Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 UDK - UDC 62-23:681.892 Strokovni članek - Speciality paper (1.04) Teoretična in eksperimentalna analiza dinamike mehanizmov Rolamite A Theoretical and Experimental Investigation of the Dynamics of Rolamite-Type Mechanisms Ričardas Viktoras Ulozas (Šiauliai University, Lithuania) Prispevek najprej poroča o teoretični raziskavi dinamičnega modela valja in jermena pri mehanizmu tipa Rolamite (RTM). Dinamični model valja in jermena mehanizma RTM je opisan z diferencialnimi enačbami ter analiziran na dva načina, tj. v primeru, ko na sistem ne vpliva vibracijsko vzbujanje, in v primeru, ko leto vpliva na sistem. Ugotovili smo, da je mogoče s parametri vibracijskega vzbujanja spreminjati parametre nezdrsnega območja. To nas je vodilo do predpostavke, da je v dejanskih mehanizmih tipa Rolamite mogoče vplivati na trenje med strukturnimi elementi mehanizma RTM. Eksperimentalni del raziskave dinamike mehanizma tipa Rolamite z vibrajočimi elementi je bil izveden v treh smereh: kot analiza dinamičnih pojavov v mehanizmu valja in jermena, kot analiza postopkov obvladovanja trenja med elementi mehanizma RTM in kot analiza dinamičnih pojavov v vibramotorjih Rolamite. Povečanje amplitude električne napetosti, zmanjšanje sile obremenitve gibkega jermena, in zmanjšanje kota, pod katerim gibki jermen ovija valj, povzročijo povečanje amplitude vibracij valjev. Mehanizem RTM z vrtečima se in vibrajočima valjema ima v primerjavi z vibrajočima valjema drugačnega tipa boljšo ležajno zmogljivost in je precej bolj občutljiv. Največjo sinhronost vrtenja rotorjev zagotavlja vibramotor Rolamite, ki se sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki hkrati vrti oba rotorja. Ta vibramotor primerjamo z vibramotorjem Rolamite z dvema rotorjema in piezo električnim pretvornikom vibracij, ki vrti le enega od rotorjev. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: Rolamite mehanizmi, zdrsavanje, vibracije, dinamični modeli) This paper looks at theoretical research of the dynamic model of the "roller-band" system of the Rolamite-type mechanism (RTM). The dynamic model of the "roller-band" system of the RTM is described by differential equations and is investigated in two ways, i.e., when the system is not influenced by the excitation of vibrations, and when it is influenced by them. We have established that with the parameters of excitation of vibration it is possible to operate the parameters of a non-slipping zone. This allows us to assume that in a real Rolamite-type mechanism it is possible to operate on the friction between the structural elements of the RTM. Experimental research on the dynamics of the Rolamite-type mechanism with vibrating elements was done in three directions: research on the dynamic processes running in the RTM roller-band system; research on the processes of friction-control between the elements of the RTM; and research on the dynamic processes running in the Rolamite vibromotors. The increase of the supply-voltage amplitude, the decrease of the force-load magnitude of the flexible band, and the decrease of the angle of the wrapping of the roller by the flexible band cause an increase in the amplitude of the roller vibrations. An RTM with rotating vibrating rollers, compared with the vibrating rollers of the other type, has a better bearing capacity and is much more sensitive. The highest synchronicity of rotation of the rotors is provided by a Rolamite vibromotor with two rotors and a piezoelectric converter of vibrations that simultaneously rotates both rotors. This is compared with the Rolamite vibromotor with two rotors and a piezoelectric converter of vibrations, which rotates only one rotor. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: Rolamite type mechanisms, slipping, vibrations, dynamic models) 26 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 OUVOD Donald F. Wilkes je izumil kotalni mehanizem tipa Rolamite (RTM) v letu 1967 ([1] in [2]). Pri mehanizmu RTM se valja brez trenja kotalita po jermenu, vendar pa avtorji [3] tudi navajajo, da valja pri določenih parametrih mehanizma zdrsneta, čeprav ne podajo nikakršne teoretične podlage za ta pojav. V viru [4] sta navedeni dve vrsti zdrsa mehanizma RTM (geometrični in vzmetni zdrs). Raziskovalci so predlagali, da bi trenje zmanjšali z uporabo vibracij [5]. Ena izmed metod za zmanjšanje trenja temelji na rabi usmerjevalnih vibracij, ki jih dovajamo stičnim telesom. Če se vibracijska amplituda vibrajočih elementov med stičnima telesoma povečuje, se pojavi plast vibracij (FV). Mehanizem nastanka plasti vibracij je temeljito opisan v viru [6], zato tu ne bo podrobno opisan. Najpogosteje uporabljeni sestavni deli vibrajočih elementov mehanizma RTM so piezoelektrični pretvorniki, tj. piezo keramični elementi. Pri mnogih konstrukcijah mehanizma RTM le-ti tvorijo dele valjev, ki imajo osi pritrjene na nepremično osnovo. Okrov mehanizma RTM se giblje premočrtno pod vplivom zunanjih sil ali sil, ki jih ustvarja kinematično delovanje valjev in jermena. Pri takšnem mehanizmu valja opravljata funkcijo vibracijske podpore (VS) ali vibramotorja (VM) [7]. Ko načrtujemo precizni mehanizem RTM z nadzorovanim trenjem za določitev ali krmiljenje napetosti gibkega jermena kakor tudi natančni mehanizem vlečnega jermena z vibramotorjem Rolamite (RVM), moramo teoretično in eksperimentalno raziskati dinamične pojave, ki potekajo v mehanizmu RTM in vibramotorju. Vibramotorje lahko v mehanizmu RTM uporabimo kot vibracijsko podporo usmerjevalnemu gibanju, mehanizmu vlečnega jermena, črevesni črpalki, mikro vpenjalni čeljusti, idr. Namen teoretične raziskave je razkritje razmer, v katerih se valja in jermen mehanizma RTM gibljejo sinhrono in brez zdrsov, saj je poznavanje teh razmer bistvenega pomena pri oblikovanju natančnega mehanizma. Drugi namen raziskave pa je analiza mehanizma RTM, ki je izpostavljen vplivu vibracij. Namen eksperimentalnega dela raziskave je seznanitev z dinamičnimi pojavi v mehanizmu valjev in jermena, analiza možnosti krmiljenja trenja 0 INTRODUCTION Donald F. Wilkes invented the Rolamite-type mechanism (RTM) in 1967 ([1] and [2]). In the RTM the rollers are rolling on the band without friction; however, the authors of [3] specify that the rollers slip for certain parameters of the mechanism, although they do not provide any theoretical substantiation for this. In [4] two variants of slipping in the Rolamite-type mechanism (geometric and springy slipping) are defined. Researchers have suggested that the friction could be decreased using vibrations [5]. One of the methods to reduce friction is to provide directional vibrations to the contact bodies. If the vibrational amplitude of the vibrating elements is increasing between the interacting bodies a film of vibrations (FV) occurs. The mechanism of the FV’s formation is comprehensively described in [6], thus we will not describe it in detail here. The most frequently used constituent parts of the RTM’s vibrating elements are piezoelectric converters i.e., piezoceramic elements. In many RTM constructions they form part of the rollers that have their axes fixed to the immobile base. The casing of the RTM under external forces or forces arising in the kinematic roller-band pair performs a rectilinear movement. The rollers of such an RTM perform the functions of vibrosupport (VS) or vibromotors (VM) [7]. When designing precision Rolamite mechanisms with controlled friction for positioning or regulating the tension of the flexible band, as well as precision band-pulling mechanisms with a Rolamite vibromotor (RVM), the dynamic processes taking place in the RTM and RVM have to be explored both theoretically and experimentally. Vibromotors may be used in a RTM as the vibrosupport of the directional movement, band-pulling mechanisms, peristaltic pumps, micro-manipulator grips, etc. The purpose of theoretical research is to reveal the conditions under which the bodies of the roller-band of an RTM are moving synchronically without slipping, because their detection is the most important problem in the design of precision mechanisms. The other purpose is to investigate the RTM that is influenced by vibrations. The purpose of experimental research is to explore the dynamic processes in the RTM rollerband system; to explore the possibilities of control- 27 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 mehanizma RTM ter analiza dinamičnih pojavov v vibramotorjih. Predmeti ekperimentiranja so izvirni mehanizmi RTM, pri katerih sta valja vzbujena z visokofrekvenčnim vibriranjem, ter vibramotor, čigar delovanje je utemeljeno na visokofrekvenčnih diagonalnih udarcih piezokeramične plošče ob vrteči se rotor. 