuators although it only has two polyphase armature conductors Chapter 6 presented a feasibility verification of the magnetic suspension of a mover capable of 3 DOF planar motions in order to eliminate friction forces
59. n Industry Applications Vol 41 No 5 pp 1159 1167 September October 2005 W Gao S Dejima H Yanai K Katakura S Kiyono and Y Tomita A Surface Motor Driven Planar Motion Stage Integrated with an XY amp Surface Encoder for Precision Positioning Precision Engineering Vol 28 No 3 pp329 337 July 2004 W Gao M Tano S Kiyono Y Tomita and T Sasaki Precision Positioning of a Sawyer Motordriven Stage Proposal of the Positioning System and Experiments of Micro Positioning Journal of the Japan Society for Precision Engineering Vol 71 No 4 pp 523 527 April 2005 in Japanese GIR MER FS BRS Ar KRI Sawyer WIRE O RIT RR LIZ BHT SHE LERDO AT ANDRE EQUIS B amp R TSE Vol 71 No 4 pp 523 527 2005 4 H S Dejima W Gao H Shimizu S Kiyono and Y Tomita Precision Positioning of a Five Degree of Freedom Planar Motion Stage Mechatronics Vol 15 No 8 pp 969 987 October 2005 253 KNa01 Kor06 Kos01 Kos04 Lee08 Lee91 Lem01 Mae01 Mae04 Mae05 K Nakagawa F Kawashima and T Arai Isotropic SmZrFeN Bonded Magnet Powder with Highest Performance TOSHIBA REVIEW Vol 56 No 2 pp 56 59 February 2001 in Japanese URS JI ES SAT PHBA ERRIO SmZrFeN SERVE REGES REL a Vol 56 No 2 pp 56 59 2001 F 2 H N Korenaga Alignment Apparatus and Exposure Apparatus Using the Same U S Patent 7 075 198 July 11 2006 J Liu and T Ko
60. n which the mover is not displaced from the base position mm F ms5 0 12 0 Mover H Ojos gt x A E aat x ms4 0 x E 2 H AA my3 0 Tad d 1 U ni HA0 O x b Case in which the mover is displaced from the base position Fig C 4 Definition of the normal vector of each surface m and the position vector of each surface center rms with respect to the sensor coordinate xyz 242 Next the mover position rj and Euler angle d with respect to the laser coordinate xyz are transformed with respect to the stationary coordinate x y z because the control system of the mover position r and Euler angle with respect to the stationary coordinate x y z were designed in Chapter 6 The laser coordinate xy are tilted by 45 deg around the z axis from the stationary coordinate xz Therefore the mover position r with respect to the stationary coordinate x y z can be represented by that r m the laser coordinate xyg as follows where R expresses a rotation matrix that generates a 45 deg counterclockwise rotation around the z axis and can be represented as follows cos 45 sin 45 0 R sin 45 cos 45 Of sscsscescsssssesssnessssecsssnecssssesssacsncsnssesassncsscasensenees C 24 0 0 1 The orientation Rm defined by the Euler angle amp a A nl based on rotations around the zm yr and x axes as shown in Eq C 21 can also be represented by the Euler angle
61. nal forces F and F are unnecessary In this condition the magnetic levitation of the mover is easy to be stabilized because there are small torques 213 T and Tx which are not restoring torques II Planar motion control with magnetic suspension In this analysis in order to verify the compatibility of both the 3 DOF planar motion control and magnetic suspension the position references are given as follows gt x 2cos a mm gt y 2sin z mm gt z 0 15mm gt Euler angle a 0 deg In this analysis the q axis currents and 1 used to generate the translational forces F and F influence the magnetic suspension characteristics and this influence was investigated Physical model Time step dt gu cotum ott S TEN OIN A HUN NNI UTR Current controller Sampling time 1 Ponp Calculation of reference forces K W d T T i Data table of E F QE Motion equation E sn J Figure 6 4 1 1 Flow chart of 6 DOF motion analysis 214 6 4 2 Numerical Analysis Results Numerical analysis of the mover motions under the previously mentioned conditions D and II in Subsection 6 4 1 were performed These analysis results are shown as follows under each of the above conditions 1 D Magnetic suspension at specific positions Figure 6 4 2 1 shows the analysis result of the mover motions under analysis condition D
