SIMULATION AND MODELING OF CYCLOID GEARS USED IN ORIENTATION MECHANISM OF ROBOTS

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1 SIMULATION AND MODELING OF CYCLOID GEARS USED IN ORIENTATION MECHANISM OF ROBOTS Ş.l. dr. ng. Luca PASCALE, Conf. dr. ng. Paul Cpran PATIC, VALAHIA Unversty of Târgovşte, Electrcal Engneerng Faculty, Automatcs, Informatcs and Electrcal Engneerng Department Ş.l. dr. ng. Adran RUNCEANU - Constantn Brâncuş Unversty of Târgu Ju, Engneerng Faculty Abstract: Cyclod reducers compared wth classcal reducers have low axal and radal gauge, hgh transmsson rato, and a better relablty. Cyclod gearng roller, through ts qualtes, has an mportant role n modern mechancal transmssons. The dfference between numbers of teeth of the cyclod gear roller can be equal to ( z - z2 ), wthout rsk of nterference, as a result, can be obtaned bg gear ratos n accordance wth n lower overall dmensons, whle the classc gear have the dfference between teeth number mn z - z2 4. In ths paper, the physcal prototype of a new verson of roller cyclod reducer s presented. Also one tres to test ths varant of cyclod gear on a modern stand tral. Keywords:Orentaton Mechansm, Cyclod Gears, Expermental Testng, Gear Prototype.. INTRODUCTION The characterstcs of cyclod reducers are: compact structures, hgh explotng safety and shock absorbng capacty, are less expensve, not nosy, long lfe functonng and hgh transmsson rato. The most essental robot perpheral s the end-effector, or end-of-arm-toolng. Common examples of end effectors nclude weldng devces (such as MIG-weldng guns, spot-welders etc.), spray guns and also grndng and debarrng devces (such as pneumatc dsk or belt grnders, burrs etc.) and grppers (devces that can grasp an object, usually electromechancal or pneumatc). Another common means of pckng up an object s by vacuum [9] and []. End effectors are frequently hghly complex, made to match the handled product and often capable of pckng up an array of products at one tme. They may utlze varous sensors to ad the robot system n locatng, handlng, and postonng products [6]. The desgn of robotc mechansms s a complex process nvolvng geometrc, knematc, dynamc, tolerance and stress analyses [5], [] and [2]. In the desgn of a real system, the constructon ofa physcal prototype s often consdered.regardng the orentaton of the gears n the prototypng machne, t s advantageous to keep ther axs vertcal for smoothness of operaton and strength [5]. The orentaton mechansms - OM of ndustral robots have two or three output rotatons. In the case of OM wth cylndrcal/concal gears, the knematc chans are n correspondence wth the known planetary mechansms [2]. Whle the partally coupled orentaton mechansms wth two rotatons (OM-2R) are smple, those wth three rotatons (OM-3R) have a complex structure [7]. Reducng of the speed s a techncal goal mposed by the need to adapt relatvely hgh speeds of modern engnes at the requrements of effectors whch they serve. 2. PROTOTYPE CYCLOID REDUCER S PRESENTATION A new varant of cyclod reducer, equpped wth a sun gear, whch s proposed by the authors, s llustrated n Fgure ; ths contans a cyclod gear par wth rollers, consstng of a 9

2 fx sun gear wth nternal cyclod teeth 3 and of more eccentrc rollers 2. The element H (whch contans an eccentrc bearng) desgnates the reducer s nput, whle the element (on whch the rollers 2 are eccentrcally artculated) desgnates the output. In the premse that the reducer uses z2 = 6 rollers (as teeth), then z3 = z2 + = 7 teeth and, mplctly, the reducer accomplsh the transmsson rato [] and [2]: 3 H H3 3 HH H H H z ( ),625 () z In the assumpton of frcton consderng, the reducer effcency H can be theoretcally establshed through the followng relaton: T 6 (2) 3 H (3) w TH H 3 where T H and T are the nput and respectvely output torque, s the reducer nternal H H H effcency ( η η3 η2 η23,995,995,99) and w s the effcency coeffcent (w = ±) that models the power crculaton n the fxed axs unt assocated to the planetary unt[, 2]: w sgn T T T sgn sgn sgn sgn 7 6 (4) H3 3 T H3 T 3 Fg.. The cyclod reducer equpped wth eccentrc rollers (2) and a sun gear (3) 3. EXPERIMENTAL TESTING The expermental testng of cyclodal roller gear was performed on tral stand equpment located n the Transylvana Unversty of Brasov. The test stand comprses two synchronous machnes Semens, brushless, two Semens converters, two torque and speed transducers, a tr-axal vbraton transducer, a PC type computer system, external data acquston equpment and a board for seral communcaton wth engne controllers. After enterng nput data were drawn graphs that represent the torques recorded by transducers. In each graph, the top s llustrated the torque engne and n the bottom s the torque brake [3].. 2

