OPTIMIZED BENDING SEQUENCES OF SHEET METAL BENDING BY ROBOT
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1 OPTIMIZED BENDING SEQUENCES OF SHEET METAL BENDING BY ROBOT Shigeru AOMURA an Atsushi KOGUCHI Grauate School o Mechanical Engineering Tokyo Metropolitan University Tokyo, Japan ABSTRACT: In the present stuy, a metho is propose which generates bening sequences o a sheet metal part hanle by a robot. I parts are hanle by a robot, the best grasping positions or each bening an the number o repositions must be inicate in avance. Using the propose metho, easible bening sequences with grasping positions are obtaine an the sequences are sorte in orer o the number o repositions. In generating the sequences, several important eatures or the sheet metal bening are consiere by iviing them into channels, which is one o the base eatures. The error accumulate uring bening operation is calculate or each sequence, an set-up positions can be selecte so as to satisy the preerential tolerance. The propose metho assists the sheet metal process planner by allowing him/her to plan in avance the best bening sequences an to conirm i the robot can perorm the hanling operation. A computer simulation was written base on the propose metho, an illustrative examples an results o various simulation moels are also given. INTRODUCTION In the sheet metal inustry, skille operators perorm bening o sheet metal parts. In orer to carry out the bening operations, a sheet o metal is place on a ie up against a backgage to locate the part precisely, as shown in Fig.1. The machine is then commane to close the gap between the punch an ie. This operation is repeate skillully within the constraine environment o the bening machine. However, skille human operators have been graually replace by robots because o the cost eectiveness o robots an the ecreasing number o skille human operators in the recent labor market. I hanling operations are also replace by robot, the best grasping positions or each ben an exact reposition timing o a robot gripper must be etermine in avance as well as the bening sequence an tools. Consequently, process planning will become more complicate an more iicult since grasping an reposition o a robot creates many aitional constraints when planning the bening process. I generation o bening sequences coul be automate, process planning woul be aster, more eicient an more consistent. Homan et al. [1] presente an algorithmic approach to evaluate bens an to in easible sequences using a computer. Fukua [2] propose motion planning o robot hanling o lexible materials. Stamp an Earl [3] irecte trens in the sheet metal inustry towars the increase use o automation an escribe an experimental cell linking a robot manipulator with a press brake. Zussman an Horsch [4] propose a motion planning approach or robot-assiste multiple-bent parts base on C-space an a potential iel. Wang an Bourne [5,6] propose the automatic process planning system. The eatures o Wang an Bounene s research, have been well investigate, an their research mentions the prouction o plans with near-minimum manuacturing costs. Vin et al. 7, 8 evelope a sheet-metal CAPP system
2 Gripper or reposition Work Hanling robot Fig.1 Press brake with a hanling robot an bening by press brake calle PART-S, which integrates cutting, nesting, bening an weling processes. Streppel et al. [9] showe the ambiguity o conventional tolerances an presente a metho which replaces conventional tolerances with geometrical tolerances. Aomura et al. [10] propose a metho which generates easible bening sequences o a sheet metal part hanle by a robot, an iscusse the etermination o the best grasping positions an repositions. The present stuy investigates the problem o computer aie generation o the bening sequences o sheet metal parts hanle by a robot. In the present stuy, a sheet metal connectivity graph is use to solve the problem o constraints or the bening sequence. The bening sequences, which contain some geometrical bening eatures, are etermine on the basis o a channel eature. As the etermination o bening sequences is a permutation problem, the number o possible bening sequences is generally large, even or only a moerately complex part. Enumerating an evaluating most or all possible sequences is not practical an sometimes impossible. In this metho the best grasping position is etermine irst an, or each grasping position, benable eges are searche. Next, the best grasping position or repositioning is etermine an the number o repositions is preicte. In this process as the preceence constraints o hanling by a robot han can be applie, trivial an uneasible sequences are remove at an early stage. This can reuce the search space rastically an the easible bening sequences can be obtaine. This paper is structure as ollows. In Section 2 the important einitions use in this paper are given. Section 3 escribes the sheet metal connectivity graph use to generate a bening sequence, in particular, the eatures an corresponing constraints are escribe in etail. Section 4 escribes a metho or calculating the errors generate uring bening. Section 5 gives etaile algorithms or generating bening sequences. In Section 6 illustrate examples are given, problems encountere when generating bening sequences are iscusse an inally, concluing remarks are given in Section 7. SHEET METAL PART AND CAD MODEL Moel an einition A inal shape an the lat pattern o a sheet metal part with multiple-bens is shown in Fig.2. The input at the process planning stage is the geometry o the part, an the inormation which inicates the bening lines is given by CAD ata o inexe eges. In the paper, the eges ( e i : i = 1,2, L, n) which make up the lat pattern moel are ivie into either bounary eges (represente by soli lines) an bening eges (broken lines), as shown in Fig.2. A grasping position o a robot gripper is represente on