62. nd rp are determined to be zero because of the suppression of the and y motions The torque references T and T can be calculated from the reference T by Eq 6 3 2 1 Then the references of the armature currents for the a directional drive lia and Le can be calculated for the torque references 7 and T as follows 1 laa _ Kas Kas IT zb e 6 3 2 3 Ie Ke Kel rn Us where Tya and T a are torques due to the armature currents i and i and can be represented as follows 209 Iu Hih Ky Ky d pm T Kg Kg Ke3 Kg ly za ly LEES 6 3 2 4 Supplying the armature currents i equal to the references in generates 7 nearly equal to Tz and controls the rotational motions with less interference to the translational motions 210 UJ T 20 i renas E E N rfa B 7 0 0 G 19 pee ias ss ee mene GA amp S 0 Yane ke m he Ke j lt M lt n M Pounu elg 7774 gie T faa Uwe i i wee T dsi II dia 4 20 cx a pcd EI R lt EB L Kas E T lIe 2 1 5 1 05 0 0 5 1 1 5 Euler angle deg tO a Kis i lig Kss Ty lia and Kes y P lig at 2 y 0 0 UJ ce Kin 7 Ty Er a o NO e gt ae o y ce K 56 P lul Mas adici A pai ice dicet ono pnm eror dee e sd iq B Y 0 0 Kao K56 Koo mN mm A 2 15 1 05 0 0 5 l 1 5 Euler angle deg Nw b K46
63. nser gus ea BEEN S x eee Serm i a m d I n yi ii n D axis du I I i 4 T EE for y drive m CIS FH ria A E amp axis Nr ria n p Ti DAN for v drive epum x g m ann N TY emis p P SM q axis ITEEELUIT dd oic ee m TE B E IN for v drive Ge 2 5 4 1 a Be W y B L X Kale e a My gt Es at dq frame and a f frame for the x y and a directional drives L b U p axis for j drive Te J I Jl cl q axis U x y or for j drive A Magnetic field I due to mover qi d axis for j drive axis for j drive y Phasor diagram showing relation between dq frame and a f frame These pairs of d and q axis currents generate the translational forces F and torques T as follows f I x dx F y I qx F K r d ly 6 3 1 7 T l gub matz L DP LEIE CETTE ELDO I OO APUCIXT TIAS WPTRITS EIER IPC TTTETI 9 Ty L da A I where K is a 6 x 6 matrix and all elements of K depend on the mover position r m and Euler angle d Where Euler angle d lt 0 K can be approximated as shown in Fig 6 3 1 3 and therefore 3 DOF translational forces Fy F and F can be independently controlled by two phase currents i and i In this study references of the translational forces Fy LE F FJ are determined from the mover positions r x y z and position references r x y z by three PID controls F P s E L D T MMC 6 3 1 8 where Py Pix Pry Pj an
64. nt Magnets on a Base of Nd and Fe Journal of Applied Physics Vol 55 No 6 pp 2083 2087 March 1984 K Sasae K Ioi Y Ohtsuki and Y Kurosaki Development of a Small Actuator with Three Degrees of Rotational Freedom 3rd Report Design and Experiment of a Spherical Actuator Journal of the Japan Society for Precision Engineering Vol 62 No 4 pp 599 603 April 1996 in Japanese fer ire RAAF KERE Bisse 3 BART 7 TA A OBA GS 3 8 HHT 7 Farny SLS L HERREG HALES amp 5 Vol 62 No 4 pp 599 603 1996 F 4 H B A Sawyer Magnetic Positioning Device U S Patent 3 376 578 April 2 1968 Shin Etsu Rare Earth Magnets N48H data sheet in Japanese SB Le T lt Pae T Ra hb INASHT A7L HJ http www shinetsu rare earth magnet jp support download html H Tajima Fundamentals of multi body dynamics Tokyo Denki University Press November 2006 in Japanese HW TPR 4 PAT 7 AOE RR ERAS 2006 2114 Y Tawara and K Ohashi Rare Earth Permanent Magnet Morikita Publishing October 2005 in Japanese kak AGE CA kAREA RIHAR 2005 10 A Texas Instruments OPA548 data sheet J tbo or Tom94 Tom96 Tru06 Tru96 Tru97 TSh06 Toy07 Toy95 Y Tomita Y Koyanagawa and F Satoh A Surface Motor Driven Precise Positioning System Precision Engineering Vol 16 No 3 pp 184 191 July 1994 Y Tomita M Sugimine and Y Koyanagawa Developme