1 DINAMIČNI MODELI VALJEV IN JERMENA PRI MEHANIZMU RTM ling the friction of the Rolamite mechanisms; and to explore the dynamic processes in Rolamite vibromotors. The objects of the experiments are the original RTM, where the rollers are induced by high-frequency vibration, and the RVM, where the functioning is based on high-frequency diagonal hits by the piezoceramic plate onto the rotor that is rotating. 1 DYNAMIC MODELS OF THE ROLLER-BAND SYSTEM OF AN RTM Dinamični modeli sklopa valjev in jermena pri mehanizmu RTM v primeru deformiranih in nedeformiranih stikov med telesi (si. 1) so opisani z deferencialnimi enačbami in analizirani. Slika 1 kaže, da so z (i - 1 do 6) pomiki elementov (v pravokotni in stri izni smeri), P 1 je vlečna sila, P6 je sila odpora gibanju, P4 je sila, ki pritiska maso m ob maso M (in povzroča pravokotno tlačno silo N). Jermen opišemo z dvojicami parametrov. V sredini stičnega predela med valjem in jermenom je zgoščena masa jermena m, preostali del jermena pa je v vzdolžni smeri spremenjen v elastični element c12 in razsipni element H12, ki sta povezana vzporedno. Masa jermena m je zbrana vzdolž površine valja. Valj je izražen kot telo z maso M. Medsebojno delovanje jermena in valja je prikazano s prej omenjeno zgoščenje mase m ter s primerno povezavo elastičnih elementov c23, c45 in razsipnih elementov H23, H45, ti omogočajo deformacije jermena, ki se dotika valja v strižni in pravokotni smeri. Zgoščena masa se deloma nanaša na maso m in deloma na maso mv ki je zbrana neposredno na površini valja in pridobljena s telesom, ki ima maso M. Dynamic models of the roller-band system of an RTM in the cases of deformed and non-deformed contact between the bodies (Fig. 1) were described by differential equations and investigated. It is shown in Fig. 1 that zi (i – 1 to 6) are the displacements of the elrements (in the normal rand tangential directions), P1 is the pulling force, P6 is r the force of the resistance to movement, P4 is the force that is pressing the mass m to mass M (causing the normal pressing force N). The band is represented by coupled parameters. In the center of the contact zone between the roller and the band is concentrated the band’s reduced mass m, the remaining piece of the band in a longitudinal direction is changed to the elastic element c12 and the dissipative element H12, connected in parallel. The mass of the band m is concentrated along the roller’s surface. The roller is expressed as a body with the mass M. The interaction of a band with a roller is shown by means of the above-mentioned reduced mass m, and connecting in appropriate way the elastic c23, c45 and dissipative H23, H45 elements, which allow deformations of the band contacting the roller in the tangential and normal directions. The part of the reduced mass of the band relates to the mass m h h SI. 1. Dinamična modela valja in jermena pri mehanizmu RTM v primeru stika med telesoma: a - deformirani stik, b - nedeformirani stik Fig. 1.Dynamic models of the roller-band system of the RTM in the case of a contact between bodies: a - deformed, b - non-deformed 28 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 Deformacija stika med jermenom in obema valjema je mogoča zaradi elastičnih in razsipnih elementov c2V c45, H2V H45 ter tudi zaradi mase my Analiziran je primer neprekinjenega gibanja mas m in M v pravokotni smeri. Poenostavljeni dinamični model natančnega mehanizma valja in jermena, kakršnega poznamo pri sistemu RTM, je opisan z diferencialnimi enačbami in analiziran. V skladu s sliko la imajo diferencialne enačbe gibanja naslednje izraze: and the part to mass m3, concentrated directly to the surface of a roller adopted by the way of a body with mass of M. The deformed contact between a band on both rollers is allowed by the elastic and dissipa-tive elements c23, c45 , H23, H45 and also by mass m3. An example of the continuous movement of the masses m and M in the normal direction is analyzed. The simplified dynamic model of a precision rollerband mechanism such as the RTM roller-band system was described by differential equations and investigated. The differential equations of movement, in accordance with Fig.1 a, have these expressions: H12(ž1-ž2) + c12(z1-z2) = P1 mz2 - H12 (ž1 - ž2 ) - c12 (z1 - z2 ) + H23 (ž2 - ž3 ) + c23 (z2 - z3 ) = 0 3ž3 - H23 (ž2 - ž3 ) - c23 (z2 - z3 ) + [H45 (ž4 - ž5 ) + c45 (z4 - z5 )] ¦ f0sign(ž3 - ž6 ) + /(ž3 - ž6 ) = 0 Mz6 - [H45 (ž4 - ž5 ) + c45 (z4 - z5 )]/0 ¦ «gn(ž3 - ž6 ) - /(ž3 - ž6 ) = -P6 (1). mž4 + H45 (ž4 - ž5 ) + c45 (z4 - z5 ) = -P4 V skladu s sliko lb imajo diferencialne enačbe The differential equations of movement, in gibanja naslednje izraze: accordance with Fig.1 b, have the following expressions: H12(ž1-ž2) + c12(z1-z2) = P1 mž2-H12(ž1-ž2)-c12(z1-z2) + Nf0sign(ž2-ž6) + f(ž2-ž6) = 0 Mz6 -Nf0sign(ž2 -ž6)-f(ž2-ž6) = -P6 (2), mz5 Hu, H2V H45 - koeficienti viskoznega dušenja; cn, c2V c45 - koeficienti togosti; f0 - koeficient suhega trenja; / - koeficient mokrega trenja. Včasih je koeficient mokrega trenja/ sorazmeren vrednosti pravokotne reakcije, tj.: +P4 = N H , H, H 12 23 45 c, c, c 12 23 45 f0 f - viscous damping coefficients; - coefficients of stiffness; - coefficient of dry friction; - coefficient of wet friction. Sometimes the coefficient of wet friction, f, is proportional to the value of the normal reaction, i.e.: - koeficient mokrega trenja. V primeru zunanjega vzbujanja: f N45= H45 V fN 1 45 f1 - coefficient of wet friction. z&5 )+c45 (z4 -z5 ) For external excitation: (3), A1, A4, A6 B1, B4, B6 D1, D4, D6 w P1 = 4 + S1i1 + D1 sin (o? + ö1 j P4 = A4 + B4ž4 + D4 sin(cot + a4 ) P6= A+ ^6+ D6sin(mt + a6) z5 =D5sin(a>t + a5) . _d_ ~ dt komponente nespremenljivih sil; A1, A4, A6 stalnice, ki določajo linearno razmerje B1, B4, B6 med silami in ustreznimi hitrostmi; amplitude komponent harmoničnih sil; D1, D4, D6 kotna frekvenca; a (5). constant force components; constants defining the linear relationship between the forces and the appropriate velocities; amplitudes of the harmonic force components; angular frequency; a , a , a , a faze. a1, a4, a6, a5 phases. f Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 29 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 Da bi ocenili delovanje sistema, moramo To estimate the work of the system's performance upoštevati osnovne značilke, na primer delo ali moč, we consider basic characteristics, for example, the work or gonilne sile, silo koristnega upora itn. power, the moving forces, the force of useful resistance, etc. Glede na sliko 1 je delo gonilnih sil opisano According to Fig.1, the work of moving kot: forces is described as: \P^=\PAdt (6). 00 T - čas integracije; T - time of integration; H - značilna razdalja opravljena v času T. H - appropriate distance covered during the time T. Dejansko delo je podano z naslednjim izrazom: The useful work is given by the expression: H, T A = \Pidz6=)p6i6dt (7). 