Study on the Dynamic Performance of Heavy-duty Forging Manipulator

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1 Sdy o he Dyamic Pefomace of Heavy-dy Fogig Maipao QINGSONG YANG, YUANXIN LUO, YONGQIN WANG, XINGCHUN YAN The Sae Key Lab of Mechaica Tasmissio Chogqig Uivesiy Rm. 30, No. 7 Teachig Bidig, No.174, Shapigba, , Chogqig PEOPLE S REPUBLIC CHINA yxo@cq.ed.c Absac: - Coopeaig wih heavy fogig pess, he heavy-dy fogig maipao is sed fo hadig he wopiece dig he fee-fogig pocess. Theefoe, he size accacy of he fogigs is eaed o he dyamics pefomace of he fogig maipao. This pape aims o sdy he dyamic pefomace of DDS heavy-dy fogig maipao. The iemaics mode is fisy bi o pedic he ajecoies of he og. The, he dyamics modes ae deived by sig igid-body mehod ad fexibe-body mehod especivey. Fiay, he simaio ess idicae ha paiay fexibe-body mode is we pediced he ajecoy of he og. Key-Wods: -Fogig maipao, Dyamics mode, Paiay Fexibe-body mehod, Tajecoy 1 Iodcio Heavy-dy fogig maipaos ae o oy he basic eqipme fo pecisio maface of heavyfogigs, b aso he ey o asse he fogig qaiy of heavy-fogigs [1-]. Fig. 1 shows a ypica fogig maipao, wih he basic moios i opeaio pocess: waig, moio of he og ad bffeig. Whie he accacy of hose moios eaized by ifig mechaism of maipao, has diec effecs o he qaiy of fogigs. So, he iemaics ad dyamic aaysis of ifig mechaism has aways bee he focs of maipao sdies. Gee a. [3] scceeded o esabish he eaioship bewee ops of edeffecos ad acao ips ad sdy he op iemaic chaaceisics fo heavy-payoad fogig maipaos. Wag e a.[4]evaaed he ma eacio oads bewee he fogig pocess ad he assisig maipao by combiig he fogig fiie eeme mehod simaio ad he iemaics aaysis. Ya e a. [5] bi he iemaic mode of he fogig maipao, ad deived he cosed-fom ivese iemaic soio by sig he homogeeos coodiae asfomaio mehod. The eseaches [6,7]aayzed he compiace pocess by bidig dyamic modeig fo fogig maipao. Paih e a.[8] addess he fowad iemaics pobem of a paae maipao ad popose a ieaive ea ewo saegy fo is ea-ime soio o a desied eve of accacy. W e a. [9]sdied he dyamic chaaceisics of he wo degee-of feedom paa paae maipao of a heavy dy hybid machie oo. X e a.[10] bi p iemaics of a ypica DDS fogig maipao. I ypica codiio, he oad of maipao mechaism was achieved hogh bidig visa 3-D dyamic simaio of miigid-body sysem by Ree a.[11]. The ieaes meioed above pese he igid-body dyamics mode of maipao. Howeve, sedom have eseaches sdied easodyamics o iodce he easic asmaio of mechaism. I coas wih easodyamics mode, igid-body dyamics mode has a geae eo of moveme aaysis as a es of igoig he fexibiiy of mechaism. Theefoe, i s ecessay o sdy he easodyamics of maipao becomes moe impoa ad meaigf fo podcio pocess. E-ISSN: Isse 3, Vome 8, Jy 013