65. nt of Six Axis Precise Positioning System Driven by Surface Motor JSME Transaction C Vol 62 No 597 pp 1840 1847 May 1996 in Japanese BAB IEEE DBI I 7 4 2 xBHwI ABBIER 4 XY AT 70p3 HP WEZ a5 C Vol62 No 597 pp 1840 1847 1996 5 H D L Trumper Levitation Linear Motors for Precision Positioning IEEJ Transactions on Industry Applications YVol 126 No 10 pp 1345 1351 October 2006 Homepage of the Precision Motion Control Laboratory Massachusetts Institute of Technology http web mit edu pmc ww w pastprojects Planar planar html D L Trumper W J Kim and M E Williams Magnetic Arrays U S Patent 5 631 618 May 20 1997 T Shikayama H Yoshitake H Honda Y Yoshida M E Kabir M Takaki and Y Tsutsui Development of Planar Servo Drive IEEJ Tech Meeting on Linear Drives SPC 06 169 LD 06 71 pp 13 19 Kanazawa December 2006 in Japanese ELU FERH AAC SAR UA FIT AW md HHEH CMR EIT TOM CASS PAREJA Y FT FIA SFAMUAS SPC 06 169 LD 06 71 pp 13 19 4 iR 2006 12 A T Mashimo K Awaga and S Toyama Development of a Spherical Ultrasonic Motor with an Attitude Sensing System using Optical Fibers The IEEE International Conference on Robotics and Automation pp 10 14 Rome Italy April 2007 S Toyama S Sugitani G Zhang Y Miyatani and K Nakamura Multi Degree of Freedom Spherical Ultrasonic Motor The IEEE International Conference on Robotics and Automation
66. ons 6 2 3 1 and 6 2 3 2 represent 3 DOF translational and rotational motion equations of the mover respectively All variables in the translational and rotational motion equations are represented with respect to the stationary coordinate XJ5z and mover coordinate x y z respectively The position r and Euler angle d of the mover can be represented by the velocity V m and angular velocity 9 respectively as follows Equations 6 2 3 1 6 2 3 4 can represent dynamic behaviors of the mover with 6 DOF 201 6 3 Planar Motion Control with Stable Magnetic Levitation This section discusses six current controls to stably levitate the mover and actively control the x y z and a motions There are two important things for the motion controls gt to generate independent translational forces F F and F with stable torques in the and f directions gt to generate torques in the a direction with less interference to translational forces F F and F This section first presents driving forces resulting from three pairs of two phase armature currents and then the driving force control system 6 3 1 Translational Motion Control In this study three pairs of two phase currents ij Uy b U x y or a as shown in Fig 6 3 1 1 are assumed to be supplied to the three pairs of two phase armature conductors as shown in the following equations e ES M mm M ER TIER 6 3 1 1 P iO mE 6 3 1 2 Figure 6 3 1 2 sho
67. ously the torques 7 and T respectively Therefore displacement of the Euler angles f and y under analysis condition II is larger than that in analysis condition I due to the greater g axis currents J and ly for the planar motions 215 Therefore I proposed a planar actuator with a magnetically levitated mover capable of large planar motions over the stator and demonstrated both 3 DOF planar motion and magnetic levitation controls by applying three pairs minimum number of two phase armature currents control by numerical analysis of the 6 DOF motion 0 18 0 16 0 14 0 12 0 1 0 08 0 06 0 04 0 02 y Z mm Displacement x 0 02 ue Uo Un 4 0 0 5 15 2 25 Time z s a Translational motions x y z Euler angle e 2 y deg Time s b Rotational motions a f y Fig 6 4 2 1 Analytically obtained mover motions under analysis condition I 216 0 05 0 1 0 15 lay A 1 o t2 0 25 0 3 0 35 0 4 0 45 0 5 Current x 0 403 l 15 2 25 3 35 4 Time s a d axis currents and 14 used to generate suspension forces F dda lda A v lyy z 0 01 5 0 02 Current 0 03 0 04 0 05 l Lh5 2 22 Time s eo U3 a 4 b d and q axis currents lyx la lda and lya used to control planar motions Fig 6 4 2 2 Analytically obtained armature currents under analysis condition I Displacement x y mm
