ACTA TECHNICA NAPOCENSIS

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1 TECHNICAL UNIVERSITY O CLU-NAPOCA ACTA TECHNICA NAPOCENSIS Sere: Appled Matheatc ad Mechac Vol., Iue I, 0 CONTRIBUTIONS AT THE CALCULATION AND CONSTRUCTION O THE SUSPENDED TTR ROBOT Ncuşor Iof URSA Abtract: I paper [] the dyac tudy of the TTR dutral robot wa perfored. Coderg the whole robot dyac ad the echacal tructure of each odule, the actuator are calculated th paper. Th calculato volve the followg tep: the detfcato fro the etablhed yte of dfferetal equato, the dfferetal equato for each odule; depedg o the cotructo of each odule, the relato betwee the drvg force fro the output ode ad the actuator power etablhed; the troducto of the drvg force expreo the oto dfferetal equato; ug the P poed or calculated uercal data the report fro th equato detered; the deterato of the actuator oet M ad choog fro a actuator catalogue the actuator that ha the oet value hgher tha calculated. The calculato for choog the actuator were ade for MTV, MTO ad MR odule fro the TTR robot tructure. Key word: actuator, drvg force, dfferetal equato, echacal tructure, tralato odule, grppg devce.. INTRODUCTION The upeded dutral robot TTR (fgure ) for heat exchager hadlg the preervato operato fro the brazg proce, copoed of two tralato odule that provde the horzotal oveet (HTM), the vertcal oveet (VTM) ad a rotato odule (RM). The robot cotructo th vero of odule cotructve arrageet, t provde the oblty eeded to g.. The TTR eral dutral robot acheve the oveet to be perfored durg the producto proce. Baed o the dyac tudy ad o the dyac equato reulted fro th tudy, the judcou choce of the actuator robot odule doe. The calculato eceary to detfy the actuator charactertc for each odule are lted below.. THE ACTUATOR S CHOICE O THE HORIZONTAL TRANSLATION MODULE Gve the horzotal tralato odule cotructo of the dutral TTR robot, (HTM, fgure ), baed o yeld the drvg force a, the geoetry trao procketbelt ychroou gear-rack ad the gude ued for ruway, ca be detered. The axal force (drvg force) requred for f g.. The horzotal tralato odule a cc the oble equpet oveet of the HTM odule, ha the expreo:

2 a cc f [ N ] () relato whch: cc the axal force developed by the trao procket-belt ychroou gear-rack ad f the gude frcto force. The developed trao force cc ha the expreo: M p cc [ N ], () D0 whch: M p [N] the torque at the po haft, D 0 [] the dvo daeter of the po. By otg P p, p the power, repectvely the po peed, the torque t ca be detered wth the relato: Pp M p 90 [N]. () The power P p detered a: Pp P ηc [ kw ]. () oted: P repreet the power output by the DC ege whch caue the oto of the tralatoal oble equpet fro the robot bae ad by η c the yeld couplg wth elatc eleet. The p po peed ut atfy the followg equalty: rot p, () whch by wa oted the haft ege peed. Coderg the relato (), () ad (), the relato () becoe: 90P p η [ N ] c cc.. (6) D0 Takg to accout the relato (), (6), the dyac equato correpodg to the vertcal tralato odule of the robot, detfe fro the etablhed dfferetal equato yte, preeted paper [] ad ha the for: 90P η c q& f. (7) D0 The frcto force calculated wth the relato: f gμ [N], (8) where g oted the gravtatoal accelerato (g 9.8 /) ad the gude coeffcet of frcto μ, adoptg the tadardzed value μ The expreo of the report P t ca be obtaed fro the relato (7) ad (8). Thu D0 P q& + gμ. (9) η c 90 Wth the report obtaed the prevou relato t ca be calculated the drvg oet of the ege, ug the relato for: M P [ N] 90, (0) fro where the actuator odule choe. The followg value are ued a uercal data: 86, kg,90 kg,9 kg ; 8, kg ; rad q &, ; 0,09 η c 0,99 ; ; D 0 ;. Accordg to relato (8), the frcto force t calculated: ( 86, +,90 +,9 + 8,) 9,8 0,00 () f 7,76 N. Eterg the value obtaed relato (9), the P report t calculated: P - kw, 0. () rot Accordg to relato (0) the drvg oet of the DC ege t calculated: - M 90, 0, 86 N. () ro the cataloque of Parker' copay the actuator choe. H cotructo beg coducted a tegrated oluto, ege ad plaetary gear et, type GM 090, wth the followg charactertc: M, 0 N ; : ; ax 700 ; 7, kg ; P calc., 06 kw. It equpped wth reolver ad electrcally brake. Ug the actual value of the ege drvg oet choe, accordg to relato (), () ad (8), the force aocated to the horzotal tralato odule t ca be calculated: M CATALOG a gμ D 0 [ N ]. () Ug the uercal data, the force ha the value: a 97,7 N.

