51 ISSN 1392 1207. MECHANIKA. 2015 Volume 21(1): 51 55 Impct of the triologicl chrcteristics on the dynmics of the ultrsonic piezoelectric motor J. Pdgursks*, R. Rukuiž**, R. Bnsevičius***, V. Jūrėns****, A. Buulis***** *Institute of Power nd Trnsport Mchinery Engineering, Aleksndrs Stulginskis University, Studentu 15, Akdemij, LT-53362 Kuno r., Lithuni, E-mil: juozs.pdgursks@su.lt **Institute of Power nd Trnsport Mchinery Engineering, Aleksndrs Stulginskis University, Studentu 15, Akdemij, LT-53362 Kuno r., Lithuni, E-mil: rimunds.rukuiz@su.lt ***Kuns University of Technology, Kęstučio 27, LT-44025 Kuns, Lithuni, E-mil: rmutis.nsevicius@ktu.lt ****Kuns University of Technology, Kęstučio 27, LT-44025 Kuns, Lithuni, E-mil: lgimnts.uulis@ktu.lt *****Kuns University of Technology, Kęstučio 27, LT-44025 Kuns, Lithuni, E-mil: vytuts.jurens@ktu.lt http://dx.doi.org/10.5755/j01.mech.21.1.10136 1. Introduction The ultrsonic motor (USM) chrcteristics driven y piezoelectric trnsducer strongly depend on the mechnicl properties of the components sttor, rotor nd contct lyer [1]. The methodology of contct zone prmeters control of USM is very importnt. The min triologicl surfce chrcteristics influencing the speed regulrity of USM in stedy regimen re mcro- nd microsperities nd friction coefficient fluctutions etween rotor surfce nd friction element. They re depend on contcting mterils nd its surfce chrcteristics of the USM rotor [2]. The reserch show tht the chnges of rotor surfce rigidity (in cse if the contct etween rotor surfce nd contcting element is not distured) nd the fluctutions of digonl impct recovering coefficient (when the contct etween rotor surfce nd contcting element is regulrly chnging) hve less influence on speed stediness of USM [3, 4]. 2. The synthesis of dynmic nd triologicl chrcteristics of piezoelectric motor The reserch were performed t the prototype of the ultrsonic piezoelectric motor with the piezoelectric plte-shped trnsducer (Fig.1), in which the lternting strin is excited y n AC electricl field, preferly operting t the mechnicl resonnce frequency. Fig. 1 presents the schemes of rottion nd trnsltion motion, which enles the dignostics of triologicl properties of USM contct zone. The dignostic system signls correlting with triologicl properties of contct zone re: mcro- nd micro-sperities of rotor surfce nd stochstic oscilltion in contct zone rising ecuse of friction coefficient fluctution etween rotor surfce nd contcting friction element which will generte electric chrges in centrl electrode 9 ecuse of direct piezoeffect; esides the electric chrges in centrl electrode 9 (which vlue will correlte with the stochstic oscilltion in contct zone) the longitudinl oscilltion of piezoelectric plte t the oscilltory node (I form, δ x = 0) will generte intensive electric chrges of min frequency (with the lgging) which will e filtered t filter 12; oscilltions of piezoelectric plte ending (II form) will not generte the electric chrges in centrl mesurement electrode (they will hve opposite chrge in ottom nd upside of electrode 9 nd the sum of their chrges will e equl to zero). The scheme of USM (Fig. 1, ) enles to get the interesting regimen of rotor s motion continuous motion with rottion oscilltions which is relised y the connecting electric voltges U 1 (t) nd U 2 (t) to the electrodes 6, 8 nd 5, 7. In order to excite specific rottionl type oscilltions within the rotor two hrmonic signls (U 1 nd U 2 ) of different frequency nd mplitude re supplied to oth groups of control electrodes. Signl expressions re presented in Eqs. (1) nd (2) [3]: U t U cos t, (1) 1 01 1 1 U t U cos t, (2) 2 02 2 2 where U 01, U 02 re voltge mplitudes, 1, 2 re ngulr frequencies, t is time nd 1, 2 re phses of hrmonic signls. Here 2 1 nd 2 1 1. In the presence of such conditions, the moving memer (i.e. rotor) performs periodic motion, which is defined y the following lw [5]: A mx cos 2 1 t, (3) 2 where A mx is the mximl mplitude nd t is time of rottionl type virtions. In this cse hrmonic oscilltions re excited in frequency rnge from 0 Hz t 2 1, A Amx. The exmple of such rotor s rottionl oscilltions is displyed in Fig. 2 [5]. It presents the cse when U 1 (t) = = U 2 (t), i.e. the verge speed of rotor is equl to zero. In order to determine the resonnce frequency of the designed piezoelectric trnsducer, n impednce nlyzer Wyne Kerr 6520 A (Fig. 3, ) is used to mesure the impednce chrcteristics of the prototype, nd the mesurement plot of electric impednce within the mesured frequencies is used (shown in Fig. 3, ).