68. ow01 Ish97 Jan07 Jun02 Joh97 Y Hasegawa K Hirata T Yamamoto Y Mitsutake and T Ota New Spherical Resonant Actuator IEEJ Transactions on Industry Applications Vol 127 8 No 5 pp 642 647 May 2008 H Nakamura Magnetic Properties of Miniature Nd Fe B Sintered Magnets IEEJ Journal Vol 124 No 11 pp 699 702 November 2004 in Japanese pim MEMI gt TLE Nd FeBRRRHA BASS BA 238 Vol 124 No 11 pp 699 702 2004 F 11 A J W Jeon M Caraiani Y J Kim H S Oh and S S Kim Development of Magnetic Levitated Stage for Wide Area Movements Bu The International Conference on Electrical Machines and Systems GCEMS2007 pp 1486 1491 Seoul Korea October 2007 Z J Butler A A Rizzi and R L Hollis Integrated Precision 3 DOF Position Sensor for Planar Linear Motors ZEEE International Conference on Robotics and Automation pp 3109 3114 Leuven Belgium May 1998 7 0 Zhu and D Howe Halbach Permanent Magnet Machines and Applications A Review IEE Proceedings Electric Power Applications Vol 148 No 4 pp 299 308 July 2001 J Ish Shalom Modeling of Sawyer Planar Sensor and Motor Dependence on Planar Yaw Angle Rotation IEEE International Conference on Robotics and Automation Albuquerque pp 3499 3504 New Mexico April 1997 J W Jansen Magnetically Levitated Planar Actuator with Moving Magnets Electromechanical Analysis and Design PhD thesis Eindhoven Univer
69. ple layered printed circuit board mounting armature conductors respectively 191 y Top view p Z AX g Vy Mover Halbach array Stator 3 layer printed circuit Two conductors for y drive Two conductors for x drive Beze md T Two conductors for a drive Side view Thickness 0 mm a Insulating layer Thickness 0 2mm 7 a Fundamental structure 909090 C Mover b Manufactured stator and mover Fig 6 1 3 4 Magnetically levitated planar actuator 192 Table 6 1 3 1 Specifications of miniaturized permanent magnet mover Material NdFeB Shin Etsu Chemical Co Ltd Residual flux density B 1 35 1 41 T Overall dimension 11 mm x 11 mm x 2mm PM component 2 mm x 2 mm x 2 mm or 2 mm x mm x 2mm Total mass 18g Table 6 1 3 2 Specifications of triple layered printed circuit board Number of conductor layers 3 Pitch of meander pattern 7 2 1mm Number of turns of meander pattern 16 Width of conductors 0 8 mm Thickness of conductors 30 35 um Thickness of insulating layer 0 1 or 0 2 mm Resistance of each conductor 1 00 193 6 2 Dynamic Behavior of Mover The mover has 3 DOF translational and rotational motions because there is no mechanical suspension mechanism When the physical quantities of the mover motion are represented it is extremely important what coordinates are respected The translational motions are often represented with respec
70. ponents in an MDOF drive 225 Appendices A Fabrication of the Smallest Halbach Permanent Magnet Mover B Structure of Manufactured Printed Circuit Board C 6 DOF Position Sensing Utilizing Laser Displacement Sensors 226 A Fabrication of the Smallest Halbach Permanent Magnet Mover In this study I fabricated the smallest 2 D Halbach permanent magnet array which measure just 11 mm x 11 mm x 2 mm The permanent magnet array consists of one group of 16 permanent magnets and one of 24 permanent magnets which measure 2 mm x 2 mm x 2 mm and 2 mm x 2 mm x 1 mm respectively Mr Koji Miyata and Mr Yuji Doi Shin Etsu Chemical Co Ltd kindly provided these permanent magnets for this study In the Halbach permanent magnet array adjacent permanent magnets are mutually subjected to repulsion forces Therefore I fabricated the permanent magnet array by bonding the permanent magnets using these excellent adhesives Araldite standard Epoxy adhesive and LOCTITE 326 LVUV Ultraviolet cure adhesive combined with LOCTITE 7649 Primer First I fabricated the permanent magnet array on a 2 mm iron plate mounting a square ruler shaped 1 2 mm iron plate in order to fix the permanent magnets using the iron plate during bonding between the permanent magnets For the bond between the permanent magnets I used LOCTITE which bonds quickly less than one minute and has a relatively high shear strength 18 5 N mm bonding only the lateral sides