3 The keatc cha for the tralato odule cot of: a electrc ege, a peraetly oble couplg wth teredate elatc eleet ad procket-belt ychroou gear-rack. By ug the ball gude, the aebly lk wth the gude eleet related to the ruway acheved. The deg crtera that were take to accout whe degg the tralato odule are: the appled oet to the po that wll be ued to obta axal force; the gude aotg that ut be ued ad alo eured by a aotg echa of the yte for prevetg ezure ad wear; the gude protecto ade wth cleag part of the ruway provded by the aufacturer factory; pleetg techology volve choog the cotructve eleet fro product catalog provded by pecalzed producer ad ther ue accordg to the techcal requreet poed.. THE ACTUATOR S CHOICE O THE VERTICAL TRANSLATION MODULE M f a Gve the vertcal tralato odule cotructo of the TTR dutral robot, (VTM, fgure, []), the drvg force baed o yeld, the trao geoetry crew-ut wth ball ad the gude ued, ca be detered. The axal force (drvg force) regured for the oble equpet oveet of the VTM odule, ha accordg to (), the expreo: [ N ]. g.. The vertcal tralato odule M a b. f () relato whch: b the axal force developed by the ball crew trao ad f the gude frcto force. The developed ball crew trao force b ha the expreo: M b. [ N]. (6) k d0tg arctg dbφ where: d 0 [] the cylder daeter that are ceter of the ball, φ [ ] the agle of the propeller lock o the edu cylder, k the frcto coeffcet at the rollg, d b [] the ball daeter, φ [ ] - the cotact agle betwee the ball ad ruway, M - the torque of the ball crew haft. By otg P, the power, repectvely the ball crew peed, the torque t ca be detered wth the relato: P M 90 [N]. (7) The power P detered a: [ kw ] P P. (8) otg: η r the yeld bearg par ad by P repreet the power output by the DC ege whch caue the oto of the tralatoal oble equpet fro the robot bae. The crew peed ut atfy the followg equalty: rot, (9) whch by wa oted the haft ege peed. Coderg the above relato, the relato (6) becoe: 9 0 P b. [ N ]. (0) k d0tg arctg dbφ Takg to accout the relato () ad the prevou relato wrtte for the b force, the dyac equato deduced fro paper [], correpodg to the vertcal tralato odule (VTM) of the robot, becoe: P 9 0 q + G & f k d0tg arctg d b φ () The frcto force f calculated wth the relato: f gμ [ N ], () where g oted the gravtatoal accelerato (g 9.8 /) ad the gude coeffcet of frcto μ, the adoptg tadardzed value

4 μ 0.0. The agle φ of the propeller lock o the edu cylder calculated wth the expreo: ph o ϕ arctg [ ], () where by p h wa oted the tep crew leader. ro relato () t ca obta a P expreo of the report. Thu, q&& G + πd p k d0tg arctg ϕ+ dbφ gμ 9 0 () Wth the report obtaed the prevou relato t ca be calculated the drvg oet of the ege, ug the relato for: P M 90 [N], () fro where the actuator odule choe. A uercal data the followg value are ued:, 90 kg ;, 9 kg ; 8, kg ; q & ; p, ; h 0 0 d 0 0, 0 ; d p 0, 06 ; k 0, 0000 ; d b 0, 00 ; 0 φ 0 ; ϕ 7,0 0 ; η r 0, 99. Accordg to relato (), the frcto force t calculated: f, 90 +, 9 + 8, 9, 8 0, 0 0, 