MODELING AND CONTROL OF A MICROGRIPPER BASED ON ELECTROMAGNETIC ACTUATION

Transcription

1 MODELING AND CONTROL OF A MICROGRIPPER BASED ON ELECTROMAGNETIC ACTUATION Veronica DESPA, Adrian CATANGIU, Ioan Alexandru IVAN, Valentin GURGU, Miai ARDELEANU ) Valaia University of Targoviste ) Université de Lyon, France Eail: duiver@yaoo.co, acatangiu@yaoo.co.uk, ioan.alexandru.ivan@gail.co, gurguvalentin@yaoo.co, iaita.nicolae.ardeleanu@gail.co, Abstract Design, fabrication and tests of a coliant flexure based icrogrier were erfored. Te bending force is alied by using a ixt interaction between two solenoids and two eranent agnets rigid fixed on cantilevers. Microaniulation tests were conducted in order to confir te ateatical odel develoed for device siulation Te siulation and exeriental data are in a good agreeent and ave roven accuracy of device control syste. Keywords: icrogrier, solenoid agnet interaction odeling, agnet agnet interaction, electroagnetic actuation force.. INTRODUCTION In order to aniulate objects wit sall diensions tere are used icrogriers in various constructive saes, wit aniulation systes based on sae eory effect, iezoelectric, electroagnetic etc. One of te ajor robles in te oeration of a aniulator is acieving reroducibility of oveents (ysteresis can becoe a roble, for exale, in case of te SMA actuators). Te icrogrier wose function is analyzed, resents a ixed tye of andling: electroagnetic for te oving in xoy lane, resectively, iezoelectric in xoz lane. Figure sows te outline constructive design of te agneto-iezoelectric device for icro-aniulation. Effector eleents are two beas rigidly attaced to te frae wose oveent is acieved by bending owed to te agnetic interaction between solenoid and te conjugated eranent agnet rigidly fixed on te active ar. Fig.. Sceatic reresentation of te agnetoiezoelectric device for icroaniulation Te iezoelectric ars rovides oveent on te erendicular direction to te lane of te figure. End effectors take contact wit te object to aniulate (fig.). Fig.. Te syste of te two actuators grous

2 . THE ACTUATION PRINCIPLE Te coliant ar oves as a result of te interaction between tree indeendent eleents: - Interaction between eranent agnets rigidly fixed to te ars, as as effect a bending of bea, osition wic becoes steady ( relative); - Magnetic force F (Fig.), as a result of te interaction between te agnetic field of a coil (solenoid) and te eranent agnet fixed to te conjugated ar; - Mecanical elasticity wic ensures te return to te equilibriu osition ( relative) of te ar in case of te current troug te solenoid is zero; Fig.4. Te osition of eranent agnets and solenoids tat oerates te actuator Interaction agnet - agnet and agnet - solenoid Fig.. Working rincile of te coliant eleent Because te dislaceents are extreely sall (tens icroeters) te deforations of coliant ar are in te elastic range. For electroagnetic acting of te ecatronic device we used ig-energy eranent agnets NdFeB tye S-4-,5-N wit te following caracteristics: - Diaeter d = 4 - Heigt =,5 - Magnetic flux density (agnetic induction) B =,5 T. Caracteristics of electroagnets: - nuber of turns 4 eac; - coil diaeter de = 9,5, - overall eigt e = 9, wic includes two sacer rings, eac aving gi = tick. Iron core of te coil as te sae radius as te eraent agnet. Te distance between eac agnet and te associated coil is x =,, and te total distance between two agnets is d = 4,. Te osition of eranent agnets and associated coils is sown in Figure 4. In an silified aroac, eac ar is subjected to te action of two forces by agnetic nature: attraction/rejection generated by te electroagnet (coil), resectively, te attraction force between te eranent agnets. Given te roxiity of eranent agnets (d = 4, ), static attraction force (witout electricity) cannot be ignored. Te agnets ave been arranged in arallel to te agnetization (in te sae way N-S, N-S) in suc a way as to attract eac oter. In literature, te roble of attraction force between two eranent agnets is analized fro several ersectives. Eac aroac is based on general interaction between a eranent agnet and a agnetizable alf-sace tat can be created by anoter eranent agnet or a solenoid. Voroobov [] develos te teory of tis tye of interaction and sows te exressions of te attraction force between two agnets laced at different distances. Te results of nuerical integration of te force are strictly deendent on te boundary conditions. One of te etods of assessing te interaction between two unifor agnetized objects is te filaent etod, in wic eac eleent is considered a current-carrying coil. Te interaction force between te two coils is given by te following relation []: F ( r,r,x) = µ I I x K( ) E( ) () f 4r r were r and r are te coil radius and x is te axial distance between te. Te functions K() and E() are te colete first and second ellitic integrals resectively wit araeter and I, I are te currents troug te coil. = () [ r + r ] + x 4r r By using te filaent etod, equations () and () can be used to calculate te force between any arrangeent of coaxial solenoids. Te force between coils is attained by couting te interaction force between eac air of turns of te searate coils (as su of tis interaction) []. In case of interaction between two eranent agnets or between a agnet and a solenoid, te eranent agnet is associated wit a solenoid wit a nuber of turns