3 ,8 Regm lber_96-6 a.,6 Regm lber_32-2,6,4,4,2,2,8,6,8,6,4,4,2, Moment_Frna Moment_Frna b. Fg.2. The torques recorded by transducers, where nput and output gear decouplng and coachng of electrc - drver machne, wth speed of 32 and 96, and electrc - brake machne, wth speed of 2 and 6 Based on Fgure 2 were obtaned the next collated results systematzed n the Table, where TM and TF are average torques recorded by the transducer of electrc-motor machne and the electrc-brake machne, n the case of the decouplng of reducer s nput and output. Regm constant_reductor_96_ Regm constant_reductor_32_ Moment_Frna Moment_Frna a. b. Fg.3. The torques recorded by transducers for: gear engaged, no-load brake and engne traned successvely wth speeds: a) 32 and b) 96 Stand wth decoupled gear s nput and output Brake average speed Drve average speed Average torques at drve transducer T M [Nm] Average torques at brake transducer T F [Nm] Table 2

4 Regm constant_reductor_32_32 Regm constant_reductor_32_ Moment_Frna a. b. Moment_Frna Regm constant_reductor_96_32 Regm constant_reductor_96_ Moment_Frna Moment_Frna c. d. Fg.4. Torques recorded by transducers for: gear engaged, brake loaded sequentally to 32 Nm (a, c) and 4 Nm (b, d) and engne traned successvely wth speeds: 32 (a, b) and 96 (c, d) In Fgure 3 are shown the torques recorded by the transducer adjacent engne and, also, by the transducer adjacent brake for: gear engaged, no-load brake and engne traned successvely wth speeds: a) 32 and b) 96. Near by, n Fgure 4 are llustrated the torques recorded by transducers for: gear engaged, brake loaded sequentally to 32 Nm (a, c) and 4 Nm (b, d) and engne traned successvely wth speeds: 32 (a, b) and 96 (c, d). After processng data from Fgure 3 and 4, one obtaned some results collated n Tables 2 and, respectvely, 3. In Table 2.a. are systematzed the average values for engne speeds (nm2) and brake (nf2), and, also, for the torques recorded by the transducer adjacent to the engne (TM2) and at the adjacent brake (TF2), n the case n whch the motor-gear-brake system works wth no load brake (dlng on the brake). In the next Table 2.b., based on results from Tables and 2, a. have been set the average resstant torques of the gear, proper to the dry runnng of brake (TF3=TF2+TF) and resdual torque engne of gearbox (TM3=TM2-TF3//η). 22

5 Table 2.a. Brake average speed Drve average speed Average torques at drve transducer T M2 [Nm] Average torques at brake transducer T F2 [Nm] Table 2.b. Brake average speed n F2 Drve average speed n M2 Average resdual engne torques of the gear T M3 =T M2 -T F3 /(.η) [Nm] Average resdual engne torques of the gear at no-load brake T F3 =T F2 +T F [Nm] Brake average speed n F4 Drve average speed n M4 Average torques at drve transducer T M4 [Nm] Table 3 Average torques at brake transducer T F4 [Nm] Resdual engne torque of the reducer represent, accordng to the calculaton expresson: TM3=TM2-TF3//η, the needed torque to drve the gearbox wthout load (no load to hs rdng). For compatblty wth common theoretcal assumptons, the resdual engne torque wll be excluded from the calculaton of effcency; n ths way, t becomes possble drect comparson between the theoretcal value of the yeld and ts values based on expermental data processng. On the bass specfed n Table 3 were systematzed, wth the prevous tables, the averages values of speeds and torques calculaton of yeld and, also, the values obtaned for the gearbox s yeld durng the tested regmes. Wth calculus, the theoretcal yeld was obtaned for the consdered reducer: η = (- )/(- /η ) = (-,625)/(-,625/,99) =, 8534 =>η= 85,34% (5) The values of yeld, based on expermental data n condton of compatblty under theoretcal assumptons, are collated n Table 4 and were determned by the expresson: η = (TF/TM)/(nM/nF) = (TF/TM)/; for the four loadng regmes, values were obtaned: a) 32 rpm-engne wth32 Nm brake => η = 74,9%; b) 32 rpm-engne wth4 Nm brake => η = 8,956%; c) 96 rpm-engne wth32 Nm brake => η = 72,827%; d) 96 rpm-engne wth 4 Nm brake => η = 8,323%; Table 4 Brake average speed n F Drve average speed n M Average engne torques wthout the resdual torque T M =T M4 -T M3 [Nm] Average resdual torques of the gear T F =T F4 +T F [Nm] Yeld η=t F /T M / % % % % 23