9 N (6) ( ). The agle of the propeller lock o the edu cylder of the ball crew, t ca be calculated wth the relato (): 0, 0 0 ϕ arctg 7, 0. (7), 0, 06 Eterg the value obtaed relato (), P the report t calculated: P - P kw 6, (8) rot Accordg to relato () the drvg oet of the DC ege t calculated: - M 90 6, , 678 N, (9) Wth whch t wll chooe the DC actuator plaetary gear corporated, fro the cataloque of Parker' copay, type GM 060, accordg to [], wth the followg charactertc:. M 7, N ; 7 : ; ax 780 ;, 8 kg ; P calc. 0, 79 kw. It equpped wth reolver ad electrcally brake. Ug the actual value of the ege drvg oet choe, accordg to relato (6) ad the eaureet prevouly calculated, the force aocated to the horzotal tralato odule, coderg M M catalog, t ca be calculated: M STAS a gμ k d0tg arctg d b φ [ N ]. (0) Thu, the force ha the value: a 7 N. The keatc cha for the tralato odule cot of: a electrc ege, a peraetly oble couplg wth teredate elatc eleet ad ball crew-ut. The coecto betwee the actuator ad crew drver perfored by a belt ychroou gearrack. The yeld ball crew-ut echa hgh (η 8-9 %). The deg crtera that were take to accout whe degg the tralato odule are: the appled oet to the drver crew that wll be ued to obta axal force; the reverblty crew drver ca ot be regarded a a at-blockg ad therefore, to obta the oble body poto of coad, the yte requre a toroal lockg of the crew; the cotact betwee the actuator ad crew drver wll be doe by afety couplg for overload protecto; regardg the tghteg, eto that the trao of hgh preco oveet ad rgdty oly poble by ug the ball crew wth two ut; the gude aotg that ut be ued ad alo eured by a aotg echa of the yte for prevetg ezure ad wear; the ruway protecto ade wth cleag part; pleetg techology volve choog the cotructve eleet fro product catalog provded by profled producer, ther tallato ad ue are accordg to the techcal requreet poed; the bearg are ued to acqure the axal force fro crew drver.

5 . THE ACTUATOR S CHOICE O THE ROTATION MODULE or the rotato odule of the dutral robot TTR, (RM, fgure ), the ege oet M, ca be detered, accordg to the detfed dyac equato fro the dfferetal equato yte etablhed paper [], corepodg to the rotato odule of the robot, aely: ( ) ( ) + l q& M. () [ ] + Steer theore appled to detere the erta oet relato wth the rotato ax, for axe parallel tuato // ). ( C + C Md [ ] kg () where: d [] the dtace betwee the axe, M [kg] the weght eleet. or detere the erta oet of the coplex geoetrcal copoet hape, they are dvded to C M ple geoetrc for for M C M plcty, th C cae the rotato odule ad the M M C grppg devce C (fgure ). C ro fgure, the relato ca be wrtte: C C C C C g.. The decopoto to ple geoetrc hap C C C & q& g.. The rotato odule, the grppg devce ad the apulated pece ( ) ( ) ( ) ( ) ( ) ( ) [ kg ]. + C C C C C C () ( ) M d [ kg ] C + C ( ) M d [ kg ] C + C ( ) M d [ kg ] C + C ( ) M d [ kg ] C + C ( ) M d [ kg ] C + C. () Coderg the relato (), the relato () becoe: ( )... M d M d C C + C + + C + C + + () M d + M d [ kg ]. C Applyg