3 one o the bounary eges in Fig.2(b). e3 2 e11 e e6 e7 e8 e9 e e12 e13e14 e15 e16 e2 e5 13 e1 e17 14 Fig.2 (a) Fig.2(b) Fig.2 Final shape an lat pattern o 13-ben sheet metal part An ege graspe by a gripper is eine as a grasping ege(fig.2(b)). A lat pattern can be separate into small regions with a minimum loop by cutting the bening eges These regions are eine as bening aces ( i : i = 1,2, L, m). The bening ace graspe by a gripper is eine as a grasping ace. The positive ben angles represent bent-up operations, an the negative ben angles, bent-own operations. The sheet metal parts consiere in this research o not have internal tabs, an bening eges are perpenicular or parallel with each other. Grasping plane an gripper The present stuy, a ive-axis robot is use to hol an position the part. The robot gripper is shown in Fig.3. The gripper is capable o grasping across a bent lange which is shorter than the knuckle height. h Fig.3 Gripper an graspe sheet metal part CONSTRAINTS FOR BENDING AND REPOSITIONING In this section, the constraints or the bening process in terms o robot hanling an a metho o generating bening sequences are escribe. Collision avoiance between tool an gripper The clearance l c between a tool an a robot gripper is require in orer to avoi collision in bening, an epth l g is neee in orer to grasp a parts as shown in Fig.4. The istance between a bening ege an a grasping position l must satisy the ollowing inequality. l lc + lg Repositioning is necessary whenever the gripper grasps across unbent bening eges or when no aequate clearance exists between the gripper an the bening machine. lg lc l Fig.4 Clearance between gripper an tool
4 Sheet metal connectivity graph A part geometry has a topological relationship between its bening eges an aces, an the bening eges an aces are connecte to each other in the part s structure. The successive eges an aces to be bent to a grasping position can be expresse by a sheet metal connectivity graph. In aition, the topological istance between a bening ege an a grasping ace can also be eine. In Fig.5, a sheet metal lat pattern graspe at a ace 1 an the corresponing sheet metal connectivity graph are shown. In the connectivity graph, noes represent aces an links represent eges. The root noe always represents a grasping ace. The topological istance between a bening ege an a grasping ace is etermine as ollows. By starting rom the root noe an moving ownwar until the link corresponing to the bening ege e i, a set o consecutive bening eges is obtaine. The set o consecutive eges ( e i ) = [ e i, e j, L] is eine as the topological istance between a bening ege an the grasping ace. I ( e j ) is a subset o ( e i ), or two bening eges e i an e j, the topological istance o e is eine as being arther out than e. i j 1 e 10 e 12 Robot gripper e 9 2 e e e 5 e e 9 11 e e 1 6 e 7 e e 12 e13 e e e16 e 11 2 e 8 8 e e 14 7 e 15 9 e 6 e e 5 e Fig.5 Graspe sheet metal part an its connectivity graph Grasping an reposition The robot gripper hols a part an then the robot re-grasps the part on the same/other ace in the grasping plane. When a robot re-grasps the part, unbent bening eges must not move out o the grasping plane. Consequently, i the bening ege has an unbent ege that is arther topologically, an i the unbent ege cannot be bent without repositioning, this bening ege shoul not be bent, an repositioning is necessary. Bening sequences an eatures Outsie an insie bens are eine relative to the current grasping position. Usually outsie bens shoul be bent irst to avoi intererence between tools an the part, or sel-intererence, that is, with the part itsel. Although in the propose system the "outsie bens irst" rule is applie as a general rule, some eatures o not ollow the rule, an a speciic sequence is allocate or each eature. As the bening sequences or these eatures are etermine or hanling by a human operator, these speciie sequences require repositioning in robot bening, with the exception o a channel eature an a hat eature. A channel, a hat an another common bening patterns are shown in Fig.6. The most simple eature channel, which oes not require repositioning, is use in orer to solve this problem. A channel is a special eature or tool selection an bening sequence etermination, an oes not require repositioning or its bens to be mae. e e 3 3 e e 3 3 e e e e e 4 1 (a) (b) (c) Fig.6 Features o sheet metal bening; (a)channel, (b)hat,(c)bening pattern issolve into channels e 5 e 1 e 2 e 1 1