2 (a) Phoo (b) CAD mode Ths, o he basis of he igid-body dyamics aaysis, his sdy esabishes he easodyamics mode of fogig maipao ad aayzes he effec of fexibe-body. Becase of he obvios diffeeces i siffess, he ifece vaies fom compoe o compoe. The fexibiiy of some membes, sch as iage, azy am ad hydaic cyides, is oy cosideed i his sdy o simpify cacaio pocess ad eease moio ow y. The es of his pape is ogaized as foow. I he secod secio, igid-body dyamics mode of fogig maipao wi be esabished o cacae he ieia foces ad exea oads acig o compoes i evey mome. Secio 3 wi se p paiay fexibe-body dyamics mode by sig he mehods fo maipao mechaism fom ieaes [1-16]. Ad he, he simaio agoihm ad he fowcha of eie aaysis pocess wi be iodced i secio 4. Secio 5 wi discss he cacaio ess wih diffee woig codiios. Eveay, secio 6 saes he cocsios. Fig.1:A ypica fogig maipao pocess, he ifig mechaism ca be pojeced io a pae deoed as x0y, as show i Fig.3. Fig.: CAD mode of ifig mechaism Rigid-body dyamics mode.1 Kiemaics mode The maipao i his sdy is a DDS fogig maipao, as he aes ad ages oage fogig maipao a ove he wod a pese, whose compoes ae age-sizead he mai movig is desiged as a paaemechaism. The maipao ca hod wopiece p o 300, is a compex mi-body mechaism sysem which aways wos de heavy-oad o exeme eviomes. As show i Fig., he mai mechaism of DDS fogig maipao is he ifig mechaism. I ode o simpify cacaio Fig. 3: Lifig mechaism The ifig mechaism cosiss of sevea pas icdig iages, hydaic dives ad moio E-ISSN: Isse 3, Vome 8, Jy 013

3 pais. Hydaic dives ae wih he ifig hydaic cyide, he bffe hydaic cyide ad he eaig hydaic cyide, which ae idividay deoed by c 1, c ad c 3. I ifig pocess, he cyide c 1 coos he veica moveme of wopiece hogh ipig ifig siga. A he same ime, he cyides c ad c 3 ae pefecy cosed. Whie, he cyides c 1 ad c ae cosed ad he cyide c 3 eaizes eaig moveme by ipig eaig siga i eaig codiio. Wih he same mechaism, he ifigopeaio ad eaig opeaio ae simia. Theefoe, he iemaics mode is bi oy fo ifig opeaio i his sdy. As isaed i Fig. 3, he egh of ifig hydaic cyide deoed 1 chages wih Eq. (1) i ifig pocess. = f() + (1) 1 1mi whee, 1mi is he miimm egh of ifig hydaic cyide, f() epese ip siga ad deoes he ifig ime. O iemaics modeig, Caesia coodiae oigi is esabished a moio pai deoed F, ad he maix eaioship, which icdes posiio, veociy ad acceeaio fo ohe moio pais. Taig he pai m ad of a membe fo exampe, he coodiae eaioship of he pais is wie Eq. (). x mx y = my 1 3 m () Whee mx, my, x ad y epese he coodiae of iemaic pais m ad i veica ad hoizoa diecios, especivey; = is 1 3 posiio maix, m is he disace fom paismo. By cacaig he Fis-Ode deivaive ad he Secod-Ode deivaive of Eq. () idividay, he veociy ad he acceeaio of he pai m ad ca be give as he foowig eqaios. x mx y = my 1 3 m x mx y = my 1 3 m (3) (4) Whee mx, my, mx ad my epese he veociy ad acceeaio of iemaic pai m i veica ad hoizoa diecios, especivey, iemaic pai is simia, m ad m ae he veociy ad he acceeaio of pai m eaive o pai i he diecio of m.. Dyamics mode By aayzig easodyamics of DDS fogig maipao, he igid-body dyamics mode is wiho cosideaio of fexibiiy of a compoes. The posiio, veociy