the relato () for (fgure 6, [6]), t ca be wrtte: ( ) ( ) [ kg ] C C. (6) C6 Takg to accout the M 6 relato (), (6), the detfed C 6 dyac equato fro the C6 C dfferetal g. 6. The apulated aeble equato yte etablhed paper [], corepodg to the rotato odule of the robot, : + M d q M C C + &. (7) 6 The followg value are ued a uercal data: C 0, 070 kg ; C 0, kg ; 0, kg ; C, 0 kg ; C 6 0, kg ; C6, 79 kg ; C 8 d 0, 0 ; d 0, 0 ; d 0, ; d 0, 0 ; M 0, 07 kg ; M, 68kg M, 9 kg ; M 6, 8 kg ; M, 9 kg ; rad M 6 60 kg ; q&,. Accordg to relato (7) the drvg oet of the DC ege t calculated: M M, 6N. (8) ro the cataloque of Parker' copay the actuator choe. H cotructo beg coducted a tegrated oluto, ege ad

6 6 plaetary gear et, type GM 090, wth the followg charactertc: M, 0 N ; :; ax 700 ; 7, kg ; P calc., 06 kw. It equpped wth reolver ad electrcally brake. The keatc cha for the rotato odule cot of: a electrc ege, a trao belt ychroou gear, a rotato eleet. The bearg rotato eleet fully aue t axal loadg. Takg to accout the operatoal requreet ad the operatoal afety crtera, the deg of the rotato odule wa ade, uch a: the bearg are ued to acqure the full axal force due to weght grppg devce ad the apulated pece ad radal load; the aotg hould be ued regularly ad alo eured by a aotg echa of the rotato yte for prevetg ezure ad wear; the ple odule cotructo ad relablty t operato; the pleetato techology volve choog the ege, trao ad bearg capable of eurg the poed paraeter. Th doe by lkg value fro calculato, wth product data heet fro aufacturer catalog.. CONCLUSION Takg to accout the whole dyac of the robot ad the echacal tructure of each odule, the actuator are calculated. Alo, for the deg of each robot odule, were take to accout the poed requreet by the operato ad the relablty crtera. 6. REERENCES [] Ura, N.I, Ipa, V., Cotrbuţ la calculul ş cotrucţa tructur ecace a roboţlor dutral eral utlzaţ la fabrcarea radatoarelor, Teză de doctorat, Cluj-Napoca, 0. [] Catalog INA, AGOR, SIEMENS, ONDRIVES. [] Docuetaţe Soft MATHEMATICA 6.0. [] Docuetaţe Soft SOLID WORKS. [] Docuetaţe Soft INVENTOR. [6] Docuetaţe Soft AUTOCAD. Cotrbuţ la calculul ş cotrucţa robotulu upedat TTR Rezuat: Studul dac al robotulu dutral TTR a fot efectuat î lucrarea []. Î prezeta lucrare e calculează otoarele de acţoare luâd î coderare daca îtregulu robot ş tructura ecacă a fecăru odul. Acet calcul preupue parcurgerea urătorlor paş: detfcarea d teul de ecuaţ dferetale tablte, a ecuaţe dfereţale corepuzătoare fecăru odul, tablrea relaţe ître forţa otoare de la eşrea d odul ş puterea otorulu de acţoare, î fucţe de cotrucţa fecăru odul, troducerea î ecuaţa dfereţală a şcăr exprea P forţe otoare, deterarea raportulu d aceată ecuaţe cu date uerce pue au calculate, deterarea oetulu M a otorulu de acţoare ş alegerea dtr-u catalog de otoare otorul care are valoarea oetulu a are decăt cea calculată. Calcule petru alegerea otoarelor au fot făcute petru odulele MTV, MTO ş MR d tructura robotulu TTR. Ncuşor Iof URSA, Drd. Ig., S.C. RAAL S.A. Btrţa