71. pplications Vol 129 No 3 March 2009 Gin Japanese to be published ERISA KAZ 2180 IRSA LCA 25 IC IA v GEH C SES DARIO 3 B RRIT Z 7 2 2 BASS D Vol 129 No 3 2009 5 3 B ARTE Y Ueda and H Ohsaki Positioning of a Maglev Planar Actuator by Controlling Three Sets of Two Phase Currents Journal of the Japan Society of Applied Electromagnetics and Mechanics Vol 17 No 1 March 2009 Gn Japanese to be published LA A AE 3180 2TBD BIG T X S ERI T 772 270 HRY AA AEM 423 Vol 17 No 1 2009 3 A ERTE Y Ueda and H Ohsaki Six Degree of Freedom Motion Analysis of a Planar Actuator with a Magnetically Levitated Mover by Six Phase Current Controls JEEE Transaction on Magnetics Vol 44 No 11 Part 2 pp 4301 4304 November 2008 Y Ueda and H Ohsaki A Planar Actuator with a Small Mover Traveling over Large Yaw and Translational Displacements ZEEE Transaction on Magnetics Vol 44 No 5 pp 609 616 May 2008 261 International Conference Proceedings P6 P7 P8 P9 P10 P11 P12 P13 P14 Y Ueda and H Ohsaki Armature Conductor Design of a Long Stroke Planar Actuator with Multiple Degrees of Freedom The 7th International Symposium on Linear Drives for Industrial Applications LDIA2009 Incheon Korea September 2009 to be submitted Y Ueda and H Ohsaki Design and Control of a High Performance Multi Degree of Freedom Planar Actuator Symposiu
72. re not stable restoring torques So next I performed a numerical analysis of the torque characteristics due to the armature currents for the a directional drive Figure 6 3 2 4 shows the torques due to the armature conductors for the a directional drive at 2 0 0 When the Euler angles 8 0 0 the d axis current 4 generates only the torque 7 and the q axis current loa generates only the torques 7 T Therefore the torques 7 and 7 cannot be independently controlled by the armature currents for the a directional drive Figure 6 3 2 5 shows the torques from the armature conductors for the a directional drive at Z 0 2 2 The d and q axis currents generates T Ty Tx but the torque D is much less than the torques T and T Therefore in this study the torques 7 and T are controlled by the two armature currents for the a directional drive When the Euler angle 0 and angular velocity 0 a linearized equation of the rotational motion can be obtained from Eqs 6 2 3 2 and 6 2 3 4 as follows 2 i ar Ra Fa Yam an In an ye eee 6 3 2 1 Rag 4 y T T F T Ll In this study Tc which is the reference of Tg is determined by a PD control from the Euler angle c and the reference a as follows Ty Pula a Dry Z bnnc pU LE ew ey 6 3 2 2 where Pra and Dra are proportional and differential parameters respectively Then the references T n a
73. refore a rotation matrix to rotate counterclockwise by around the y axis Ri can be calculated as follows cos sin a 1 cos cosa sina 1 cos cosa sin Ra cosa sina U cos p cos f cos a 1 cos p sina sinf 6 2 2 6 cosa sin B sina sin f cos B Finally the unit vector of the x axis with respect to the coordinate x2y2Z2 Ams iS represented as follows l cosa cos D Ans Ry R 0 sin cosg ern 6 2 2 7 0 sin B Therefore a rotation matrix to rotate counterclockwise by y around the x axis Rom can be calculated as follows Ra E AD c cc ce E 6 2 2 8 cos y 4 cos a cos t cos y Rom sin sin y cosa sina cos 8 1 cos y sina cos f sin y cosa cos sin 1 cos y sin sin y cosa sina cos B 1 cos y Rim cosy sin a cos 8 0 cosy cosa cos f sin y sina cos f sin 1 cos y sina cos f sin y L cosa cos sin 1 cos y R343 cosa cos f sin y sin cos 8 sin B 1 cos y RR 6 2 2 11 cos y sin 1 cos y The rotation matrix of the mover coordinate x y z with respect to the stationary coordinate x y z Rsm can be calculated from the rotation matrices Rs R12 R as follows 198 Ron ES RyRy Ron cosa cos D sina cos f sin D sina cosy cosa sinf siny cosa cosy sina sin siny cosf siny sing siny cosg sin J cosy cosa siny sina sinB cosy cosff cosy