5 The metho or extracting a channel is explaine as ollows. First, a 4-noe sub-graph o the sheet metal connectivity graph is mae by starting at the root noe an taking the next our noes ownwar. This operation is repeate, incrementing the starting noe by one until the 4th noe reaches the lea noe. Next, the obtaine sub-graph is matche with the bening pattern o a channel by relating the ben angles. The possible patterns or channels by three ben angles are (,, ) or (,, ). I two or more channels are recognize in the operation mentione above, the insie channel is bent irst. As the channel has a particular bening sequence orer that violates the "outsie bens irst" rule, the orering rule o a channel takes preceence. The easible bening sequence o a channel is ( e 2, e1, e3), as shown in Fig.6(a). I an other ege is to be urther outsie than the eges o the channel, this ege is bent beore the last ege o the channel. This rule can also be applie when etermining the bening sequence o other eatures. In the case o a hat eature (Fig.6(b)), the sub-graph [ 1, 2, 3, 4 ] o the sheet metal connectivity graph is recognize as a channel. Although the sequence o the channel is ( e 2, e1, e3), the ourth ege e 4 shoul be bent beore e 3. Consequently, the sequence ( e 2, e1, e4, e3) is given or a hat. This metho can be evelope into more complex sequences. Sub-graphs [ 1, 2, 3, 4 ] an [ 3, 4, 5, 6 ] are recognize as a channel as shown in Fig.6(c). As the insie channel shoul be bent irst, the irst two eges o the insie channel e 2 an e 1 are bent irst. Then, the irst two eges o the secon channel, e 4 an e 3, are bent. Finally, e 6 an e 5 are bent accoring to the outsie bens irst rule. Finally, the easible sequence e, e, e, e, e, ) is obtaine. ( e5 TOLERANCES IN SHEET METAL PRODUCTS Tolerance prescriptions eine on a rawing must be taken into account in process planning an in manuacturing. A methoology to eal with errors generate uring the bening operation is iscusse in this section. Possible errors uring the bening operation may be groupe into the ollowing three ierent types: - positioning error. - error in angle ormation. - error in length o the bent section. The generation o bening sequences inclues the selection o a set-up position against the inger stop o the press brake. The set-up positions irectly inluences the accuracy o proucts since new errors is generate in each bening set-up. The selection o the set-up position in robot hanling is much more important than in human hanling because sheet metal bening operations involve placing sheet metal on a ie up against a backgage to locate the part precisely, an a robot cannot touch the inger stop as elicately as a human worker can. In robot hanling, a backgage is esigne to move in orer to absorb the shock when a robot touches the backgage with a sheet metal part. The error cause by the small movement o the backgage is estimate as ±0.1 in avance. In this paper the most serious error in robot bening, the positioning error which epens on the set-up position on a inger stop, in the present stuy, this is taken into account. 0.1mm c Finger stop c a b 0.2mm a b 0.3mm 0.1mm (a) (b) Fig.7 Set-up positions against a inger stop an error positioning
6 In Fig.7, the possible set-up positions an ierent errors or a bening are shown. As the positioning error in each bening is accumulative an will, in general, not compensate each other, total error is ±0.3 in both cases. In the set-up o Fig.7(a) the error between a an is guarantee to be within ±0.1 but the error between an may become ±0.3. In Fig.7(b), the error between a an b is guarantee to be within 0.1, but the error between a an may become ±0.3. The errors converge between a an b in case Fig.7 (a), whereas the errors are istribute in case Fig.7 (b). The accumulate error in a bening operation is calculate with the ai o error evaluation graphs, as shown in Fig.8. In this graph, ajacent noes are the bening ege an the ege touching the inger stop. A parent noe is the touching ege an a chil noe is the bening ege. A new noe is ae to the error evaluation graph or every set-up in the bening process, an a new graph is generate or every grasping position ater repositioning. The accumulate error between two eges is calculate using the epth between two noes correspon to each ege. In the example shown in Fig.8, ege 5 is bent by setting ege 1 at the inger stop, an then ege 6 is bent by setting ege 5 to the inger stop. Ater repositioning, 8 is bent by setting 3, an then 7 is bent by setting 8. Using each tolerance graph, the accumulate error ater bens between 1 an 6 is calculate as ±0.2 ater bens an the error ater bens between 3 an 7 is ±0.2. I the imension is relate by two graphs, the total error is calculate by aing the errors obtaine rom each graph together. In Fig.8, the error between 6 an 7 is ±0.4. I a set-up cannot be oun or the bening sequence which satisies the prescribe tolerances, this sequence is remove. I all the caniate sequences are remove, a longer measuring time which yiels a smaller error or each bening is taken as a last resort, however, total manuacturing time will be longer Fig.8 Flat pattern an error