52 Fig. 1 Schemes of rottion () nd trnsltion () motion, which enles the dignostics of triologicl properties of piezoelectric motors contct zone: 1 rotor (1 slipper), 2 frictionl contct element, 3 plte-form piezoelectric trnsducer, polrised ccording to the plte thickness, 4 spring, 5, 6, 7, 8 symmetric electrodes sectionlised y the trnsducer, 9 centrl electrode for the mesurement of electric chrge, 10 genertor of hrmonic signls, 11 control unit, 12 filter, 13 detector/recorder Fig. 2 Wveform of mximl oscilltions of the rotor t the frequency of 2 Hz (f 1 = 44100 Hz, f 2 = 44102 Hz) nd mplitude of hrmonic signls voltge U 1 = U 2 = 60 V 44.1 khz Fig. 3 The mesurement of the impednce (Z) nd phse (θ) of the piezoelectric trnsducer vs. excittion frequency (opertionl (resonnt) frequency 44.1 khz) with n nlyser Wyne Kerr 6500B
53 By oserving the mesured impednce vs. frequency chrcteristic, shown in Fig. 3, there re three resonnt frequencies (round 44 khz, 92 khz nd 132 khz) when the impednce reches mximum. The opertion frequency of the USM is 44.1 khz nd ws determined experimentlly. The feedck synthesis etween the prmeters of dignostic system nd the oscilltion prmeters of USM trnsducer is relised y: controlling the oscilltion mplitude of signls genertor it is the simplest wy to regulte the rotor s speed in wide rnge. Fig. 4 presents the exmple of such control [6]. It is evident tht the condition ω mx /ω min = 3...5; is relised esily, especilly t lower loding of the rotor; controlling the frequency of hrmonic signls which is in the opertionl resonnce zone of USM trnsducer. Such exmple is presented in Fig. 5 [6]. This method is used less often, ecuse the time quiescent of frequency chnge is usully higher thn the mplitude chnge of the hrmonic voltge; Fig. 5 Angulr velocity vs. frequency feeding 57V nd 67V mplitude signls there is the method used in piezoelectric step motors - controlling the filling coefficient of the supply impulses completed with the hrmonic resonnce signls; nother method is the use of oth signls of sme resonnce frequency U 1 (t) nd U 2 (t), ut chnging the phse of second signl to zero. In tht cse (Fig. 1) only trnsducer s longitudinl oscilltions re generted nd the speed of USM is equl to zero. 3. Rotry speed stilistion system of USM Fig. 4 Controlling of rottion speed of USM y the chnging the supply voltge of hrmonic signl nd lod of the rotor The outside ring 1 of rotor (Fig. 6, ) should e mde of the low coustic resistnce mteril (steel, cermic etc.). It is mounted on internl prt of rotor 2, which is mde from composite mteril with high coustic resistnce. Outside ring is contcting with the plte of piezoelectric trnsducer 3 (hving the polristion vector perpendiculr to the plte) through the intermedite frictionl element 4. One electrode of piezoelectric trnsducer is erthed nd other is divided in sectors 5 nd 6. Acoustic contct etween trnsducer nd rotor is mde y the spring 7. Fig. 6 Speed stilistion system of piezoelectric motor () nd superposition result U 1 (t) () of signls U 11 (t) nd U 12 (t)
54 The trnsducer s electrodes re connected to the electric signl genertor 8 through the controller 9. Genertor s voltge U cos2πλt is connected to the electrodes groups 5 nd 6 through the switcher 10, which is steered y the controller lso connecting the free electrode to the nd the filter of higher frequency hrmonics 11. Filtered signl pss to the detector 12, which exit is connected to controller. The mesurements h 1 nd h 2 of rotor s outside ring 1 (Fig. 6, ) should e significntly lower thn the wvelength of excited oscilltion (frequency λ) t the mteril of outside ring (for the reflection minimistion of diffusive wves). The voltge of genertor Ucos2πλt is exciting in piezo-trnsducer two types of oscilltions ecuse of the symmetry of electrodes groups: longitudinl first form oscilltions (distriution of mplitudes in length δx of the plte is presented in scheme) nd ending oscilltions (second form, δy). There is not ig difference etween the resonnce frequencies of oth forms cusing the elliptic oscilltion trjectory of contct element 4 nd consequently the rotor s revolution which direction decides the switcher 10. Complicted dynmic processes re tking plce during the oscilltions in contct zone (dependently on the oscilltion mplitudes from high frequency digonl impcts to the sliding which is regulrly chnging friction force in contct zone) etween rotor s outside ring 1 nd intermedite frictionl element 4. It cuses genertion of hrmonic oscilltions of min frequency λ nd higher frequencies. Becuse