ad acceeaio ae diecy cacaed fom iemaics aaysis, wih cosideaio of he ieia foces ad exea oads acig o membes i evey mome. Accodig o he dyamic saics mehod fom ieaes [3-5], igid-body dyamics eqaio ca be se p fo each membe, sch as he dyamics Eq. (5) of membe. Fiay, dyamics eqaios of eie mechaism ae gaied by combiig evey membe eqaio. N xid xi + N yid yi + m gi J ε = 0 i= 1 Nx1+ Nx + + Nx max = 0 (5) Ny 1+ Ny + + Ny mg may = 0 whee, N x ad N y epese oad acig o -h pai of membe deoed i veica ad hoizoa especivey, m, J ad ε ae mass, oaioa ieia ad age acceeaio of membe, whie a x ad ay ae acceeaios of ceoid i wo diecioa (veica ad hoizoa) fo membe, sepaaey. d xi, d yi ad i doaed he foce am of N x, N y ad gaviy. 3Paiay fexibe-bodydyamics mode 3.1 Easodyamics aaysis fo iages As he ifig mechaism of DDS fogig maipao is paae fo coecio ods of mechaism, i ca be eseached as paa iage fo moveme of i veica pae. De o he effec of paiay fexibe-body, ie iage, azy am ad hydaic cyides, is eaivey obvios. Theefoe, easodyamics aaysis i his pape oy aes hose membes as fexibe-body, is caed paiay fexibe-body dyamics mode. Wha s moe, his mode cosiss of easodyamics aaysis of azy am, iage ad hydaic cyides. E-ISSN: Isse 3, Vome 8, Jy 013

4 I is a effeciveappoach o aayseeasodyamics fo azy am ad iage by fiie eeme mehod (FEM). The basic idea of FEM is ha mechaism is see as a seies of isaaeos iage i evey mome; he, igidbody dyamics ad easodyamics ae cacaed sepaaey fo aisaaeos iages; fiay, easic-moio espose of mechaism ca be obaied by way of combiig wih he wo ess [14-15]. Accodig o he FEM, azy am ad iage, deoed asig ad idividay, ae fexibe-body simpified as discee mped-mass mode, ad he, hei eeme dyamics eqaios ae bi by meas of he FEM heoy ad Lagage s eqaios, as foows. m δ + δ = Q (6) ⅠⅠⅠⅠⅠ m δ + δ = Q (7) ⅡⅡⅡⅡⅡ Besides,Eqs. (6) ad (7) ae ewie i maix as show i beow: m ⅠⅠⅠⅠ δ δ Q Ⅰ + = m ⅡⅡⅡⅡⅡ δ δ Q (8) Whee, m Ⅰ, m Ⅱ, Ⅰ ad Ⅱ ae show i Appedix. Fhemoe, he dyamics fomaio ca be achieved by asfomig fom oca coodiao ogobbe coodiao sysem. Uimaey, Eq. (8) ca be simpified as, Mq + Kq = Qs (9) Whee, M, K ad Q s ae he mass maix, he siffess maix ad geeaized foce; q ad q ae heesposes of eie sysem. 3. Eqivae siffess fo cyide of maipao Becase of he maipao i his sdy which he oa mass of og ad wopiece exceed 700, he ifece of hydaic siffess fo mechaism moio shod o be egeced. I ifig pocess, hoizoa bffe cyide ad eaig cyide ae oced ad see as oiea spig havig saic siffess; wha s moe, eqivae siffess is eaded io esabished dyamics mode i his sdy. Accodig o iqid capaciy effec of hydaic cyide, V dp Q = βe d (10) Whee, Q, V, P ad β e epese he vaiaio of fow, iqid vome i cyide, hydaic pesse ad he eqivae easic mods of iqid. Eq. (10) is mipied by d ad he is iegaed, as show beow, V V = P (11) βe F By sbsiig P = io EQ.