Industrial Robots used in Forges Applications

Transcription

1 Industral Robots used n Forges Applcatons Lvu Cuptu, Ivanescu Andre Nck 2 and Sorn Brotac 3 Department of Mechancal Engneerng and Mechatroncs, Poltehnca Unversty of Bucharest, Romana E-mal: lvu.cuptu@omtr.pub.ro URL: 2 Department of Automatcs and Computers, Poltehnca Unversty of Bucharest, Romana, 3 S-Ind Process Control S.R.L., Bucharest, Romana, Abstract. Industral robots are used especally n sectors where the human body s n danger or s workng n extreme condtons. One of these sectors s the forges sector where the manpulatng objects are hot, and the vbratons and nose are bg. The problem of manpulaton the hot parts mples the choosng of the rght grpper mechansm n order to obtan the best coolng of t and of the robot tself. The coolng of grpper and robot s realzed n the movement phase when no hot payload s present. So, the trajectory of movement s mportant and also the optmum poston of robot wth respect to the applcaton postons. The proposed paper s dealng wth the subject of movng the base of robot wth respect to the applcaton ponts so that an objectve functon representng the accumulated heat durng a cycle to be mnm. Keywords. Industral Robot, Forge, Optmum Poston. Introducton Industral robots are used especally n sectors where the human body s n danger or s workng n extreme condtons. One of these sectors s the forges sector where the manpulatng objects are hot, and the vbratons and nose are bg. The problem of manpulaton the hot parts mples frstly the choosng of the rght grpper mechansm n order to obtan the best coolng of t and of the robot tself. In papers (Smonescu and Cuptu, 24) and (Smonescu et al., 28) grppers wth 2 DOF are presented and could be used as well. But the poston of robot wth respect to the applcaton, by taken nto consderaton the accumulated heat from work pece durng the manpulaton of t as an objectve functon, t s also a very mportant problem. An emprc soluton of determnng the poston of robot base by computng only the three coordnates of the orgn of the Cartesan coordnate system assgned to the robot base s gven n (Kovacs and Cojocaru, 982.). Ths emprc soluton s not taken nto consderaton the way of movng of robot between the applcaton ponts but s taken nto consderaton the weght of object (tool) that the robot s movng between these. The proposed soluton s not demonstrated by any mechancal and mathematcal reasons. In (Tan and Collns, 25) an optmzaton problem of placement of a smple two-lnk planar manpulator by usng a genetc algorthm s presented. Also n paper (Mts et al., 28) a hybrd genetc algorthm s used n order to determne the optmum locaton of the base of robot wth respect to mposed dscrete postons of end-effector. The locaton of robot base wth respect to the applcaton s chosen so that all the nterest pont of applcaton to be stuated n the workng space of robot. An optmzaton of ths locaton by taken nto consderaton the mnmum tme of movement was presented n papers (Feddema, 996) and (Cuptu and Smonescu, 27). In paper (Cuptu et al., 28) an optmum synthess of moton law together wth mnmum tme of moton was performed. In paper (Cuptu and Ivanescu, 2) the problem of optmal locaton of an ndustral robot used n a forge applcaton were formulated. The mechancal structure of the ndustral robot chosen by the manufacturers (for examples: Renault from France and Rahm from Italy), that are usng t n

2 forges sector, s of artculate knd wth 6 DOF. Sometme the openng area of forge makes dffcult the nsertng of hot part nsde the forge even wth 6 DOF. But an ndustral robot wth a mechancal structure of cylndrcal type wth at least 5 DOF may solve the problem too. Anyway the grpper used n such an applcaton should have a specal shape wth long fngers n order to dsspate the heat accumulated from manpulatng part. 2. Forgng Manufacturng Process Usually the forged peces are nserted from a bunker nto a furnace n order to be heated (Fg. ). The hot part comes out from a medum frequency furnace wth a random orentaton or that can be fxed by specal mechansms, dependng of the shape of part. But because of hgh temperature of part the ndvdualzaton and orentaton of part s dffcult to be made wth a good accuracy. So, a vson system to recognze the poston of part and to communcate wth the robot controller (Fg. 2) n order to make the poston and orentaton correctons of pckng confguraton, s necessary. (Cuptu et al., 29). Fg. 2 Communcaton scheme From delverng port of furnace the part s nserted by lateral nto the forge and left down nsde the forgng mold. The nsertng wndow s relatvely small and requres a long lnk 6 (Fg. 3) or long grpper fngers. Safe P 3 P 2 P P 4 P 5 Sometmes another task of sprayng the parts of forge s done by the same robot wth the ad of a specal dose fxed to the robot arm or to the grpper. Anyway, the dfferent planes n whch the pck-andplace are done, and the small wndow of forge where the robot arm must be nserted, mpose a 6 DOF spatal mechansm for robot mechansm. Fg. 3 Artculate ndustral robot wth 6 DOF Fg. Applcaton scheme An ndustral robot wth a mechancal structure of cylndrcal type wth at least 5 DOF (Fg. 4) may solve the problem too, but the translatoral jonts are pretentously even n case of cold manufacturng processes. Actuatng system s electrc one for robot and pneumatc one for ts grpper. The end-effector could be cooled by the ad of a fan or by pressure ar n some stuatons when the temperature of manpulatng part s hgh and the heat cannot be elmnated by the movement of the robot durng one cycle. INDUSTRIAL ROBOTS USED IN FORGES APPLICATIONS October 2 268/269