00 Izkoristek je podan z naslednjim izrazom: T The efficiency is given by the expression: ]p6ž6dt J>_______ (8). Au h= A JW P^dt Nepravilnost hitrosti gibanja je podana z o The irregularity of the motion velocity is naslednjim izrazom: given by the expression J Z (9), Z-tZ- (10). Z vnosom nove spremenljivke dobimo naslednje: By entering a new variable we obtain: 3 m (11), zi i /-\ \cv d co H N M m, x. =— (i = l,...,o); p =, ^ ; t = pt; = — ; v =— ; 2h =----- (rs = 12, 23,45) ; N =— ; u = — ; lu= — 1 I U dr p " pm p 2 ml M m m Aj Bj Dj D Ff=J = ^ (/- = 1,4,6); af=-L; 6,=—L; d, =—L ; d5 =^-; Sn =^ ; S45=^-pml c12l cnl pm cnl I l - dolžina jermena; / - band length; p in t sta novi spremenljivki. p and t are new variables. Če upoštevamo novo spremenljivko (11), Considering a new variable (11), the differential diferencialne enačbe gibanja (1) spremenimo takole: equations of movement (1) are converted to the type: 2Aj2 [x[-x'2) + [x1-x2) = Fl, /hA-2^23 {x'2 -x'3)-S2i (x2 -x3) + [2h45 (x'4 -x'5) + S45 (x4 -x5)] ¦ [f0sign(x'3 -x'6)] + f(x'3 -x'6) = 0 (12), ßx"6-\_2h45(x'4-x'5) + ö45(x4-x5)\f<3-sign(x[-x'6)-f(x[-x'6) = -F6 x"4 + 2h45 (x'4 - x'5 ) + S45 (x4 - x5 ) = -F4 hn, hiv h4S so koeficienti dušenja A hw A45 - coefficients of damping. Če upoštevamo novo spremenljivko (11), Considering the new variable (11), the differenti- diferencialne enačbe gibanja (2) spremenimo takole: al equations of movement (2) are converted to the type: 2Aj2 (x1'-x2) + (x1 -x2) = Fl x"2-2hl2(x[-x'2)-(xl-x2) + N'f0sign(x'2-x'6) + f(x'2-x'6) = 0 ^^ ß4-N%sign(x'2-x'6)-f(x'2 -x'6) = -F6 x"5+F4=N' Nato enačbo (3) spremenimo: Furthermore, Equation (3) is converted to the type: f = fl[2h45(x'4-x'5) + S45(x4-x5)\ (14). Zunanje vzbujanje (5) v neparametričnem The external excitation (5) in the non-para- izrazu vodi v naslednje: metric expression leads to: A 30 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 F1=a1+ ft1X1 + d1 sin (vt + a1 ) F4=a4+ b4x'4 + d4 sin (vt + a4 ] F6=a6+ b6x'6 + d6 sin (vt + a6} (15), x5 = d5 sin(nt + a5) kjer je v=w /p. here v=w /p. Izkoristek je podan z naslednjim izrazom: The efficiency is given by the expression: ]fx dt F^dz (16). Nepravilnost hitrosti gibanja je podana takole: 2 ANALIZA DINAMIČMH POJAVOV V DELOVANJU SKLOPA VALJEV IN JERMENA PRI MEHANIZMU RTM, KADAR NANJE NE VPLIVA VIBRACIJSKO VZBUJANJE The irregularity of the motion's velocity is given by the expression: c ' __ s max______,? min (s =1,2,6) 2 (17), (18). 2 THE ANALYSIS OF DYNAMIC PROCESSES OCCURRING IN THE “ROLLER-BAND” SYSTEM OF THE RTM, NOT INFLUENCED BY THE EXCITATION OF VIBRATIONS Namen te raziskave je definiranje dela, ki ga opravi sklop valjev in jermena pri mehanizmu RTM v odsotnosti vibracijskega vzbujanja. Raziskava je opravljena na nezdrsnem območju (NZ) upoštevajoč parametre mehanizma. Nezdrsnost je okoliščina, v kateri se telesa raziskovanega mehanizma pomikajo skupaj brez zdrsovanja, tj. x’ = x’2 = x’6 (si. 2 do 7): d1 = d4 kakor se to dogaja v obravnavanem primeru. Raziskava analizira dinamične pojave, ki potekajo v mehanizmu valjev in jermena v sistemu natančnega valja, tj. v jermenskem mehanizmu z nedeformirajočim stikom med telesi. Značaj dinamičnih pojavov v mehanizmu valjev in jermena z deformirajočim stikom med telesi v enakomernem gibanju je analogen pojavom, ki so v primeru nedeformirajočega stika. Iz krivulj diagrama zato lahko določimo razmerja med enakomernim gibanjem in njegovimi parametri. Pod vsakim diagramom so v oklepaju prikazani parametri sistema z deformirajočim stikom med telesi. Glede na sliko 2 pri definirani vrednosti a, hitrosti x\, x\ in x\ proučevanih teles postanejo istovetne, kar pomeni, da telesa ne zdrsujejo v tolikšni meri, da bi se znatno povečal koeficient suhega trenja The purpose of the research is to define the work of the “roller-band” system of the RTM in the absence of vibrating excitation. It is presented in the research of a non-slipping zone of bodies (NZ), depending on the parameters of the system. The non-slipping zone is understood as the condition when the bodies of the investigated system are moving together without slipping, i.e., x’1= x’2= x’6 (Figs. 2 to 7): =d6 =0 (19), as in the considered case. It is presented as research of the dynamic processes occurring in the “roller-band” system of a precision roller, i.e., band mechanisms with a non-deforming contact between the bodies. The character of the dynamic processes occurring in the “roller-band” system with a deforming contact between the bodies in steady motion is analogous to the processes occurring in this system with a non-deforming contact. Furthermore, from the graphical curves we can determine the relations of steady motion with its parameters. In brackets, under the figures, the parameters of the system with a deforming contact between the bodies are indicated. According to Fig. 2, at a defined value a4, the velocities x’1, x’2 and x’6 of the investigated bodies become identical, i.e., the bodies do not slip between themselves at a sufficient increase of the coefficient of 0 Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 31 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 x' 0.8 0.4 -0.4 x. = x'2 /o =0 /fo =0.1 i/o =0.3 ffoM\ /o=i.oVy Kjo= 0.6 /o= 0.8\V Lv v- /o= 0.6N)ç /fOaJ/ ynix'jS' VJU0 =01, /0 =0 0.8 0.4 0.4 ¦0.4 a4 0 -^l -lt:2 a4 =0.3 /"4 =0.6 a4 = l-Oj* K =0^^ « a4 =0.3 *6 0.4 /0 a b SI. 2. Gra/fl kažeta odvisnost hitrosti teles sistema pri enakomernem gibanju od parametrov gibanja Fig. 2. Graphs showing the dependence of the velocity of bodies of a system in steady motion on the parameters of motion a = 0,5; a = -0,2; b= b6 = -0,5; 2h12= 0,2; ju =1,0; f= 0,1 (2h2=2h4=2,0; S2=S4 = 10; ju= 0,01; b=-0,5) /0 (sl. 2 a). Spoznali bomo, da večja ko je vrednosto, pri/0 = konst, hitreje nastane nezdrsno območje med telesi (si. 2 b). To pokaže tudi slika 3. Tako je, pri definirani vrednosti /, zvečanje vrednosti a4 pomembno le, dokler se približuje vrednosti NZ. Ko pa to vrednost doseže, izgubi pomen, saj se telesa zdaj začnejo gibati z enakimi hitrostmi (si. 2 in 3). S povečanjem a4, pri koeficientu suhega trenja f0 = konst., NZ postane definirana vrednost a4 ne glede na koeficient viskoznega trenja/; (si. 4 a). Pri dani vrednosti a4 povečana vrednost/, povzroči le rahlo zmanjšanje hitrosti x \ (krivulje odvisnosti v diagramu postanejo bolj izbočene) (si. 5 b); vendar pa NZ, pri dani vrednosti/, postane definirana vrednost a4, hitrosti x\, x’2, x ; pa se izenačijo (si. 4 a in b). Pri definirani vrednosti a4 se hitrosti x \, x \, x ; obravnavanih teles izenačijo, hkrati pa se zmanjša vrednost ap kar pomeni, da manjša ko je vrednost av večje je nezdrsno gibanje med telesi (si. 5 a). Pri al = konst. se zdrsovanje teles zmanjša ob povečanju a4 (si. 5 b). Krivulje odvisnosti na sliki 5 se ostro prelomijo ob vstopu v NZ. Če je a, = konst. in se vrednost a4 zveča, se poveča hitrost nastanka pojava NZ. Če je a4 = konst, se navor nezdrsnosti med telesi pojavi ob povečanju a6 do svoje določene vrednosti (si. 6 a in b). V času povečevanja a6 se povečajo tudi hitrosti x \ = x \ = x \ (SI. 6 a); kljub temu je pojav NZ x[ -x'6 ' 1.2 0.9 0.6 0.3 W^^ /o = ° /„= 0.6 / /o = 0.3 / /„=i-o 7 0.2 0.4 0.6 0.8 a4 SI. 3. Graf kaže odvisnost hitrosti zdrsovanja med telesi sistema pri enakomernem gibanju od parametrov gibanja Fig. 3. The graph showing the dependence of the velocity of slipping between bodies of a system in steady motion on the parameters of motion a = 0,5; a= -0,2; b= b6 = -0,5; 2h12= 0,2; ju=l,0; f= 0J(2h 2=2h4=2,0; S2=S4 = 10; ju3= 0,01; b=-0,5) dry friction,/ (Fig. 2 a). It wiUbe clear that the greater the value a4 at/ = const, the faster it makes a non-slipping zone of the bodies (Fig. 2 b). Fig. 3 also shows this. Furthermore, at a defined value,/, the increasing value of a4 is meaningful only up to NZ. After reaching this value it loses sense, as the bodies start to move with an identical velocity (Fig. 2 and 3). With increasing a4 at the coefficient of dry friction/ = const, NZ becomes a definite value a4, irrespective of the coefficient of viscous friction,/ (Fig. 4 a). The increasing/ resulted only in a minor decrease of the velocities x \ at a given data a4 (the dependence curves in the figure have a more convex character) (Fig. 5 b); however, NZ at a given data/ becomes a defined value a4, and the velocities x\, x \, x \ become equal (Fig. 4 a and b). At a defined value a4 the velocities x\, x\, x \ of the investigated bodies level off, with a decreasing of value av i.e., the smaller is ap the faster the non-slipping movement between the bodies comes (Fig. 5 a). At ax = const the slipping of the bodies decreases with an increase of a4 (Fig. 5 b). The curves of dependences in Fig. 5 break sharply when going into NZ. If a6 = const and value a4 increases, NZ becomes faster. If a4 = const, the moment of non-slipping between the bodies comes with an increase of a6 up to its definite value (Fig. 6 a and b). During the increase of a6 the velocities of bodies x \=x \=x \ are increased (Fig. 6 a); however, o 32 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 x' 0.8 0.4 //i= 0 yf\ = 0.1 x[ = x'2 ^ //,= 0-2 A ^ = 0.2 Yi=o.i ~7i=o X 0.35 0.3 0.25 0.4 0. 