(11), i ca be A ewie as: β A e F = x V (1) Whee, F ad A deoe exea oad acig o βe A cyide ad effecive aea of cyide, Kq = V epeses he eqivae siffess of hydaic cyide ad is ead io dyamics mode of bffe cyide ad eaig cyide, ad easodyamics mode ca be deived i he ed, as show beow. Mq + K q = P() (13) q 4 Simaio agoihm I easodyamics eqaios, mass maix ad siffess maix of sysem is fcio wih sce paamee ad posiio, so he moda feqecy is chageabe accodig o vaied posiio of mechaism. Sysem easodyamics eqaios of maipao ae soved by sig he mode speposiio mehod which is a semi-discee FEM ad combies wih FEM i space domai ad diffeece-mehod i ime domai. Based o he caoica modes maix of sysem obaied fom aa feqecy ad modes, he easodyamics eqaios of DDS fogig maipao ae deived as d ode diffeeia eqaios wiho copig i oma coodiae. z1+ ω1 z1 = p1() z + ωz = p() z + z = p ω () (14) E-ISSN: Isse 3, Vome 8, Jy 013

5 Wih he iegaio of Eq. (14), Dhame iega foma of easodyamics espose fo sysem is wie as, 1 z p d A B ( ) = ( )si ( ) si cos 0 ω τ τ ω ω ω + + (15) BY aig he deivaio ad iegaio opeaio o Eq. (15) wih iodced iiia codiios as give i Eq. (16), he easodyamics espose ca be obaied as showi Eq. (17): T { φ } [ ]{ } T { φ } [ ]{ } z = M q z = M q = 0 0 = 0 0 (16) z 0 p() z = siω+ z0 cosω+ [ 1cosω] ω ω p () z = z 0cos ω ωz0siω+ siω ω (17) I easodyamics aaysis of DDS fogig maipao, mass maix, siffess maix ad geeaized foce ae vaiabe wih ime, ad i is diffic o idicae mode dispaceme i expessios abo ime. As a es, ecsive fom of sysem espose is deived by way of dispesig ime io eqidisa ime segmes deoed which a paamees ae cosa. Recsive fom is show i he foowig eqaios, ad he easodyamics es of maipao ca be achieved by sovig Eq. (18) i he ed. T { φ} { } T { φ} { } z0 = M q0 z 0 = M q0 + 1 z 0 p() z0 = siω + z0cosω + 1 cosω ω ( ω) + 1 p () z = z 0cos ω ωz 0siω + siω ω q = { φ }{ z0 } q = { φ }{ z 0 } (18) Fiay, Eq. (19) idicaes he dyamics espose of whoe machie ad og o he basis of smmig p esposes of easodyamics ad igid-body dyamics. Fhemoe, he fowcha of eie aaysis pocess cod be achieved, as show i Fig.4. { X} = { U} + { Z} whee { X }, { U} ad { } (19) Z epese he dyamics espose, he easodyamics espose ad igidbody dyamics espose, especivey. Taig hydaic cyides as fexibe-bodies Easodyamics mode of maipao Taig iage ad azy am as fexibe-bodies Smmig p esposes Res Fig.4 Fowcha ofcacaio Kiemics aaysis of maipao Dyamics mode of maipao 5 A case sdy ad discssios I his sdy, DDS fogig maipao wih he oad imi is 300, ad he oad codiio, ip siga (Eq. (1)) ad pimay paamees of maipao mechaism ae show i Tabe 1. To ivesigae he effec of fexibiiies boh i ifig codiio ad eaig codiio, diffee ifig oa-ime deoed τ ad posiios icdig he owes, he midde adhe highes posiio ae appied o he ifig moveme ad he eaig moveme fo maipao mechaism, especivey. I ifig pocess, he age vae of τ epeses he owe speed of ifig cyide ad he vaes ae 0s, 50s, 100s ad 00s i his pape. Whie he speed of eaig cyide deoed v 0 is 35mm/s a each eaig posiio. Fig. 5 ad Fig.6 show he ajecoy of og igidbody dyamics espose ad fexibe-body