3 A = a cosθ a snθ s cosθ snθ snθ cosθ cos sn cos snθ cosθ sn cos sn Fg. 4 Cylndrcal ndustral robot wth 5 DOF The same nsertng mode s used to put the work pece nto the burrng forge (Fg. ). That can be done by another robot or by a human operator, but the work pece should be cold enough to not be deformed when the burrng s done. So, a coolng area s nterposed between man forge and burrng forge, by usng some fans. The transfer from man forge to the conveyer can be done by frst robot or by the forge mechansm tself. Fnally the forged pece s drected to another bunker and transported to another manufacturng cell. By choosng the axes systems n a specal manner, the number of unknown parameters between 2 Cartesan coordnates systems chosen anyway on each lnk s reduced from sx to four: a - the length of common perpendcular measured from O axs to O + + axs; s - the dstance between O and O + + axes, measured upon O axs; - angle between O and O + + axes, measured around + axs; θ - angle between O and O + + axes, measured around O axs. For example for a robot mechansm wth an open chan wth 6 moble lnks (Fg. 2), the coordnates transformaton of a pont P j from O axes system attached to the end-effector and the coordnates n base system O could be wrte as follow (Smonescu and Cuptu 27): = A A 2 A 3 A 4 A 5 A 6 7Pj 7Pj 7Pj () 3. Optmsaton Problem In order to formulate the optmzaton problem 2 models must to be known: the mechancal structure model of robot wth mnmum and maxmum acceptable values for each jont ndependent parameter and the forge applcaton gven by: coordnates of postons (confguratons) that the robot must reach, the trajectores and moton laws between these ponts, the temperature of work peces and the weght of them. 3.. Robot Mechansm Model Usual the mechancal structure model of a robot s mplemented n robot controller by usng Denavt- Hartenberg formalsm n order to fnd a transformaton from tool tp to the base of robot. The matrx transformaton of coordnates of a pont P expressed n a O coordnates system to coordnates of the same pont n another O coordnates system s: 3.2. Forge Applcaton Model The model of forge applcaton s smplfed composed only by the 5 ponts P j, j =, 5, that the robot must reach durng the moton, wthout any obstacles defned (excludng the robot tself): P - n front of forge (watng pont); P 2 - upper of the pckng poston; P 3 - pckng poston from the ext of furnace; P 4 - nsde forge; P 5 - extreme poston of elmnatng the pece from forge to the coolng on conveyer. Also the order of reachng these 5 ponts n a complete cycle (8 ntervals of moton: P ->P 2 ->P 3 - >P 2 ->P ->P 4 ->P ->P 5 ->P ) and the motons laws between these are supposed as known. Usual the robot controllers are mplemented wth only few moton laws between 2 postons (confguratons) from workng space: of snusodal shape and of parabolc shape (Inteltek, 23). Transmsson functons gven numercally, and resulted for example from an optmzaton process done off-lne (Cuptu et al., 28), could be used for movng robot to a specfc trajectory. In forge applcatons, where the work peces are hot, the temperatures of them and of the envronment are nfluencng the temperature of robot and the precson of t The heat accumulated by the robot