of direct piezo-effect the electric chrges re excited in piezo-trnsducer, which re filtered in the filter 11 of λ nd higher frequency hrmonics. Excited λ frequency oscilltions pss lso to outside ring 1 where they re chnnelized into two sides: clockwise nd counter clockwise. When the direction of rottion speed ω is s in fig. 6, counter clockwise in the rotting ring 1 diffused oscilltions (U11) re reching the contct zone with the dely nd its frequency registered y the free electrodes is reduced (Doppler Effect): λ 11 = [V/(V + ω R)] λ, here V is sound speed in rotor s outside ring, 2R is dimeter of outside ring. When the oscilltions re diffusing in outside ring clockwise (U 12 ) its frequency increse: λ 12 = [V/(V - ω R)] λ. The summry signl U 1 (t) fter the filter 11 of λ nd higher frequency hrmonics is pssing to detector 12 nd controller 9 forms the signl U(ω), which is proportionl to the rottion speed ω of frequency f m = λ 11 - λ 12. Dependently on the size of this signl, the controller 9 chnges the mplitude of signl genertor 8 stilizing the rottion speed ω. The coustic mesurement oscilltions could e excited y the seprte trnsducer enling the extension of its frequency rnge nd the increse of the preciseness of the mesurement. Such scheme presented in Fig. 7 where the rnge of λ frequency could rech up to 5 MHz. Thus using the feedck etween the prmeters of dignostic system nd the prmeters of piezoelectric trnsducer oscilltions there is possile to control the speed of USM t the impct of the externl disturnces: temperture, wer, rheologicl chnges of the surfce etc. Fig.7 Modifiction of rotor speed stilistion system with high frequency coustic mesurement oscilltions ɣ. 4. Conclusions The following conclusions on the influence of contct zone triologicl prmeters on the stilistion of rottion speed of piezoelectric motors could e formed: creted speed control schemes of rottion nd trnsltion motion piezoelectric motors llows to dignose the triologicl properties of USM contct zone; experimentl results show the possiility to excite
55 the rotry low frequency oscilltions t USM rotor when two ultrsonic frequency hrmonic signls re supplied to the piezo-trnsducer; presented three USM schemes enle the regultion of speed control prmeters of piezo-trnsducer: mplitude, frequency nd phse; two rotor speed stilistion schemes with the use of Doppler Effect were nlysed. Acknowledgement This reserch ws funded y the Reserch Council of Lithuni (Project TrioPjezo, contrct No MIP- 079/2012 nd Project PiezoTle, contrct No MIP 094/12). References 1. Storck, H.; Wllschek, J. 2003. The effect of tngentil elsticity of the contct lyer etween sttor nd rotor in trvelling wve ultrsonic motors, Interntionl Journl of Non-Liner Mechnics 38: 143-159. http://dx.doi.org/10.1016/s0020-7462(01)00048-8. 2. Pdgursks, J.; Bnsevičius, R.; Žund, A.; Rukuiž, R.; Andriušis, A. 2013. Investigtion of Triologicl Properties in Piezoelectric Contct, Surfce Engineering nd Applied Electrochemistry 49(5): 401-407. http://dx.doi.org/10.3103/s1068375513050104. 3. Rgulskis, K.; Bnsevicius, R.; Brusks, R.; Kulvietis, G. 1988. Viromotors for Precision Microroots. Hemisphere Pul. Corportion, New York, ISBN 0-89116-549-5. 310p. 4. Grys, I.; Bnsevičius, R.; Buulis, A.; Jūrėns, V.; Kulvietis, G. 2013. Development of two modifictions of piezoelectric high resolution rotry tle, Journl of Viroengineering 15(4): 2203-2208. 5. Grys, I.; Buulis, A.; Bnsevičius, R.; Jūrėns, V. 2014. Reserch of rotry piezotle driven y two hrmonic signls, Mechnik 20(6): 573-576. 6. Finl Report of High Technology PiezoAdpt Project R&D of Mechtronic Nno Resolution Actutors/ Sensors Systems. Kuns University of Technology, 2009 (compiled y R. Bnsevicius, V. Jurens, et l.) (in Lthunin). J. Pdgursks, R. Rukuiž, R. Bnsevičius, V. Jūrėns, A. Buulis IMPACT OF THE TRYBOLOGYCAL CHARACTERISTICS ON THE DYNAMICS OF THE ULTRASONIC PIEZOELECTRIC MOTOR S u m m r y The pper presents the methodology of triologicl prmeters control in the contct zone of ultrsonic piezoelectric motors. The min triologicl surfce chrcteristics influencing the speed regulrity of USM in stedy regimen (mcro- nd micro-sperities nd friction coefficient fluctutions etween rotor surfce nd friction element) were nlysed. Presenting control schemes of piezoelectric motors cn dignose the triologicl properties of the contct zone nd stilise the rottion speed of piezoelectric motor. Keywords: triology, friction, piezoelectric motor, resonnt frequency, mplitude, virtions. Received Novemer 03, 2014 Accepted Ferury 02, 2015