6 4. CONCLUSION Theoretcally yeld of the gear reducer s determned, n classc premse, takng nto account only the frcton losses of cyclod gear and those from the rotaton couples of the radal couplngs. Under these condtons, the theoretcal yeld was obtaned for the consdered reducer: η = 85.34%. From the above comparson values, can thus be consdered that n the manufacturng cyclodal teeth condtons, by copyng after tracng, the results obtaned through prototype testng confrms satsfactory the theoretcal model. 5. REFERENCES [] Daconescu D.V., Products Conceptual Desgn, TransylvanaUnversty Press, Brasov, 23. [2] Mlou G., Dudta F. and Daconescu D.V., Modern Mechancal Transmsson, Ed. Tehnca, Bucharest (n Romanan). [3] Neagoe M., Daconescu D.V., Mechansms. Structure analyss and gear mechansms, Translvana Unversty Press, Brasov, 24, ISBN: [4] Pascale L., Comparatve analyss of modern planetary gears and a new reducer synthess (n Romanan), PhD thess, Translvana Unversty of Brasov, 27. [5] Imme Ebert-Uphoff, Clement M. Gosseln, Davd W. Rosen & Therry Lalberte, Rapd Prototypng for Robotcs, Open Access Database, pp [6] Stacu Stefan, Inverse dynamcs of a planetary gear tran for robotcs, Mechansm and Machne Theory, Volume 43, Issue 7, July 28, pp [7] Antonescu O., Lung I, Udrste D, Antonescu P., Contrbutons to Analyss and Synthess of the Orentaton mechansms (Wrst) Used on the Industral Robots, The Romanan Revew Precson Mechancs, Optcs & Mecatroncs, 28 (8), No. 34, pp [8] Neagoe, M., Daconescu, D., Pascale, L., Săulescu, R.,On the effcency of a cyclodal planetary reducer wth a modfed structure. Internatonal Conference on Economc Engneerng and Manufacturng Systems ICEEMS, Translvana Unversty of Brasov, October 27, publshed n Recent Journal, Vol. 8, No. 3b(2b), November, 27, pag (B+), ISSN [9]Pascale L., Neagoe M., Daconescu D., Patc P.C., The Dynamc Modelng of a New Cyclodal Planetary Gear Par wth Rollers used n Robots Orentaton System, The Scentfc Bulletn of Electrcal Engneerng Faculty, No. (), p. 35-4, ISSN , 29. [] Pascale L., Popescu C., Patc P.C., Neagoe M., Daconescu D., Pattern Makng Geometrcal of a Internal Cyclodal Gear Par wth Rollers used n Robots, Proceedngs of the st Workshop on Energy, Transport and Envronment Control Applcatons ETECA 9, The Expert Publshng House, p. 83-9, ISBN , ISBN , 2. [] Pascale L., Patc P. C., Duţă L., Runceanu A., Modelng and Smulaton of Cyclod Curves wth Applcaton n Robotcs, Revsta de Fabltate ş Durabltate / Fablty & Durablty Journal, October, 2, Academca Brâncuş Publshng House, Târgu Ju, ISSN X, No. 2 (6), pp [2] Pascale L., Patc P. C., Duţă L., Runceanu A.,Modelng and Smulaton of Cyclod Curves wth Applcaton n Robotcs, 3 rd INTERNATIONAL SYMPOSIUM DURABILITY AND RELIABILITY OF MECHANICAL SYSTEMS, Târgu Ju, Romana, May 2-2, 2, ISBN , pp. -6. [3] Sscă, S., Mogan, G.,Modular test bench used as a versatle tool n the mechancal product desgn cycle, The 6 th Internatonal Conference "Research and Development n Mechancal Industry", RaDMI 26, September 26, ISBN X (HTMS) 24