74. rrent control algorithm were conceptually designed Furthermore I validated the designed planar actuator by numerical analysis of the 6 DOF motions The results obtained in this thesis indicate the possibility of the realization of a high performance MDOF planar actuator gt gt gt gt gt decoupled 3 DOF motion control and magnetic levitation on a plane wide movable area by a small number six of armature conductors extendible movable area regardless of the number of armature conductors smal millimeter sized mover no problematic wiring to adversely affect drive performance As the next step it is necessary to design an experimental system for the verification of the 6 DOF motion characteristics and conduct experimental tests 220 Chapter 7 Conclusions This chapter concludes this thesis and suggests future work 221 7 Conclusions This chapter presents the accomplishments and technical contributions of this thesis as conclusions and also makes suggestions for future work 7 1 Conclusions In this study I designed planar actuators that have a small mover capable of traveling over a wide movable area on a plane and which is driven by a small number of armature conductors These planar actuators form spatially superimposed magnetic circuits for the MDOF motion controls Magnetic circuits are the most innovative of all planar actuators and enable the extensions of the movable area regardless of th
75. seki 3 Degrees of Freedom Semi Zero Power Maglev Scheme for Two Dimensional Linear Motor The International Symposium on Linear Drives for Industry Applications LDIA2001 pp 114 119 Nagano Japan October 2001 Y Makino J Wang and T Koseki Control of 6 Degrees of Freedom Motion and Design of a Mover Consisting of Three Linear Induction Motors and Three U Type Electromagnets The International Symposium on Power Electronics Electrical Drive Automation and Motion SPEEDAM 2004 pp 430 435 Capri Italy June 2004 L Yan I M Chen C K Lim G Yang W Lin and K M Lee Design and Analysis of a Permanent Magnet Spherical Actuator IEEE ASME Transactions on Mechatronics Vol 13 No 2 pp 239 248 April 2008 K M Lee and C K Kwan Design Concept Development of a Spherical Stepper for Robotic Applications IEEE Transactions on Robotics and Automation Vol 7 No 1 pp 175 181 February 1991 LEM LA 55 P data sheet K Takemura and T Maeno Design and Control of an Ultrasonic Motor Capable of Generating Multi DOF Motion JEEE ASME Transactions on Mechatronics Vol 6 No 4 pp 499 506 December 2001 K Takemura Y Ohno and T Maeno Design of a Plate Type Multi DOF Ultrasonic Motor and Its Self Oscillation Driving Circuit IEEE ASME Transactions on Mechatronics Vol 9 No 3 pp 474 480 September 2004 K Otokawa K Takemura and T Maeno Development of an Arrayed Multi Degree of Freedo
76. sity of Technology November 2007 H S Cho and H K Jung Analysis and Design of Synchronous Permanent Magnet Planar Motors IEEE Transactions on Energy Conversion Vol 17 No 4 pp 492 499 December 2002 J Ormerod and S Constantinides Bonded permanent magnets Current status and future opportunities Journal of Applied Physics Vol 81 No 8 pp 4816 4820 April 1997 252 Kan04 Key01 Key02 Kim97 Kim98 Kim05 Kiy04 Kiy05a Kiy05b Y Kaneko Toward the Theoretical Value of Nd Fe B Sintered Magnets IEEJ Journal Vol 124 No 11 pp 695 698 November 2004 in Japanese ATAI BSR Z BHT Nd Fe B HEKA BAFA BAFS amp 5 Vol 124 No 11 pp 695 698 2004 F 11 B Keyence CCD Laser Displacement Sensor LK 2000 Series Instruction in Japanese X cr A ICCDv JXZrEz3 LK 2000 7 2 WRAAE Keyence High Speed and High Precision CCD Laser Displacement Sensor LK G Series User s Manual in Japanese ALA eR BRE CCD PRI ST LK G VY 2Y A aJMJ W J Kim High Precision Planar Magnetic Levitation PhD thesis Massachusetts Institute of Technology June 1997 W J Kim and D L Trumper High Precision Magnetic Levitation Stage for Photolithography Precision Engineering Vol 22 No 2 pp 66 77 April 1998 S Verma WJ Kim and H Shakir Multi Axis Maglev Nanopositioner for Precision Manufacturing and Manipulation Applications IEEE Transactions o