4 durng a cycle depends by the temperature of work pece T and by the tme when the work pece s manpulated by the robot. From 8 ntervals of motons only n 4 the robot grpper s n contact wth hot pece. Fnally, especally for optmzaton problems that s dealng wth forces and energy or power consumpton, the weghts G jk, j =, 5, k =, 5, of objects moved by robots between applcaton ponts must to be known Optmzaton Problem In order to start the formulaton of optmzaton problem we have to dentfy the unknown parameters. The unknowns of optmzaton problem are the parameters that are defnng the poston and the orentaton of Cartesan coordnates system assgned to the base of robot O wth respect to an nertal Cartesan system assgned to the world of robot (or to the applcaton) denoted by O. These parameters are composed by the 3 Cartesan coordnates of orgn O expressed n Cartesan system O ( O, O, O ) and the 3 ndependent angles that s gvng the orentaton of Cartesan system assgned to the robot base O wth respect to Cartesan system O from the cosnes drectores matrx: = (2) The number of unknown parameters could be reduced by choosng the Cartesan system O n a Denavt-Hartenberg manner. So, by choosng the O axs perpendcular to the O axs (chosen randomly perpendcular to the O axs), only 4 parameters are enough: a, s,, θ. In ths stuaton the coordnates of applcaton ponts are constant wth respect to the Cartesan system O and the coordnates transformaton equaton s: Pj Pj Pj = A (3) The known parameters of problem were formulated n prevous paragraphs as follow: Denavt-Hartenberg parameters: a, s,, θ, = =, 6 ; Cartesan coordnates of applcaton ponts: Pj, Pj, Pj, j =, 5 ; trajectores between these ponts: T jk, j =, 5, k= =, 5, j k; maxmum speed and maxmum acceleraton accepted for each drvng motor of robot jonts: v max, a max, =, 6 and the other parameters of motons laws that are specfyng completely the transmsson functons of second degree; temperature of workng pece: T. weghts G jk, j =, 5, k =, 5, j k. The objectve functon of optmzaton problem s a sum (or ntegral) of mnmzed parameter: 8 O = Q l (4) l= where Q l s the heat accumulated by the robot n each nterval of moton from a cycle. The heat transfer by conducton between two plane surfaces s gven by the followng relaton: Q = χ A t T hot d T cold, (5) where: Q s the heat transfer n tme t; χ s the thermal conductvty of the barrer; A s area of contact surface; T hot and T cold are the temperatures of plane surfaces n contact; d s the thckness of barrer. The process of fndng the optmum set of parameters {a *, s *, *, θ * } s a numercal one where these parameters are changed durng the computaton accordng to a specfc algorthm. At the begnnng of computaton, startng by an ntal set {a (), s (), (), θ () }, a complete verfcaton of applcaton ponts P j, j =, 5 so that to be nto workng space of robot s performed. Ths verfcaton mples the computng of coordnates of all applcaton ponts n O Cartesan system: () () () = A - Pj Pj Pj, j =, 5. (6) By nverse knematcs a set of jont ndependent varables {θ (),j, θ () 2,j,, θ () 6,j } s determned for each pont P j, j =, 5. A pont P j, j =, 5 s n workng space of robot f all ndependent varables values are between mnmum and maxmum acceptable values for each jont: θ mn θ,j θ max, =, 6, j =, 5. (7) Condtons (7) represent the nequalty constrans of optmzaton problem: θ mn θ,j, =, 6, j =, 5, (8) θ,j θ max, =, 6, j =, 5. (9) INDUSTRIAL ROBOTS USED IN FORGES APPLICATIONS October 2 27/27