2 *1 = X2 Î4= 0.5 \ / I4= 1.0 y; J4 = 0.5 / 0 0.1 0.2 /. a b SI. 4. Gra/fl kažeta odvisnost hitrosti teles sistema pri enakomernem gibanju od parametrov gibanja Fig. 4. Graphs of the dependence of the velocity of the bodies of a system in steady motion on the parameters of motion a= 0,5; a = -0,2; b = b6 = -0,5; 2h12= 0,2; ju =1,0; f= 0,6 (2h2=2h4=2,0; 82=84 = 10; ju= 0,01; b=-0,5) x' 0.6 0.2 -0.2 -0.6 -0.2 0.2 0.6 a4= 0.3x a4= 0.5\ «4=l-0\/ '/ x[ a4= 0'.5\y\ = x2^t / jL * / yk-M "l - "^6 0.8 0.6 0.4 0.2 0.2 0.4 0.6 a b SI. 5. Grafa kažeta odvisnost hitrosti teles sistema pri enakomernem gibanju od parametrov gibanja Fig. 5. Graphs of the dependence of the velocity of the bodies of a system in steady motion on the parameters of motion b,= b6 = -0,5; 2hn= 0,2; f0= 0,6; fi= 0,1; a6= -0,2 (2h23=2h45=2,0; 023 = 045= 10; jUs= 0,01; b4= -0,5) mogoč, in sicer pri zmanjšani vrednosti a4 (SI. 7 a). Če je a = konst, NZ nastane ob povečanju f, v nasprotnem primeru pa, ko je/0 = konst, NZ nastane ob povečanju fl4 (SI. 7 b). Glede na sliko 7 povečanje a4 in a6 povzroči nezdrsno območje med telesi. Pri definirani vrednosti a6 naraščanje vrednosti a4 po vstopu teles v območje NZ nima več pomena, ker se telesa zdaj gibljejo z enakimi hitrostmi. Na spodnjih slikah je območje NZšrafrrano. Poudariti je treba, da je/0 a4 = konst. the coming of NZ is possible, and at a smaller value of a4 (Fig. 7 a). At a= const NZ comes with increasing^ and, in contrast, at/0= const with increasing a4, we achieve NZ (Fig. 7 b). According to Fig. 7, the increasing a4 and a6 resulted in a non-slipping between the bodies. At a defined value a6 the increasing value of a4 after the arrival of the bodies in NZ has no sense, because they are moving with identical velocities. NZ is hatched. It is necessary to point out that/0 a4 = const. 0.2 -0.2 \ \ / a4= 0 3 a4= 0 49 «4 = 1 0\ \ 1 \ ¦¦ X' I -1 =-2 \y- 1.0 0.8 0.6 0.4 0.2 0 -0.5 -0.3 -0.1 0.1 0.3 a6 -0.5 -0.3 -0.1 0.1 a6 a b SI. 6. Grafa kažeta odvisnost hitrosti teles sistema pri enakomernem gibanju od parametrov gibanja Fig. 6. Graphs of the dependence of the velocity of the bodies of a system in steady motion on the parameters of motion b= b6 = -0,5; 2h12= 0,2; f= 0,6; f= 0,1 (2h2=2h4=2,0; S2=S4 = 10; /u = 0,01; b=-0,5; a = 0,5) 0.75 0.5 0.25 ^ // v/ Va Y/ v/ 7// i <4 V/ V/ v i  0.75 0.5 /// /// /// -0.5 -0.3 -0.1 0.1 0.3 0.25 0.5 0.75 a4 a b SI. 7. Področja obstoja menjavajočih se enakomernih režimov gibanja teles, odvisnih od parametrov gibanja Fig. 7. The areas of existence of varying steady regimes of motion of a system of bodies depending on its parameters a= 0,5; b= b6 = -0,5; f= 0,1; 2h]2= 0,2 (2h2=2h4=2,0; 82=84 = 10; /u = 0,01; b=-0,5): a- f= 0,6; b- a= -0,2 o a a 4 a Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 33 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 3 ANALIZA DINAMIČNIH POJAVOV V DELOVANJU SKLOPA VALJEV IN JERMENA, KADAR NANJE VPLIVA VIBRACIJSKO VZBUJANJE 3 THE ANALYSIS OF THE DYNAMIC PROCESSES OCCURING IN THE “ROLLER-BAND” SYSTEM, INFLUENCED BY THE EXCITATION OF VIBRATIONS Namen te raziskave je definiranje razmer pri delu, ki ga opravi sklop valjev in jermena, kar omogoči nadzor nad pojavom NZ med telesi sistema z vibracijskim vzbujanjem. Analiziramo delovanje sklopa valjev in jermena pri mehanizmu RTM, na katerega vplivamo z vibriranjem, tj. z ustvarjanjem naslednjega pogoja: dpd4, d5, d6*0. Da bi zagotovili pojav NZ, moramo povečati f0 (pri tem je v = konst), kar omogoči zmanjšanje vrednosti a. povečanje vrednosti v (pri čemer je/. = konst.) pa povzroči neznatno zmanjšanje vrednosti a. (si. 8 a). Če na sistem ne vplivamo z vibracijami, kar pomeni, da je d4 = 0, NZ, in je/ = konst., ima a4 manjši pomen kakor sicer (si. 8 a in b). Slednje lahko razložimo z zmanjšanjem sile trenja v primeru, ko vibracije delujejo na sistem in nastane območje NZ, ki ima povečane vrednosti a4. Večja ko je amplituda vzbujajočih vibracij d4, večja mora biti vrednost a4, kar je potrebno za zagotovitev območja NZ (sl. 8 b). Vrednost povprečne hitrosti X se zveča, medtem ko se vrednost % zmanjša s povečanjem amplitude vibracijskega vzbujanja dp koeficient izkoristka r| se tako strmo zmanjša (si. 9). Dogajanje lahko razložimo z zmanjšanjem sile trenja med telesi, zaradi česar se poveča zdrsno območje, posledično pa se zniža vrednost h . Pri dejanski konstrukciji mehanizma RTM lahko moč sile trenja nadziramo z uporabo vibracij (si. 10). Kakor je razvidno iz dosedanje raziskave, se nezdrsno območje zmanjša, če začnemo na sistem The purpose of the research is to define the conditions of work of the “roller-band” system, ensuring an opportunity to control the NZ between bodies of the system by the excitation of vibrations. The case is investigated for the “roller-band” system of RTM when it is influenced by vibrations, i.e., dpd4, dpd6i0. To ensure NZ, it needs to increase/ (having v=const), which ensures the decrease of a4 and the increase of v (having/0=const) ensures the non-considerable decrease of a4 (Fig. 8 a). If the system is not influenced by vibrations, i.e., d =0, NZ, when the meanings of/ = const, it will appear to have fewer meanings of a4 (Fig. 8 a and b). This can be explained by the friction force decreases in the case of vibrations influencing the system and NZ is reached, having greater meanings of a4. The greater the amplitude of the exciting vibrations d4, the greater must be the meaning of a4; which is necessary to ensure NZ (Fig. 8 b). The value of the average velocity x[ increases, and % decreases with the increase of the amplitude of the vibrating excitations d5; the coefficient of efficiency, r|, thus sharply decreases (Fig. 9). It is explained in such a way that the force of friction between the bodies of the system decreases, owing to which the slipping zone of the bodies is increased, and consequently the value of n decreases. In the real construction of an RTM we can control the magnitude of the friction force with the vibrations (Fig.10). As can be seen from this material, the non-slipping zone recedes when the influence of the SI. 8. Polja gibanja teles v različnih razmerah, odvisnih od parametrov vibracijskega vzbujanja Fig. 8. Fields of movements of bodies in different types of conditions, depending on the parameters of the exciting vibrations a = 0,5; a= -0,2; b= b=-0,5; f = 0,1; x’= x,'= x.'=0,3; a) d = 0,1; b) f = 0,6; v/2n = 0,5. 34 Ulozas R. V. SI. 9. Prikaz odvisnosti povprečnih hitrosti gibanja teles in izkoristka od parametrov vibracijskega vzbujanja, ko je f0 = 1,0 Fig. 9. The diagram of the dependence of the average velocities of the movement of the bodies and the efficiency on the parameters of the vibrating excitation at f =1.0 vplivati z vibracijami. To pomeni, da je v dejanskem sistemu mogoče nadzirati zdrsovanje med elementi mehanizma RTM, tj. nadzirati navor odpornosti za gibanje. To je pomembno, kadar oblikujemo konstrukcije RTM, saj lahko tako zagotovimo boljšo kakovost in natančnost ter ustvarimo bolj natančne dinamične značilke. 