77. t 2 D Halbach permanent magnet array 228 B Structure of Manufactured Printed Circuit Board As mentioned in Chapter 3 in the experiments on 3 DOF motion control on a plane a double layered printed circuit board was utilized in order to generate a multipole magnetic field that has arbitrary amplitude and phase in the x and y directions The printed circuit board consists of two 35 um thick conductor layers and a 100 pm thick insulating layer sandwiched between the two conductor layers In each conductor layer 0 8 mm wide strips of copper film are aligned at 1 76 mm corresponding to one third of the pitch length of the 3 DOF planar actuator intervals Three phase conductors for the x and y directional drives are then formed by inserting the external circuits shown by dashed lines in Fig B 1 The figure shows how exciting two pairs of three phase conductors generates a multipole magnetic field above the centered 90 mm x 90 mm area of the printed circuit board The intervals between the strips of copper film near the end of each strip are longer than those near the center in order to secure areas wide enough to solder and 2 5 mm diameter lands are aligned at 3 5 mm intervals Figure B 2 shows the manufactured double layered printed circuit board In Chapter 6 a triple layered printed circuit board was designed in order to generate a multipole magnetic field that has arbitrary amplitude and phase in the x y and x directions shown in Fi
78. t to the stationary coordinate and the rotational motions are often represented with respect to the mover coordinate This section introduces an equation for the 6 DOF motions of the mover that describes the dynamic behavior 6 2 1 Mass and Inertia Tensor The mass M and inertia tensor J of the mover are determined by mass density and dimensions The mass M was measured using an electronic scale LIBROR EB 3200B Shimadzu Corp that has a 0 1 g resolution The scale indicated that mass M E 8 g which agreed with the theoretical value calculated from mass density p 7 60 x 109 kg m and volume V 224 mm The inertia tensor J with respect to the mover coordinate axes X y z With an origin at O corresponding te the center of mass of the mover shown in Fig 6 2 1 1 can be represented as a 3 x 3 matrix as follows Ju da ae Jaca abge d esie MEET p PC E Ja oJ da where the diagonal elements Je Jy and L are the moments of the inertia about the Xm Ym and z axes passing through the center of mass of the mover respectively and the off diagonal elements Jy Ax Az Jy L and L are the products of the inertia These elements can be defined as the following equation J jk r L 76 jk FF ja F SLR NENS RIO Aca de NN dag R H AR NR R ARARATS ORO UNES 6 2 1 2 where p is mass density z ln r rF is a position vector from rotation center with respect to the mover coordinate axes XmYmZm r and rm Y k tL 2
79. the armature conductors which determine an allowable maximum width of those as shown in Fig 6 1 3 2 The width of the armature conductors also determines an allowable maximum current of those and so design of the armature conductors including pitch lengths as a parameter tends to become complicate In this study new armature conductors with different relative distances in the yaw direction from the armature conductors for the x and y directional drives are introduced to control the yaw motion as shown in Fig 6 1 3 3 188 Levitation force INISINISINISIN Mover AUI NSNSNSNSNSN Stator Negative d axis Current Z lt 0 a Generation of the levitation forces F Restoring torque n isi Mover names displaced in for y ttt NSNSNSNSNSN Stator Negative d axis Current Z lt 0 b Generation of the restoring torques T and Ty Propulsion force Mover INISINISINISIN ARENA Stator SNSNSNSNSN q axis Current 4 c Generation of the propulsion forces F and F Fig 6 1 3 1 Conceptual design of a magnetically levitated planar actuator 189 Fig 6 1 3 2 Allowable maximum width of the armature conductors determined by pitch length of those 4 G U G SOY Fig 6 1 3 3 New introduced armature conductors tilted in the yaw direction 190 Figures 6 1 2 3 and 6 1 2 4 indicates that the d axis current generates translational forces F and torques 7 and the q axis current generates tr
80. ting on Transportation and Electric Railway and Linear Drives TER 04 31 LD 04 52 pp 1 6 Nagoya July 2004 265 Others P32 Y Ueda H Uesugi M Nara Y Fujii and E Ohkuma Campus Life is Changed The Journal of IEEJ Vol 126 No 12 pp 775 778 December 2006 in Japanese LAHA LE BR RR RT EH BOE ARE A Xx LA24723 Iai BAFSH Vol 126 No 12 pp 775 778 2006 12 A P33 Y Ueda Systematized technologies of multi degrees of freedom motors Section 7 3 Lens Drive for Optical Memories JEEJ Technical Report No 1140 pp 59 63 November 2008 in Japanese LAHA l amp BmBE E A40747 U EQmU 3 81 362 U OLY ARH BATS Diu No 1140 pp 59 63 2008 11 B 266