dyamics espose fo ifig codiio by cosideig pai F as coodiae oigi i Fig.. Accodig o compae wih he esposes, he eo ca be see obviosy a he iiia sage of ifig pocess. Fhemoe, Fig.5 eves ha he effec of fexibe-body which hydaic cyides ae sigificay geae ha iage ad aze am whose effecio ca be igoed amos compeey. Measwhie, he highe he speed of ifig cyide, he geae he effec of fexibe-body, as show i Fig.6. Howeve, Fig.7 ad Fig.8 isae he E-ISSN: Isse 3, Vome 8, Jy 013

6 fexibe-body affec he dispaceme of og maiy i hoizoa diecio owig o he smae siffess of hoizoa hydaic cyide show i Fig.. Tabe1 Cciapaamees of DDS fogig maipao The imi oad of 300 maipao M max / The soe of og m 3800 /mm The soe of ifig hydaic cyide /mm The soe of eaig hydaic cyide /mm AH /mm 9679 /mm 6355 DE /mm 3315 β e /Mpa 1000 P /Mpa 3 Ip siga i ifig 1 π 1 1mi 1 si codiio τ Ip siga i eaig 1 = v 0 + 1mi codiio π = + + Fo he eaig codiio, Fig.9 show he ajecoy of og whe maipao mechaicsm is a he owes, he midde ad he highes posiio idividay.neveheess, he effec of fexibebody is o oabe, i coas o he ifig codiio, as a es of he posio of maipao mechaicsm is fxed ad each pai foce chages a ie. I addiio, he pefomace of he ifece appea maiy i he secod haf of eaig pocess. Fig.5 The ajecoy compaiso of igid-body dyamics ad fexibe-body dyamics fo og Fig.6 The ajecoy of fexibe-body dyamics fo og i diffee codiios Fig.7 The hoizoa dispaceme of og i diffee codiios E-ISSN: Isse 3, Vome 8, Jy 013

7 Fig.8 The veica dispaceme of og i diffee codiios (a) camp am a he owes posiio (b) camp am a he midde posiio Fig.9 The ajecoy of og i eaig codiio a diffee posiios 6 Cocsios A copig dyamics mode cosideig paiay compoes as fexibe-body is poposed i his eseach fo evaaig he effec of fexibe-body o fogig maipao. The a case wih diffee codiios is iodced io his mode o simae he ifig ad eaig movemes. The mai cocsios ae as foows: (1) This eseach sggesed ha he copig mode i his pape is effecive ad he ime of cacaio is sho. Wha s moe, fexibe-body, paicay hydaic cyide, have obvios effec o he moveme of og i he fis haf of ifig pocess. Aohe impoa aspec, he highe he speed of ifig cyide, he geae he effec of fexibe-body.wih he eaig pocess, he fexibebody has a iceasig ifece o he ajecoy of og, whie he eo of dispacme is js isigifica. () I ode o obai a good coo saegy fo maipao i ifig codiio, i is easoabe ha hydaic cyides shod wo a a owe speed, especiay i he fis haf of ifig pocess ad he secod haf of eaig pocess idividay. So, his appoach povides a mehod o se dow coo paamees ad desig maipao mechaism. Wih Fhe aaysis, he dyamics mode ca iodce ohe ifeia facos sch as edda acaio, joi ceaace ad he fexibiiy of ohe compoes. Eve, he dyamics mode ca be se p i spaia coodiae o easodyamics of maipao ca be aayzed fo fogig pocess. Acowedgeme This eseach is sppoed by Naa Sciece Fodaio Pojec of CQ CSTC (Ga No. 011BB0051), Fdamea Reseach Fds fo he Sae Key Laboaoy of Mechaica Tasmissio (Ga No. SKLMT-ZZKT-01MS1) ad Naioa Sciece ad Techoogy Majo Pojec of he Miisy of Sciece ad Techoogy of Chia (Ga No.010ZX ). (c) camp am a he highes posiio Refeeces [1] F. Gao, W. Z. Go, Q. Y. Sog, F. S. D, Ce Deveopme of Heavy-dy Mafacig Eqipme, Joa of Mechaica Egieeig, Vo. 46, No. 19, 010, pp [] Y. Zhao, Z. Q. Li, H. Wag, Maipaio Pefomace Aaysis of Heavy Maipaos, E-ISSN: Isse 3, Vome 8, Jy 013