evaluation on graphs GENERATION OF BENDING SEQUENCES Taking all these constraints into account, the proceure or generating the bening sequences is as ollows: - the initial grasping position is etermine on a grasping ege in a lat pattern. - benable eges in the previously obtaine grasping position are searche. I any other eges exist that cannot be bent in the current grasping position, repositioning is necessary. - the grasping position or the reposition is searche. This operation is repeate until no eges that require bening remain. The low iagram or generating bening sequences is shown in Fig.9. Start Search or caniate grasping positions 2.Search or benable eges or one o the grasping positions More eges to be bent? Yes No 3.Re-grasping Fig.9 Flow iagram or generating bening sequences En
7 Search or the caniate grasping eges an grasping positions First the caniate grasping eges are searche an the grasping position is etermine or each grasping ege. Normal to the bounary eges are rawn at the center o gravity o the lat pattern. The bounary ege which crosses the normal becomes a caniate grasping ege, an the crossing point becomes the caniate grasping position. Next, lines parallel to each bening ege (istance rom the bening ege ± l ) are rawn an the points where these parallel lines an the caniate grasping eges cross are ae to the caniate grasping positions. In orer to avoi collision between the gripper an a tool, The robot gripper cannot grasp the part beyon these bounary grasping positions. Search or the benable eges or each bening ege The nearest grasping position to the center o gravity o the lat pattern is selecte rom the previously obtaine caniate grasping positions to be the initial grasping position. In general, the election o the sheet metal ecreases as the istance rom the center o gravity to the grasping position. Consequently, the sequences with relatively smaller election take preceence, an so the ollowing rule is applie the nearest grasping position to the center o gravity o the lat pattern is taken irst. Once a grasping position is selecte, the benable eges to the grasping position are searche. I an ege has the length l, as escribe in Section 3.1, an satisies the topological conition o reposition explaine in Section 3.2, then this ege is recognize as a benable ege or the current grasping position. Search or grasping position or reposition I any bening eges exists which cannot be bent in the current grasping position, repositioning is necessary an a new grasping position or the repositioning must be searche. When searching or the new grasping position, the rule the nearest grasping position to the center o gravity o the lat pattern is taken irst is applie. In this stage, the eges which have been bent become the new bounary eges by removing aces which have been move out o the grasping plane by bening. The lat pattern is moiie by removing the bent aces. The operation is repeate by moiying the lat pattern every time repositioning is require. When no bening eges are oun, the search operation or one bening sequence is inishe an one sequence is obtaine. I bening eges which cannot be bent still remain in a bining sequence, the sequence is remove. Once a sequence is obtaine the next sequence is searche starting rom another grasping position out o the previously obtaine caniate grasping positions an all easible sequences are searche. The sequences obtaine are sorte in orer o the number o repositions require. COMPUTER SIMULATION AND DISCUSSION A computer simulation has been perorme. In this section, the results o the computer simulation an problems encountere when generating bening sequences are iscusse. Simulation moels In the present stuy, computer simulation was perorme or 106 sheet metal parts, which are actually use in a sheet metal manuacturing company. Nine moels having internal tabs but no vertical or perpenicular bening eges were eliminate rom the stuy. Each o the remaining 97 sheet metal parts Number o moels (1)Completely agree with the sequence by human (2)Partly agree (3)Do not agree total 97moels Number o bening eges Fig.10 Relation between the number o bening eges an agreement ratio
8 have a robot hanling bening sequence esigne by a human esigner. The sequences obtaine by computer simulation were veriie by comparison with those o a human expert esigner. The simulation results o the 97 sheet metal parts were categorize into the ollowing three groups by calculating the agreement ratio with the sequence esigne by the human expert; (1)the sequences agree completely (53 moels), (2)goo agreement was obtaine or the sequences an grasping positions but the repositioning timing is slightly ierent, (27 moels), (3)practical an easible sequences were obtaine but i not agree with that o the human expert, (14 moels). The relation between the number o bening eges an the agreement ratio is shown in Fig.10. No correlation can be observe between the number o bening eges an the agreement ratio. Computer simulation an iscussion The inal shape, the lat pattern an the table o bening sequences obtaine or a 6-ben sheet metal part are shown in Fig.11(a). In the sequences table, the bening sequences