81. ts and the system constant matrix K 7 is expressed approximately as follows F F y I dx F I 3 a m 6 1 28 f I dy fy I qy T where Krc Krc and Kr are constant in this analysis for a 0 5 mm air gap Kre 17 mN Krc x 12 mN mm and Kr 4 5 mN mm Equation 6 1 2 8 indicates that the driving forces due to the d axis currents Ix and Ia are equal because of the symmetry of the actuator Therefore even if the two currents and are controlled only 1 DOF driving forces can be controlled in the range within a 0 deg 0 deg and y 0 deg Therefore controlling the four armature currents in the dq frame controls the 3 DOF motions of the mover for instance x y and z motions or x y and a motions In order to realize both 3 DOF motion controls on a plane and magnetic suspension the planar actuator needs to be redesigned 6 1 3 Conceptual Design of Fundamental Structure In order to suspend the mover suspension forces that balance the force of gravity need to be generated Equation 6 1 2 3 indicates that negative d axis currents x lay lt 0 generate suspension forces F gt 0 Figure 6 1 3 1 shows schematic views of when the d axis currents are supplied Negative d axis currents to actively control levitation forces F gt 0 always generate restoring torques against the f and displacements The restoring torques stabilize the G and motions of the mover Equation 6 1 2 3
82. ura Development of a 2DOF Control Type Spherical Piezoelectric Motor with Wide Dynamic Range The 2007 JSPE Autumn Technical Meeting J44 pp 751 752 Asahikawa September 2007 in Japanese SRTR MHE Kise ANS TSTS Y YAR 2 B E REB SR EE 7 ORK 2007 FE R T EE KEKR CY fi sei Z J44 pp 751 752 TB 2007 9 A 255 Nis08 Ohs03 Ohi04 Ohi06 Ohi98 Oza08 Phi06 H Takahashi O Nishimura and H Nukada Development of a 3DOF Spherical Piezoelectric Motor The 2008 JSPE Autumn Technical Meeting L36 pp 929 930 Sendai September 2008 in Japanese mata PEE MARC 3 B BEMEGY ORJ 2008 F E Ma LEG KEKS FWA L36 pp 929 930 ME 2008 9 B H Ohsaki N Teramura X Huang Y Tsuboi and Y Ootani Electromagnetic Characteristics of a Coreless Surface Motor Using Halbach Permanent Magnets The International Symposium on Linear Drives for Industry Applications LDIA2003 Birmingham UK PL 06 pp 105 108 September 2003 Homepage of Ohira Inui Laboratory Nihon University ohira 16nensotuken html S Inui N Inubushi and Y Ohira Simulation of Controller Characteristics Applied to Magnetic Levitation for an X Y Linear http gtl ce nihon u ac Synchronous Motor ZEEJ Transaction on Industry Applications Vol 126 No 10 pp 1298 1302 October 2006 Y Ohira M Karita and E Masada Fundamental Characteristics of the Transport Switch System with Levitation Using
83. ws phasor diagrams for the relation between the dg frame and a B frame The currents and J generate the opposite phase magnetic field to that resulting from the permanent magnet mover when the mover position in the x and y directions x y x y and the Euler angle 0 0 0 The a axis are aligned to the opposite side of the current axis and the f axis leads the a axis by 90 deg The current lia generates a magnetic field that is tilted by 9 24 7 deg around the a direction from that caused by current Bearing this in mind the armature currents in the dg frame Iy and Iy can be represented by the currents l and b as follows Iu cos xx r sin z 15 E prs Ir cos m 7 h AAA 6 3 1 3 cos zy r sin ay r I5 l E one 5 10 69 48 6 3 1 4 EE ler ma t sin ze Jd GERE sin za r cos za r Ii Q X COSP Y Sing eee pul dm M M MM A 6 3 1 6 202 Fig 6 3 1 1 Fig 6 3 1 2 a LE ux E x tcc cn den oed am M D axis A for x drive d axis RT for a drive D axis 4 for a drive G NIS for a drive a axis l for x drive amp q axis for a drive E 44 for x drive BM E auus U 4 D d p for x drive d MUI Vi T i E opem cs gt TT va m m R v lt A E Un ETa RO 3 gp qw des Wn a

Chapter 6 - 東京大学学術機関リポジトリ

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