4 ANALIZA DINAMIČNIH POJAVOV MEHANIZMA RTM Meritve vibracij v mehanizmu RTM so težavna naloga, toda ne le zaradi majhne amplitude vibracij v valjih, ampak predvsem zaradi dejstva, da poleg vibracij zabeležimo tudi njihove številne medsebojne vplive. Ti nastanejo zaradi vibriranja podstavka in geometrične nenatančnosti izdelave posameznih delov mehanizma; ti vplivi se najpogosteje pojavljajo naključno. Veliko pozornosti namenjamo razvoju metod meritev vibracij in izločevanju vplivov. Metode stične raziskave so omejene, ker vplivi pogosto popačijo rezultate beleženja in tako znatno vplivajo na izid poizkusa. Precej obetavne pa so nestične optične metode meritev, ki v polni meri izpolnjujejo zahteve poizkusov, tj. potrebe po nestičnih, zelo natančnih meritvah in veliki ločljivosti. Te metode so bile uporabljene v analizi značilk vibriranja v valjih mehanizma RTM. SI. 10. Teoretična raziskava poenostavljenega dinamičnega modela RTM z valjema in jermenom Fig. 10. Theoretical investigation of the simplified dynamic model of RTM “roller-band” system a = 0,5; a6 = -0,2; b = b =-0,5; f = 0,l; %i ’= x2’= x6’=0,3; 2hu= 0,2; 2h23 = 2h4S = 2,0; S23 = S45 = 10; |i = 1,0, \±3 = 0,01; Sistem: 1 - vibriranje ni aktivirano {d4 = 0 ); 2 - vibriranje je aktivirano (d4 = 0,1; v/2'n = 0,1), območje NZ je šrafirano The system: 1 - vibrations do not influence (d4 = 0), 2 - vibrations influence (d4 = 0.1;(v/2n) 0.1), NZ is hatched system by vibrations starts. This means that in a real system it can be possible to control the slipping-by between the elements of the RTM, i.e., control of the moment of resistance to motion. This is important when designing the constructions of the RTM, which ensures higher quality and precision and more precise dynamic characteristics. 4 RESEARCH OF THE DYNAMIC PROCESSES RUNNING IN THE RTM ROLLER-BAND SYSTEM The measurement of vibrations in Rolamite-type mechanisms is quite a complicated task, not only because of the small amplitude of vibrations in the rollers, but mainly because of the fact that along with vibrations there is plenty of interference registered. This arises because of the vibration of the base, the geometrical imprecision of the produced parts, and most often the interference is random. Much attention is paid to the development of the methods of measuring the vibrations and the separation of interference. The methods of contact research are limited, because the interference quite often distorts the results of the registration and significantly influences the results of the experiment. Quite promising are the non-contact optical methods of measurement, which fully meet the demands of the experiment, i.e. non-contact, high-precision measurements, high dimensional resolution. These methods were used in the research of the characteristics of vibration in the RTM rollers. Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 35 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 Raziskana sta bila dva tipa vibrirajočih valjev Two types of RTM vibrating rollers were mehanizma RTM (si. 11). explored (Fig. 11). Ko elektrode piezokeramičnega obroča When the electrodes of the piezoceramic ring pritrjenega valja št. 7 (SI. 11 a), ki je ovit z gibkim of the fixed RTM roller No 1 (Fig. 11 a) wrapped by a jermenom, sprejmejo visokofrekvenčni električni sig- flexible band receive a high-frequency electric signal, nal, valj začne vibrirati. Dejansko področje stika med the roller starts to vibrate. The actual area of the gibkim jermenom, ki ovija valj 7, in piezokeramičnim contact zone between the flexible band wrapping the obročem 2, ki obdaja elastični torni obroč 3, se roller 1 and the piezoceramic ring 2 wrapping the elastic zmanjša in pojavi se plast vibracij. Valj 7je namenjen frictional ring 3 reduces and the film of vibrations zmanjšanju trenja v napravah, ki vključujejo occurs. The roller 1 is intended to reduce the friction mehanizem RTM. Os valja 7 je čvrsto pritrjena na in devices containing an RTM. The axis of the roller 1 osnovo, tako da se valja mehanizma RTM ne kotalita is fixedly attached to the base, and the rollers of the po gibkem jermenu, ampak drsita. RTM do not roll on the flexible band, but slip. Eksperimentalni valjšt. 2 (sl.llb) je namenjen The experimental roller No 2 (Fig. 11 b) is zmanjšanju trenja v napravah, ki vključujejo intended to reduce the friction in devices contain- mehanizem RTM. Toda valja takšnega mehanizma se ing an RTM. But the rollers of such an RTM roll on kotalita po gibkem jermenu. the flexible band. Valj (si. 11 b) je sestavljen iz osi 7, ki je The roller (Fig. 11 b) consists of an axis 1, fixedly čvrsto pritrjena na osnovo, ter iz piezokeramičnega attached to the base, and of an assembled piezoceramic obročastega elementa, ki je montiran na os. Na ring element that is put on it. It is made of a piezoceramic notranjo stran piezokeramičnega obroča 2 je ring 2, in which the internal side of an elastic frictional pritrjen elastični torni obroč 3, ki je v stiku z osjo ring 3 is fixed; this contacts axis 1, and on the outside 7 ; z zunanje strani pa je obroč 2 prekrit s togim ring 2 is wrapped by a rigid ring-like cover 4, attached obročastim pokrovom, ki je čvrsto pritrjen na obroč to it fixedly, which in turn contacts with the wrapping in je v stiku z ovijajočim gibkim jermenom. Vibracije flexible band. A vibrations-pressed gas film (VPGF) is valja med montiranim obročnim piezokeramičnim produced by vibrations of the roller between the elementom, elastičnim tornim obročem 3 in covering assembled ring-like piezoceramic element pritrjeno togo osjo 7 ustvarjajo tlačeno plinasto elastic frictional ring 3 and the fixed rigid axis 1. plast (PGF). The vibrations of the rollers in a radial direction Raziskali smo vibracije valjev v prečni smeri in the loaded and unloaded functioning modes were ter v primerih obremenitve in neobremenitve (si. investigated (Fig 12). 12). In the loaded mode, the roller is wrapped by V primeru obremenitve je valj ovit z gibkim the flexible band at angles from p /4 to 3/2 p. One end jermenom pod kotom od p /4 do 3/2 p. En konec of the band is fixed to the rigid basis, and a weight is jermena je pritrjen na togo osnovo, utež pa je fixed on the other end of the band. As is obvious from pritrjena na drugi konec jermena. Kakor je očitno the data of the performed experiment, the amplitude iz izvedenega preizkusa, se amplituda in and resonant frequency of the roller vibrations, 1 2 3 4 b SI. 11. Vibrirajoča valja mehanizma RTM: a - pritrjeni valj (1); b - vrteči se valj (2);1 - os, ki je trdno pritrjena na osnovo; 2 - piezokeramični obroč; 3 - elastični torni obroč; 4 - tesno prilegajoči se obročasti pokrov, ki ga ovija gibki jermen Fig. 11. RTM vibrating rollers: a - fixed (1); b - rotating (2); 1 - axis, fixedly attached to the base;2 -piezoceramic ring; 3 - elastic frictional ring; 4 - tight ring-like cover, wrapped by a flexible band 36 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 resonančna frekvenca vibracij valja ovitega z jermenom pod enakima kotoma in z različno obremenitvijo, zmanjšata s povečanjem ravni bremena jermena (si. 12 a). Ko analiziramo odvisnost amplitude vibracij valja od električne moči z nespremenljivo resonančno frekvenco in različno stopnjo obremenitve jermena, lahko ugotovimo, da se amplituda vibracij valja zmanjša, če se obremenitev jermena poveča (si. 12 b). Kadar je obremenitev jermena majhna, je odvisnost amplitude vibracij valja skoraj linearna. Če je dovedena napetost povečana, se poveča tudi amplituda vibracij. Iz grafov (si. 12 c in d), ki opisujeta odvisnost sprememb amplitude in frekvence vibracij valja od kota, pod katerim jermen ovija valj pri različnih ravneh obremenitve, lahko povzamemo, da se amplituda in frekvenca zmanjšata, če se kot ovijajočega jermena poveča. Krivulje eksperimentalne raziskave valja št. 2 so prikazane na sliki 13. Značilnosti frekvenčne amplitude vibracij valja št. 2, ki se sestoji iz piezokeramičnega obroča piezokeramičnega elementa 2 z dejujočo (notranjo) wrapped by a band at equal angles and with loads of different magnitude, diminish when increasing the level of load of the band (Fig.12 a). When analyzing the dependence of the amplitude of the roller vibrations on the magnitude of the power-supply voltage, with a constant resonance frequency and a different level of load on the band, one can draw a conclusion, that if the load of the band is increased, the amplitude of the roller vibrations diminishes (Fig. 12 b). When the load on the band is small, the dependence of the amplitude of the roller vibrations is almost linear. If the power-supply voltage is increased, the amplitude of the roller vibrations increases as well. From the graphs provided (Fig. 12 c and d), describing the dependence of the changes of amplitude and frequency of the roller vibrations on the angle of the roller wrapping band, with a different level of load applied, one may draw a conclusion that, if the wrapping angle of the band increases, the amplitude and frequency become reduced. The curves of the experimental research of the RTM experimental roller No 2 are presented in Fig. 13. The frequency amplitude vibration characteristics of the roller No 2, consisting of the piezoceramic ring of the piezoceramic ring element 2 A, 0.60 -1 ,2 0 45 3 /ffliuL 4 0.15 A, um 1y 0.60 2~> 3X 0.30 0 00 N4 N5 94.8 95.2 f, kHz 9.0 16.2 a b u,V a, um 0.75 0.45 1 2- f, kHz 95.35 95.25 s V *N N \ * S ^ ^¦1 .