5 The nequalty constrans (8) and (9) can be transformed n equalty constrans: h k = θ mn θ,j + w 2 k =, =, 6, j =, 5, (8 ) h k+3 = θ,j θ max + w 2 k+3 =, k =, 3, (9 ) by ntroducng the unknown parameters w l, l = =, 6. The Lagrange method for solvng of the mnmzaton problems s based on transformng a gven constraned mnmzaton problem nto an unconstraned mnmzaton problem. Ths operaton s accomplshed by defnng an approprate auxlary functon, n terms of the problem functons, to defne a new objectve functon whose mnma s unconstraned n some doman of nterest. The Lagrange functon has the next form: 6 L = O + l= λ l h l, () where λ l, l =, 6 are Lagrange multplers. The necessary condtons for the mnmzng the Lagrange functon are: L a =, L w l L s =, =, L L =, =, θ L =, l =, 6. () λ l The non-lnear system composed by equatons () wth 24 unknowns s solved wth a proper numercal method. The problem has nfnty of solutons accordng to the ntal soluton. 4. Conclusons The optmum locaton of robot base depends to the robot structure and to the applcaton. Wth same robot but dfferent applcaton postons and condtons results dfferent locatons for robot base. The problem of fndng the optmum locaton of robot base wth respect to the applcaton ponts accordng to an objectve functon s very mportant and could lead to major mprovements (Cuptu and Smonescu, 27), (Mts et al., 28). Sometmes the condtons of applcaton mpose specal adjustments n order to protect the robot. The placng of robot base n an optmum locaton from the very frst begnnng s an essental ntal task especally for large seres productons. The economy of tme or/and energy (money fnally) for each product s decreasng t's prce to almost a quarter (Feddema, 996) but the protecton of ndustral robot parts s much more mportant because wthout robot no producton. A mult-crteral optmsaton by taken nto consderaton the protecton of ndustral robot whch s workng n a hazardous envronment and the economy of tme and energy s maybe the best soluton. 5. References [Cuptu 27] Cuptu, L. and Smonescu, I. 27. Optmal Locaton of Robot Base Wth Respect to the Applcaton Postons, Annals of DAAAM for 27 & Proceedngs of the 8 th Internatonal DAAAM Symposum, ISBN , ISSN , pp. 82, Edtor B. Katalnc, Publshed by DAAAM Internatonal, Venna, Austra, pp [Cuptu 28] Cuptu, L., Smonescu, I. and Ivanescu, A. N. 28. Optmum Synthess of Moton Laws Used By Robot Controllers, , Annals of DAAAM for 28 & Proceedngs of the 9 th Internatonal DAAAM Symposum, ISBN , ISSN , pp. 4, Edtor B. Katalnc, Publshed by DAAAM Internatonal, Venna, Austra 28. [Cuptu 29] Cuptu, L., Brotac, S., Chvescu, S. 29. Optmum Poston of an Industral Robot Used n Forge Applcatons, Proceedngs of the 4 th Internatonal Conference on "Optmzaton of the Robots and Manpulators" OPTIROB 29, Constanta-Mamaa, Romana, May 28 th 3 st, 29. [Cuptu 2] Cuptu, L. and Ivanescu, A. N. 2. Optmal Locaton of an Industral Robot used n Forge Applcatons, , Annals of DAAAM for 2 & Proceedngs of the 2 st Internatonal DAAAM Symposum, ISBN , ISSN , pp 227, Edtor B. Katalnc, Publshed by DAAAM Internatonal, Venna, Austra 2. [Feddem 996] Feddema, J.T Knematcally optmal placement for mnmum tme coordnated moton, In: Proceedngs of the 996 IEEE Internatonal Conference on Robotcs and Automaton, Volume 4, Apr 996, Mnneapols, pp [Inteltek Inc. 23] Inteltek Inc.23. Advanced Control Language for Controller-B, Reference Gude, Verson F2.28, Catalog #85 Rev. A

6 [Kovacs 982] Kovacs, F. and Cojocaru, G Manpulatoare, roboţ ş aplcaţle lor ndustrale, Edtura Facla, Tmşoara, 982. [Mts 28] Mts, S., Bouzaks, K.-D., Sagrs, D. and Mansour, G. 28. Determnaton of optmum robot base locaton consderng dscrete end-effector postons by means of hybrd genetc algorthm, Robotcs and Computer-Integrated Manufacturng, 24 (28) Elsever Scence, pp [Smonescu 24] Smonescu, I. and Cuptu, L. 24. Two Degrees of Freedom Grppers for Industral Robots. Proceedngs of I th Internatonal Conference on the Theory of Machnes and Mechansms, Techncal Unversty of Lberec, Czech Republc, August 3-Sept. 2, 24, ISBN , pp [Smonescu 28] Smonescu, I., Cuptu, L., Ionescu, C. 28. Optmum Desgn of 2-DOF Robot Grppers, Proceedngs of the 3 rd Internatonal Conference on "Optmzaton of the Robots and Manpulators" OPTIROB 28, Predeal, Romana, May 29 th June st, 28, pp [Tan 25] Tan, L. and Collns, C. 25. Optmal placement of a two-lnk planar manpulator usng a genetc algorthm, Robotca Journal, Cambrdge Unversty Press, Issue 2 - Mar 25, Volume 23, pp INDUSTRIAL ROBOTS USED IN FORGES APPLICATIONS October 2 272/273