8 Joa of Mechaica Egieeig, Vo. 46, No. 11, 010, pp [3] H. Ge, F. Gao, Type Desig fo Heavy-payoad Techoogy Vo. 34, 007, pp Fogig Maipaos, Chiese Joa of [10] Y. D. X, J. T. Yao, Y. S. Zhao, Kiemaic Mechaica Egieeig, Vo. 5, No., 01, pp [4] W.R. Wag, K. Zhao, Z.Q. Li, H. Wag, Aaysis of a Typica DDS Fogig Maipao, Joa of Mechaica Egieeig, Vo. 48, No. 3, 01, pp Evaaig ieacios bewee he heavy [11] Y. P. Re, Q. K. Ha, T. X. Zhag, B. C. fogig pocess ad he assisig maipao We, Dyamic Simaio of Fogig combiig FEM simaio ad iemaics Maipao Based o Via Pooypig, aaysis, Ieaioa Joa Advaced Joa of Nohease Uivesiy(R Sciece Mafacig Techoogy, Vo. 48, 010, pp. Ediio), Vo. 31, No. 8, 010, pp [1] B. Kag, J. K. Mis, Dyamic Modeig [5] C. Ya, F. Gao, W. Go, Coodiaed iemaic modeig fo moio paig of heavy-dy ad Vibaio Coo of High Speed Paa Paae Maipao[C]// Poceedigs of 001 maipaos i a iegaed ope-die fogig IEEE/RSJ Ieaioa Cofeece o cee, Joa of Egieeig Maface, Vo. 3, No. 10, 009, pp Ieige Robos ad Sysems, Vo. 3, 001, pp [6] G. Li, D.S. Li, Dyamic Behavio of he [13] J. F. H, X. M. Zhag, Dyamic modeig Fogig Maipao de Lage Ampide Compiace Moio, Joa of Mechaica ad aaysis of a igid-fexibe paa paae maipao[c]// Poceedigs of 009 IEEE Egieeig, Vo. 46, No. 11, 010, pp Ieaioa Cofeece o Ieige [7] K. Zhao, H. Wag, G. L. Che, Z. Q. Li, Y. B. He, Compiace Pocess Aaysis fo Fogig Compig ad Ieige Sysems (ICIS009) Vo. 1, 009, pp Maipao.Joa of Mechaica Egieeig, [14] W. J Wag, Y. Q. Y, Dyamic Aaysis of Vo. 46, No. 4, 010, pp Compia Mechaisms Based o Fiie [8] P. J. Paih, S. S. Lam, Sovig he fowad Eeme Mehod, Joa of Mechaica iemaics pobem i paae maipaos Egieeig, Vo. 46, No. 9, 010, pp sig a ieaive aificia ea ewo [15] K. J. L, J. P. Shi, X. L. Gao, Da Bocho, saegy, Ieaioa Joa Advaced Easic-dyamics of Paa Fexibe Paae Mafacig Techoogy, Vo. 40, 009, pp Mechaism, Joa of agica machiey, Vo. 41, No. 6, 010, pp [9] J. W, J. S. Wag, T. M. Li, L. P. Wag, [16] Q. G. Fag, Desig ad Sdy of Liqid Dyamic aaysis of he -DOF paa paae maipao of a heavy dy hybid machie oo, Ieaioa Joa Advaced Mafacig Impedace ad Capaciace i Expeime of Swich Vave Fow Chaaceisic, Machie Too & Hydaics, No. 10, 004, pp Appedix I Eq. (8), m Ⅰ ad m Ⅱ aehe mass maixwhie Ⅰ ad Ⅱ aehe siffess maix fo eeme dyamics eqaios (Eq. (6) ad Eq. (7)), hose maix is comped wih he foowig eqaios: m Ⅰ m IG = E-ISSN: Isse 3, Vome 8, Jy 013

9 m Ⅱ m = Ⅰ = ( EA) ( EA) Ⅱ = Whee, m IG ad ae he mass ad egh of azy am, especivey; E, A ad I deoe easic mods, secio aea ad ieia mome of membe, emaiig he same. E-ISSN: Isse 3, Vome 8, Jy 013