-2 S \ N 0.25 ji 0.75 ji ç), rad ' 0.25n 0 75 ti çj, rad c d SI. 12. Krivulje eksperimentalne raziskave vibrirajočega valja 1, ovitega s tesno prilegajočim se (obremenjenim) jermenom Fig. 12. The curves of an experimental research of an RTM vibrating roller 1, wrapped by a tight (loaded) band: a - A=f(f), ko/if U = 40 V; ->>. 4 2.25 V ¦"-* < l\ *~— *—, 3 1.35 ,2 0 45 1 36.9 37.2 f, kHz 0.25 p 0.75 p f, rad ^5 *4 *-3 ,_ 14 x2 1 0 a b A, mm 1.8 0.9 0.25 p 0.75 p f, rad 0 6 12 c d SI. 13. Krivulje eksperimentalne raziskave vibrirajočega valja 2, ovitega s tesno prilegajočim se (obremenjenim) jermenom: a - A = f(j) - velja za montirani piezokeramični obročasti element (si. 2 b), ko je U = 60 V; 1 -velja za delovno površino piezokeramičnega obroča; 2 - velja za zunanjo površino togega obročastega pokrova 4 Fig. 13. The curves of an experimental research of RTM vibrating roller No 2, wrapped by a tight (loaded) band: a - A=f(f) for an assembled piezoceramic ring element (Fig 2 b), when U = 60 V; 1 - for the working surface of the piezoceramic ring; 2 - for the outer surface of a rigid ring-like cover 4; b - A=f( SI. 15. Vibrirajoči valji RTM: a - nepremični (1), glej sliko 11 a; b - nepremični (1) z valovnim vodilom; c - rotacijski (2), glej sliko 11 b Fig. 15. RTM vibrating rollers: a - immovable (1), see Fig. 11 a; b - immovable (1) with a waveguide; c - rotary (2), see Fig 11 b dolžine premika s (razdalje, za katero se valj premakne v enem obdobju krmilnega sunka) od dolžine sunka t. , - s = fit. ), od natezne sile jermena Gv- s = fiGx), od vlečne sile valja G2, - s = fiG2), in od kota, pod katerim jermen ovija valja a - s = f(a). Iz grafa (si. 16 a, krivulja 1) je razvidno, da je ob daljšem sunku t. daljša tudi razdalja s, ki jo naredita valja v enenTobdobju krmilnega sunka. Sila trenja Ftr in čas t sta potrebna, da valja naredita razdaljo s, ko se vlečna sila jermena G2 = konst. zmanjšuje, če na valja vpliva večja amplituda dovedene napetosti in ju vleče večja sila Gl (si. 16 b). Del preizkusa smo izvedli tako, da smo vibrajočim valjem energijo dovajali zvezno pri a = 530°, G2 = 2,0 N = konst.. Razdalja s, na kateri se premakneta valja v eni dobi krmilnega sunka, se poveča, kadar je povečana vlečna sila valja G.. To je razvidno iz grafa (si. 16 a, krivulja 2). Če je G, > FQ in jcF0 zanemarljiva vrednost sile lepenja, se v primeru, ko je ta vrednost presežena, se valja začneta gibati the roller skip length s (the distance covered by the roller in one period of regulating impulse) on impulse duration tim , - s = ft ), on te rollers’ stretching force G1, - s = f(G1), on the band’s pulling force G2, - s = f(G2), on the angle of the band wrapping the rollers a - s = f(a). As is clear from the graph (Fig. 16 a, curve 1), the longer is the duration of the impulse t , the longer is the distance, s, that is covered by the im rollers in one period of the regulating impulse. The friction force Ftr and time, t, is needed for the rollers to cover the distance s, when the pulling force G2 = const of the band is decreasing if the rollers are influenced by a larger amplitude of feeding voltage and they are pulled by a greater force G1 (Fig. 16 b). An experiment was made so that the vibrating rollers were fed by a continuous power-supply mode, when a = 530°, G2 = 2.0 N = const. The distance s covered by the rollers in one period of regulating impulse increases, when increasing the force of the roller pulling G1. This is clear from the graph (Fig. 16 a, curve 2). If G1 > F0, where F0 is the marginal value of the still friction force, so that when it is exceeded the rollers start moving c 40 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 SI. 16. Krivulje odvisnosti: a - pomiki valja 1 v obdobju krmilnega sunka: 1 - s = f(timp ); 2 - s = f(G1 ); 3 - s = f(G2; 4 - s=f(a); b - odvisnosti Ftr = f(G1 ) - 1 do 3; t = f(G1 ) - 4 do 6 (za mehanizem RTM z valji 1); Ftr = f(G1 ) - 7 do 9 (RTM z nepremičnimi valji z valovnim vodilom). Napajanje napetosti U je naslednje: 3, 4 in 7 - 10 V; 1, 5 in 8 - 20 V; 2, 6 in 9 - 30 V. Fig. 16. Curves of dependencies: a - displacements of RTM roller 1 per one period of regulating impulse: 1 - s=f(t. ); 2 - s=f(G,); 3 - s=f(GJ; 4 - s=f(a); b - dependencies F =f(G.) - 1 to 3; t=f(G.) - 4 to 6 (for ROTamite mechanisms with the rollers 1); F^GJ - 7 to 9 (RTM with immovable rollers with waveguides). Feeding voltage U equals: 3, 4 and 7 - 10 V; 1, 5 and 8 - 20 V; 2, 6 and 9 - 30 V. brez stimulacije visokofrekvenčnih električnih signalov. Območje, v katerem je G1 >F0, je dodatno označeno s pikčasto črto (si. 16 a). Dane razmere pri preizkusu so naslednje: mehanizem RTM deluje na diskretni način; G2 = 2,0 N = konst; a = 530°; f = 88,5 kHz; U = 51 V; fimk = 5 Hz; tim = 1,5 ms; e - G. = 3,0 N; f - G, = 3,5 nTg - G, = 3,6 N; h - G = 3,7 N. Razdalja s, na kateri se premakneta valja v enem obdobju krmilnega sunka, se poveča, kadar se zmanjša natezna sila jermena (vlečna sila valja Gl = konst). To je razvidno iz grafa (si. 16 a, krivulja 3). Kadar je sila G2 (nategnjeni jermen) zelo majhna, se valja začneta premikati brez stimulacije z visokofrekvenčnimi električnimi signali. P Razmere pri preizkusu so v tem primeru naslednje: mehanizem RTM deluje na diskretni način; a = 530°; fr = 88,5 kHz; U = 51 V; G1 = 3,0 N = konst.; fim k = 5Rz; tim =l,5 ms; G.: j - 4,0 N; k - 2,0 N; l -I,7 N; m -l,5 N. Razdalja s, na kateri se premakneta valja v enem obdobju krmilnega sunka, se zmanjša, kadar ta poveča kot, pod katerim jermen ovije valja. To je razvidno iz grafikona (si. 16 a, krivulja 4). Ko je kot zavoja jermena zelo oster, G1>F0, se valja začneta premikati brez stimulacije z visokofrekvenčnimi električnimi signali. Razmere pri without being influenced by the high-frequency electrical signals. The zone in which G1 >F0 is additionally marked by a dotted line (Fig. 16 a). The conditions of the experiment are given as follows: RTM operating mode is start-stop; G2 = 2.0 N = ccwrf; «= 530°;^= 88.5 kHz; L/= 51 V; / = 5 Hz; t = 1.5 ms; e - G1 = 3.0 N;/- G1 = 3.5 N; g - G1 = 3.6 N; -^ = 3.7 N. The distance s covered by the rollers in one period of the regulated impulse increases when this is decreasing the stretching force of band (the pulling force of roller G1 = const). This is clear from the graph (Fig. 16 a, curve 3). When the force G2 (stretching the band) is very low, the rollers start moving without being influenced by the high-frequency electrical signals. The conditions of the experiment are as follows: RTM operating mode is start-stop; a = 530°;/ = 88.5 kHz; L7= 51 V; G1 = 3.0 N = const; f ,= 5 Hz;^ = 1.5 ms; G2: j - 4.0 N;yfc- 2.0 N; /- 1.7 N; m - 1.5 N. The distance s covered by the rollers in one period of the regulated impulse is decreasing when this is increasing the angle of the rollers’ wrapping by the band. This is clear from the graphs (Fig. 16 a, curve 4). When the wrapping angle is very low, G1>F0, the rollers start moving without being influenced by the high-frequency electrical signals. The conditions of the Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 41 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 preizkusu so v tem primeru naslednje: mehanizem RTM deluje na diskretni način; za a velja naslednje: n - 450°; o - 4S0°; p - 500°; r - 53Qr; G1 = 3,01 i '1 -2 0.1 0.4 G1, N 20 40 u, V 450 480 a b c a, rees SI. 18. Mehanizem RTM z valjema 2 (glej sl. 11 b in sl. 15 c) krivulje odvisnosti Fig. 18. RTM with rollers 2 (see Fig. 11 b and Fig. 15 c) dependency curves a - Ftr = f(G), ho/if a = 500°; G2 = 5,0 N; U je/is: 1 - 50 V; 2 - 35 V; 3 - 20 V; b - F& = f(U), ho/if Gt = 0,5 N; a = 500°; G2 je/is: 7 - 4,0 N; 2 - 5,0 N; 3 - 7,0 N; 4 - 8,0 N; 5 - 9,0 N; c - Ftr = f(a); Gt = 0,5 N; G2 = 5,0 N; U je/is: 1 - 50 V; 2 - 30 V The curves from the theoretical research were used when designing the Rolamite vibromotors. 