3 wic rovide te agnetic flux density B equivalent to te solenoid one. Anoter way to aroac te roble of interaction between agnets is integral etod. An integral exression for te force resulted fro te interaction of a solenoid wit a agnet is derived by using te teory of Furlani []. It is considered tat te solenoid can be odeled as a voluic current density and te eranent agnet as a surface current density around te circuference. A solenoid wit te voluic current density J generates a agnetic field B at a distance of d given by te integral over te wole coil volue V c []. µ J ( ) ( d ) [ d d ] () B d = dv Vc c 4π d d Te analytical exression of te force exerted by te agnetic field on a eranent agnet []: l / R B {,} N I c c (4) Fz = [ e f z ] drdz lc[ R c rc ] l / r e c c fz = K( ) E( ) 4R r =, = [ r + r ] + z e l z + N nuber of turns I - te current in te coil r - te agnet radius R c, r c te coil external radius, resectively te coil internal radius. Te analytical integration etod is also based on te first and second order ellitic integrals. Vokou [4] uses a siilar aroac and resents an analytical exression for calculating te interaction force between two cylindrical eranent agnets in te conditions of a unifor-considered agnetization. Te forula for te silified nuerical integration in tis case describes te axial interaction force between two eranent agnets of radius r and lengt for te secific local conditions of te analyzed device (5): π K d 4 πb 4 F( x ) = r = r (5) 4µ ( ) ( ) = + x x + x + µ agnetic ereability of air (te nature of sace between te agnets), 4π 7 T /A K d te agnetostatic energy constant µ M K d =, B M = µ M te agnetization of te agnet B - agnetic flux density of te agnet, T x - distance between te agnets, - lengt (te eigt of te agnet),. Magnet s agnetization M is roortional to te agnetic flux density B, te roortionality factor being te air ereability. Tis silified exression of te agnet-agnet interaction force will be used to calculate te attraction force of te agnets arranged corresonding to Fig. 4. In order to analyze te solenoid-agnet interaction witout losing generality, we can use te sae silified relation if te core of te solenoid as te sae diaeter as te agnet diaeter, and its lengt is considered te lengt of te coiled zone ( ). Interaction force solenoid-agnet is described by exression: π B N I 4 F( x ) = r (6) 4 = + x ( + + ) + x x + µ NI te solenoid s induction in air Bs = te coil lengt (solenoid equivalent eigt) te eranent agnet eigt x te distance solenoid-agnet.. THE MODELING OF ELECTROMAGNETIC ACTUATION Mateatical odeling of te actuation is based on estiation of deendence between te current I troug solenoid and te dislaceent of ar at te eleent effector level and is based on te following silifying assutions: a). Te ar is a bea wose deforation is considered to be erfectly linear (te strain in te alication of electroagnetic force zone is directly roortional to te strain in te eleent effector zone); b). Te deflection of te ar under te action of te bending force F is acieved by te integration of te bending oent. In case of a concentrated force, te bea deforation in alication oint of te force is deendent on tis force by relation: F l w = (7) I ze w - te bea deflection at te force alication oint (agnet zone) l lengt of te bea I z - bea inertia oent E - te elastic odulus of te aterial (CoCrMo obtained by selective laser sintering tecnology). c). Because te agnet-agnet interaction as as results an equal bending to bot ars of te actuator, we use in odeling te assution tat agnet-agnet interaction force as a colete effect on te bea bending. Under tese conditions, te total force wic roduces te bending of a single ar will be:

4 F + F = F + Fs = F( x ) F( x ) (8) πb 4 r I ze 4µ π B N I 4 = w = + r (9) l 4 π B N I r 4 4 I ze πb = w l 8µ r 4 () Fro equations (9) and () it can be deduced te value of current troug coil in order to create a necessary force wic as as effect a dislaceent w. EI z B I = w () 4 πb Nr l Nµ It can be observed te linear deendence between te deendent variable I and indeendent variable w (). dislaceent w, by using te relation () is illustrated in Figure 6. Te curve is caracteristic for te deforation of te aniulator ar at te force alication oint (te fixing zone of te eranent agnet), and te curve reresents te dislaceent at te end-effector level. Force [N] y = 6x R = THE TESTING AND CHARACTERIZATION OF ELECTROMAGNETIC ACTUATION. RESULTS AND DISCUSSIONS Te elastic caracteristics of te aniulator ar were estiated by a bending test of a secien wit a testing acine tat allowed te onitoring of te force values, resectively, of te dislaceent [6] by using a data acquisition card. Te values of te force wic can be catured by te acine are large enoug to roduce strain tat exceed te deforations of icroaniulator ars, te forcedislaceent curve can not be used as a references data for siulation of te actuator, but can by used for estiation of te aterial elastic odulus. Te aroriate reresentation of data (te force vs. exression w I z, according to equation (7)) it can be l used for longitudinal elastic odulus estiation, as it can be seen in Figure 5 (E = 6MPa). Te siulation of te deendence between te value of current I used for actuation of te ar and its.5 Elastic odulus [w**iz/l^] Fig.5. Te estiation of te longitudinal elastic odulus Regarding te current sense troug te solenoid, because of te fact tat te results ay see confusing, soe clarifications are needed. Te estiated deforations sown in Figure 6 are easured according to te osition " abs" fro Figure 4. Wen eranent agnets are fixed on te icroaniulator ars, te attraction force of tese ones as as effect te bending of ars and a dislaceent in osition " rel". For decrease te distance between ars, it is necessary an extra force wic can be rovide by increasing values of current troug solenoid. In case of oving away fro te osition " rel" (close to " abs"), it is necessary a canging of current sense in order to coensate te initial interaction between te eranent agnets. Actuation current [A] Dislaceent [icroeters] - Fig.6. Deforation at te alication oint of te force and end effector according to te current troug te solenoid 4

5 In order to validate te considered ateatical odel, tere were necessary exeriental deterinations of te icro-aniulator dislaceent involving te use of a subicroetric recision dislaceent sensor [7]. Tus, we used a laser triangulation easuring syste, odel Keyence LK-GPV. Te syste selected for a easuring range of ±, as a,% linearity, a,5 µ reeatability and range of saling rate adjustable between µs. Te sensor contains a class II laser,,95 W at te wave lengt 655 n, wic is caracteristic of red color fro te ligt sectru (Fig. 7). Te syste allows a local easureent, te sot being focused on a easuring surface wit µ diaeter. Because te easureent of dislaceent was erfored at end-effector level, te equilibriu being considered caracteristic for te osition " rel", te values fro te siulated version ave been corrected by a constant wose value is te dislaceent according to te osition " rel" (current troug solenoid is zero). In Figure 8 are sown te results of te device siulation (te correlation between te current in te solenoid and te ar dislaceent at te level of te force alication oint (), resectively, at te level of te end-effector (). Te differences between te siulated curve at te endeffector level and te exeriental one could be inaccuracie in estiation of agnetic induction value, unifority of agnetic field, errors in assution tat a coil can be considered a eranent agnet wit te sae agnetisation. Fig.7. Te exeriental setu for electroagnetic actuation of te device ars Fig.8. A coarison between te current dislaceent siulated caracteristic and te exeriental caracteristic 4. CONCLUSIONS:. Te tests erfored on eac ar of te aniulator sown a narrow ysteresis loo (ε ax =,5%), as well as a good linearity (ε lin ax =,8%).. For an intensity I = ± 5 A, tere is a dislaceent w=µ/ar, wic corresonds to an actuation coefficient of about, µ/a. In icroreensor configuration, te axiu distance between te ars is double, d = 4 µ, enoug for aniulation of objects wit icroeter size (saller tan µ, in tis case).. Tere is a good correlation between te data of te siulated curve and te data fro te exeriental one. 5

6 ACKNOWLEDGEMENT National Project, Young Researc Teas, PN-II-RU-TE-- -99, no. 85/5.., Advanced Devices for Micro and Nanoscale Maniulation and Caracterization (ADMAN). REFERENCES: []. Voroobov V., Interaction of cylindrical agnet wit sei-sace, Magnetoydrodynaics Vol. 46 (), No.,.. []. Robertson W., Cazzolato B., Zander A., Axial force between a tick coil and a cylindrical eranent agnet: otiising te geoetry of an electroagnetic actuator, IEEE Transaction on Magnetics, ISSN (Vol. 48, Issue 9),, []. Furlani E.P., Peranent agnet and electroecanical devices, I. Mayegoyz, Ed. Acadeic Press,. [4]. Vokoun D., Beleggia M., Heller L., Šittner P. Magnetostatic interactions and forces between cylindrical eranent agnets, Journal of Magnetis and Magnetic Materials, Vol., Issue, Noveber 9, [5]. Babic S., Akyel C., Magnetic force between agnetic disks, IEEE Transaction on Magnetics, Vol.44, No.4, , Aril 8. [6]. Desa V., Catangiu A., Ivan I.A., Mecanical beaviour of CoCrMo alloy sales ade by selective laser sintering, Te Scientific Bulletin of Valaia University Materials and Mecanics, Year, No.8 (), ISSN , ag. 9-. [7]. George G., Siona I., Desa V. Cirstoiu A., Researcs regarding intelligent sensors and actuators of ig recision used in recision Mecanics, Mecatronics and Robotics doain, Te Roanian Review Precision Mecanics, Otics & Mecatronics, No.8 (),