6 RESEARCH OF THE DYNAMIC PROCESSES RUNNING IN THE ROLAMITE VIBROMOTORS Prvi vibramotorji so izkoriščali diagonalno udarjanje piezokeramičnega pretvornika vibracij (piezokeramični elementi) ob gibljiv element, tj. ploščo ali valj [7]. Ko na elektrode pretvornika dovedemo visoko frekvenčni električni signal, se končni del piezoelektričnega pretvornika, ki ima netogi stik z rotorjem, prične eliptično gibati in obračati rotor (sl. 19). Določili smo najboljši kot piezokeramičnega pretvornika vibracij 2, ki udarjajo ob rotor 1, pri katerem je zagotovljeno največje število vrtljajev rotorja 1. Pri raziskovani konstrukciji vibramotorja je najboljša vrednost kota a 125°. Ob konstruiranju vrtilnega vibramotorja Rolamite ter mehanizmov vlečnega jermena je bilo treba ugotoviti, kakšen vpliv ima na sinhronost vrtenja valjev uporaba načela Rolamite v mehanizmih vlečnega jermena. Model mehanizma prenosa gibanja je bil oblikovan kot vrtilni vibramotor Rolamite (sl. 20 a), na podlagi tega pa je bilo oblikovano eksperimentalno stojalo (sl. 20 b). The first vibromotors used diagonal hits by the piezoelectric converter of the vibrations (piezoceramic elements) onto a movable element, i.e., a plate or a roller [7]. After providing a high-frequency electrical signal on the electrodes of the converter, the end of the piezoelectric converter, elastically connected to the rotor, starts making elliptical movements and turns the rotor (Fig. 19). The optimal angle of the piezoelectric converter of the vibrations 2 hitting the rotor 1, at which the maximum rotations of rotor 1 are ensured, was found. The optimal value of the angle a in the explored design of the vibromotor is 125°. When designing the rotary RVM and the mechanisms of band pulling, it was necessary to find what impact the applying of the Rolamite principle in the mechanisms of band pulling has on the synchronicity of the rotation of the rollers. The model of a mechanism of movement transmission was designed as a rotary Rolamite vibromotor (Fig. 20 a), and based on that an experimental stand was designed (Fig. 20 b). 6 0 3 Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 43 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 SI. 19. Pot vrhnjega dela menjalnika (a - v trenutku, ko na elektrode pretvornika dovedemo visokofrekvenčni električni signal; b - ko se delovanje ustali) in model mehanizma z vlečnim papirnim jermenom, ki uporablja vibramotor: 1 - rotor; 2 - piezoelektrični pretvornik vibracij; 3 - žica, ki piezoelektričnemu pretvorniku vibracij dovaja visokofrekvenčno električno napetost; 4 - papirni jermen Fig. 19. Path of the tip of the changer (a - at the moment of providing a high-frequency electrical signal on the electrodes of the converter; b - when the working mode has been stabilized) and a model of the mechanism of paper s band pulling, using a vibromotor: 1 - rotor; 2 - piezoelectric converter of vibrations; 3 - power supply wire of piezoelectric converter that provides a high-frequency voltage; 4 - the paper band Pogonsko vozlišče sestoji iz piezoelektričnega The drive node consists of a piezoelectric pretvornika vibracij 1, ki ustvarja vrtenje valjev - converter of the vibrations 1, which is providing a rotorjev 2 in 3. Valja -rotorja 2 in 3, kakor tudi tesno rotation of the rollers-rotors 2 and 3. The rollers-rotors 2 prilegajoči se valj manjšega premera 4, so oviti z and 3, and also a roller of a smaller diameter 4 that is tight neskončnim jermenom 5. Valja 2 in 3 sta ovita z are wrapped by an endless band 5. The rollers 2 and 3 are neskončnim jermenom 5 pod kotom, ki je večji od wrapped by an endless band 5 by an angle of more than 270°, valj 4 pa je ovit pod kotom, večjim od 180°. 270°, and a roller 4 by an angle of more than 180°. The Shema meritev je predstavljena na sliki 20 b. scheme of measurement is presented in Fig. 20 b. Na gredi rotorjevlin 2 sta pritrjena dva enaka On the shaft of rotors 1 and 2 two identical raster rastrska diska 3 in 4 z znakom, ki se odziva na disks 3 and 4 with a raster mark that interacts with the svetlobni zaznavali 5 in 6. Predojačevalnika 7 in 8 sta photo sensors 5 and 6 are fixed. The former-amplifiers 7 a) b) SI. 20. Model mehanizma prenosa gibanja kot rotacijski vibramotor Rolamite (a): 1 - piezoelektrični pretvornik vibracij; 2 in 3 - valj - rotor;4 - valj manjšega premera; 5 - neskončni jermen in shema eksperimentalnega stojala (b): 1 in 2 - rotorja; 3 in 4 - rastrska diska; 5 in 6 - svetlobni zaznavali; 7 in 8 - predojačevalnika; 9 in 10 - merilnika frekvence; 11 in 12 - razločevalnika frekvence; 13 - blok dvojnega kanala registracije; 14 - napajalnik piezoelektričnega pretvornika vibracij Fig. 20. The model of a mechanism of movement transmission as a rotary Rolamite vibromotor (a): 1 - piezoelectric converter of vibrations; 2 and 3 - roller-rotor; 4 - roller of smaller diameter; 5 - endless band and scheme of experimental stand (b): 1 and 2 - rotors; 3 and 4 - raster disks; 5 and 6 - photosensors; 7 and 8 - former-amplifiers; 9 and 10 - frequency meters; 11 and 12 - frequency discriminators; 13 - block of double channels of registration; 14 - power-supply unit of piezoelectric converter of vibrations 44 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 povezana z merilnikoma frekvence 9 in 10 ter prek enakih razločevalnikov frekvence 11 in 12 tudi na blok dvojnega kanala zapisa 13. Elektrode piezoelektričnega pretvornika vibracij so priključene na napajalnik 14 in zaradi visokofrekvenčnega električnega signala, ki prihaja iz napajalnika 14, začne piezoelektrični pretvornik vibracij vibrirati in vrteti rotorja lin 2. Na ekperimentalnem stojalu (si. 20 b) smo raziskali dva rotorja RVM, katerih vrtilno gibanje je spodbudil piezoelektrični pretvornik vibracij. Nastavili smo najboljši kot (120° do 130°) stika pretvornika vibracij z vrtečim rotorjem. Najprej smo raziskali vibriranje dveh rotorjev vibramotorja pri prostem (neobremenjenem) teku, ko je bil pretvornik vibracij togo pritrjen na sredino vibramotorja. Ko se amplituda dovedene električne napetosti U zveča, se poveča tudi število rotorjevih vrtljajev n, vendar pa nenatančno pritrjen piezoelektrični pretvornik povzroči nesinhrono vrtenje rotorjev (si. 21, krivulji 7 in 2). Če sta rotorja vibramotorja ovita z neskončnim jermenom v obliki mehanizma RTM in se oba rotorja vrtita, nesinhronost vrtenja dveh rotorjev izgine, kar pomeni, da A«=0 (si. 21, krivulja 5). Ko se poveča zunanja obremenitev enega od rotorjev, se močno poveča tudi nesinhronost vrtenja obeh rotorjev (si. 22, krivulja 7). Povezava dveh rotorjev z neskončnim jermenom v obliki mehanizma RTM zmanjša nesinhronost njunega vrtenja na najmanjšo vrednost (si. 22, krivulja 3). S slike 22 tudi izhaja, da je nesinhronost vrtenja rotorjev vibramotorja Rolamite, ki sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki vrti oba rotorja, dosti manjša od nesinhronosti vrtenja rotorjev vibramotorja Rolamite, ki sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki vrti le enega od rotorjev (si. 22, krivulja 2). Iz navedenega je mogoče sklepati, da največjo sinhronost vrtenja rotorjev zagotavlja vibramotor Rolamite, ki se sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki hkrati vrti oba rotorja. Pomanjkljivost vibramotorja, ki uporablja diagonalno udarjanje piezo električnega pretvornika vibracij (piezokeramični elementi) ob rotor, je njegova nezmožnost spremeniti smer vrtenja rotorja. and 8 are connected to the frequency meters 9 and 10, and through identical frequency discriminators 11 and 12 to a block of double channels of registration 13. The electrodes of the piezoelectric converter of vibrations are connected to a power-supply unit 14, and during a high-frequency electrical signal from a power-supply unit 14, the piezoelectric converter of the vibrations starts to vibrate and rotates the rotors 1 and 2. On an experimental stand (Fig. 20 b) the two RVM rotors were investigated, where the rotors rotational movement was obtained from one piezoelectric converter of vibrations. The optimal angle (120° to 130°) of contact for the converter of vibrations with a rotor rotated by it was used. First, the vibration mode of the two rotors, with the vibration’s converter rigidly fixed to the middle of it, is investigated in the empty (unloaded) working mode. When the amplitude of the feeding voltage U is increased, then the number of turns n of rotors increases; however, inexact fastening of the piezoelectric converter leads to non-synchronous rotations of the rotors (Fig. 21, curves 7 and 2). If the two VM rotors are wrapped by an endless band in the form of RTM and both rotors are rotating, the nonsynchronicity of the rotors’ rotations disappears, i.e., A«=0 (Fig. 21, the curve 3). When the external loading incereases on one of the rotors, the nonsynchronicity of the rotations of both rotors sharply increases (Fig. 22, the curve 7). The connection of the two rotors by an endless band in the form of an RTM reduces to a minimum the nonsynchronicity of their rotations (Fig. 22, the curve 3). From Fig. 22 it also follows that the magnitude of the nonsynchronicity of the rotation of the rotors of the Rolamite vibromotor of two rotors with a piezoelectric converter of vibrations, which rotates both rotors, is much less than the magnitude of the nonsynchronicity of the rotation of the rotors of the Rolamite vibromotor of two rotors with a piezoelectric converter of vibrations, which rotates only one rotor (Fig. 22, the curve 2). From this it is necessary to draw a conclusion that the highest synchronicity of rotation of the rotors is provided by the Rolamite vibromotor of two rotors with a piezoelectric converter of vibrations that simultaneously rotates both rotors. A weakness of the vibromotor that used diagonal hits of the piezoelectric converter of vibrations (piezoceramic elements) onto a rotor is the impossibility of reversing the rotation of a rotor. Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 45 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 An, min-' SS -Si n. min-' SS K / 40 ® 2\ // / 3 S UV SI. 21. Krivulji odvisnosti za nesinhrono vrtenje rotorjev vibramotorja pri prostem (neobremenjenem) teku: krivulji 1 in 2 - ko je n=f(U) pri dveh rotorjih, ki nista povezana z neskončnim jermenom in čigar vrtenje ustvarja splošni piezoelektrični pretvornik; krivulja 3 - ko je An=f(U) pri vibramotorju dveh rotorjev s splošnim piezoelektričnim pretvornikom vibracij potrebnim za vrtenje obeh rotorjev Fig. 21. Dependency curves for non-synchronous rotations of rotors VM in the empty (unloaded) mode of working: curves 1 and 2 - when n=f(U) for two rotors unconnected by an endless band and getting the rotation from the general piezoelectric converter of vibrations; the curve 3 - when An=f(U) for RVM of two rotors with general piezoelectric converter of vibrations for rotating both rotors 7 SKLEPNE OPOMBE SI. 22. Krivulje odvisnosti vrtilne nesinhronosti rotorjev od moči zunanje obremenile enega od rotorjev A = f(M), ko je U = konst. = 50 V: 1 - za primer dveh rotorjev, M nista povezana z neskončnim jermenom in ju vrti splošni piezoelektrični pretvornik vibracij; 2 - za primer vibramotorja Rolamite, ki se sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, M vrti le en rotor; 3 - za primer vibramotorja Rolamite, ki se sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki vrti oba rotorja Fig. 22. Curves of the dependencies of the rotations nonsynchronicity of the rotors on the magnitude of the external loading on one of the rotors A=f(M) when U=const=50V: 1 - for two rotors not connected by an endless band and both getting rotation from the general piezoelectric converter of vibrations; 2 - for the Rolamite vibromotor of two rotors with a piezoelectric converter of vibrations, which rotates only one rotor; 3 - for the Rolamite vibromotor of two rotors with a piezoelectric converter of vibrations that rotates both rotors 7 CONCLUDING REMARKS S teoretičnim delom raziskave smo dokazali naslednje: 1. Povečanje koeficienta suhega trenja omogoči hitrejše oblikovanje nezdrsnega območja med telesi mehanizma RTM. 2. Parametri vibracij mehanizma RTM se spremenijo takoj, ko elementi sistema RTM dosežejo nezdrsno območje, kar pomeni, da lahko na nezdrsno področje vplivamo z vibracijskim vzbujanjem. 3. Če povečamo amplitudo vibracij, se sila trenja med telesi sistema zmanjša; če se poveča zdrsno področje med telesi sistema, se zmanjša izkoristek. Z eksperimentalnim delom raziskave smo dokazali naslednje: 1. Povečanje amplitude električne napetosti, zmanjšanje sile obremenitve gibkega jermena in Theoretical research proved: 1. The increasing magnitude of the dry-friction coefficient makes it faster to achieve a non-slipping zone between the bodies of the “roller-band” system of the RTM. 2. From the “roller-band” system of the RTM the vibration parameters depend as quickly as bodies of the system achieve a non-slipping zone, and this means that the non-slipping zone can be operated by the excitation of vibrations. 3. If the amplitude of vibrations is increasing, then the force of friction between the bodies of the system is decreasing; if the zone of slipping between the bodies of the system is increasing, the magnitude of the efficiency is decreasing. Experimental research proved: 1. The increase of the supply-voltage amplitude, the decrease of the force load magnitude of the flexible 46 Ulozas R. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)1, 26-47 zmanjšanje kota, pod katerim gibki jermen ovija valj, povzročijo povečanje amplitude vibracij valja. 2. Mehanizem RTM z vrtečima se, vibrirajočima valjema, ima v primerjavi z vibrirajočima valjema drugega tipa boljšo ležajno zmogljivost in je bolj občutljiv. Zato je priporočljivo, da ga uporabljamo v izredno občutljivih sistemih. 3. Če primerjamo vibramotor Rolamite, ki se sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki sočasno vrti oba rotorja, ter vibramotor Rolamite, ki se sestoji iz dveh rotorjev in piezoelektričnega pretvornika vibracij, ki vrti le enega od rotorjev, prva možnost omogoči večjo sinhronost vrtenja rotorjev. band and the decrease of the angle wrapping of the roller by the flexible band cause the increase in the amplitude of the roller vibrations. 2. The RTM with rotating vibrating rollers, compared with vibrating rollers of another type, have a better bearing capacity and are much more sensitive. Therefore, it is advisable to use them in exceptionally sensitive systems. 3. If we compare the Rolamite vibromotor of two rotors with the piezoelectric converter of vibrations, which simultaneously rotates both rotors, and the Rolamite vibromotor of two rotors with a piezoelectric converter of vibrations, which rotates only one rotor, the first variant provides the highest synchronicity of the rotation of rotors. 8 VIRI 8 REFERENCES [1] Wilkes, D.F. (1967) Rolamite: A new mechanical design concept.-Research report SC-RR-67-656 A, Sandia Laboratories, December, 223p. [2] Wilkes, D.F. (1968) Rolamite: A new mechanism. Mechanical Engineering. April, v. 90, No 4, 11-29. [3] Percival, CM., Norwood, FR. (1969) A theoretical and experimental investigation of the dynamic response of Rolamite. Trans. ASME, Ser.B, v. 91, No 1, 235-239. [4] Ulozas, R.V. (2004) Raziskava zdrsa v mehanizmu med valjem in trakom - An investigation of slipping in Rolamite-type mechanisms. Strojniški vestnik - Journal of Mechanical Engineering, v.50, No 6, 302-309. [5] Fridman, H.D., Levesque, P. (1959) Reduction of static friction by sonic vibration.-J. Appl. Phys., v. 30, No 10. [6] KaHaneHac, P. M. (1984) Bn6poonopi,i.- Bhjibhioc, MoKCJiac, 208 c. [7] EaHCJiBiiHioc, PK)., ParyiBCKHC, K.M. (1981) BH6poflBHraTenH.-BHni.Hioc, MoKCJiac, 193 e. [8] Invention of USSR JV° 609074. Avtorjev naslov:prof. dr. Ričardas Viktoras Ulozas Univerza Šiauliai Vilniaus 141 LT-76353 Šiauliai, Litva ulozas@tf.su.lt Author’s address: Prof. Dr. Ričardas Viktoras Ulozas Šiauliai University Vilniaus 141 LT-76353 Šiauliai, Lithuania ulozas@tf.su.lt Prejeto: Received: 17.10.2005 Sprejeto: Accepted: 23.2.2006 Odprto za diskusijo: 1 leto Open for discussion: 1 year Teoretična in eksperimentalna analiza - A Theoretical and Experimental Investigation 47