obtaine are sorte in orer o the number o repositions. The inex o the sequence number is written in the irst column. The inex h enotes the sequence obtaine by human expert. The next column labele G.P., represent the initial grasping ege, an the columns labele Rpo.1, Rpo.2, an Rpo.3, show the re-grasping ege ater irst reposition, secon reposition an thir reposition, the columns labele B.L. the benable eges to the grasping ege are written. The benable eges connecte with mean that the bening orer shoul not be change, whereas those ivie by, mean the bening orer is exchangeable. In case o the sequence perormance by a human or example, benable eges corresponing to the initial grasping ege 0 are 20, 21, In this case, the bening orer o 23 an 22 shoul not be change, but 20, an 21, (23-22) are exchangeable with each other. One sequence is represente in a line with the sequence number, an initial grasping ege, eges to be bent, a grasping ege or repositions, eges to be bent, an so on. In the table, the sequences are sorte in ecreasing orer in terms o the number o repositions. For sequences with the same number o repositions, the sequence, that has the nearest initial grasping ege to the center o gravity comes irst, an the election is comparatively small. The relation between the istance rom grasping position to the center o gravity an part election cannot be compare simply because the stiness an election change not only locally, but also globally, as well as with each bening uring the bening process. However, in the selection o grasping positions in the early stage o the bening process, the initial grasping position above all is important because, in the bening process, the stiness o a part increases an the election ecreases as more langes are bent. In the irst bening sequence in Fig.11(a), the initial grasping ege is 0 an the corresponing benable eges are 20, 21, Ater bening 20, 21, 23-22, robot re-grasps, an eges 22, 18 an 19 are bent. In this simulation moel, the sequence obtaine irst agree completely with the sequence esign by a human expert. Figure 11(b) shows the orthogonal rawing an the accumulate positioning errors. In this case, the general tolerance is 0.4 an important imensions are 4, 19.5±0.2, an 9, 32.5±0.2. In this simulation moel, just one result o error calculation or all sequences was obtaine an prescribe tolerances are satisie or all sequences. The error in the imensions 1 an 6 in particular is high, an the accuracy is not guarantee. Figure12 shows a sheet metal part or which the obtaine sequence i not agree with the sequence esigne by a human expert. Although this sheet metal part has very ew bening eges, a sequence that completely agree with that esigne by a human expert coul not be obtaine. In the bening sequence esigne by a human, the initial grasping eges 0 an 15 is bent. Then, although 13 an 14 can be bent, they are let unbent intentionally, because i either 13 or 14 is bent, the ace surroune by 4, 14, 8 an 15 moves out o the grasping plane, an 15 cannot be the uture grasping ege. Thereore, ater bening 15, repositione an re-grasps 15 an ben 13,14 an 12. However, in computer simulation, since 13, 14 an 15 are bent to the initial grasping ege 0, ater re-grasping 13, 12 cannot be bent by inaequate clearance between a gripper an a tool. Consequently, in computer simulation, the initial grasping ege 6 is selecte instea o 0, an 13, 14 an 12 are bent an re-grasps 14, 15 is bent inally. In orer to obtain the sequence which completely agrees with that esigne by a human, the grasping position is repositione so that to all obtaine sequences must be reevaluate an the sequences must be
9 calculate again ater the evaluating the result. This has serious implications on the robustness o the whole system an makes the planning process more complicate an iicult No G.P B.L Rpo1 B.L Rpo2 B.L Rpo3 B.L h ,21, ,20, , , , , (a) Dimension Error (b) Fig.11 Bening o a sheet metal part with 6 bens; (a)inal shape, lat pattern, bening sequences table, an orthogonal rawing an (b)error table No. G.P B.L Rpo1 B.L h Figure 12. sheet metal part or which the sequence oes not agree with the sequence esigne by human expert. (1), 7-ben (2), 7-ben (2), 6-ben (2), 22-ben (1), 6-ben (1), 4-ben (1), 8-ben (3), 5-ben Figure 13. Veriie example categorize into three groups by agreement ratio
10 In computer simulation, the easible an seemingly to be rather goo sequences can be searche even or the moels which are categorize into groups (2) or (3). In Fig.13, a number o veriie examples taken rom the 97 simulation moels are shown together with the group number an the number o bening eges. The computing time require is within one minute or all 97 moels, an or all 97 simulation moels, easible an practical sequences were obtaine. CONCLUSION In this paper, the metho which generates bening sequences o sheet metal parts hanle by a robot was propose. A sheet metal connectivity graph is introuce to solve the problem o constraints or bening sequence. In etermining bening sequences, some geometrical bening eatures are issolve into channel eatures an then use. In robot bening, the best grasping position or each ben an exact timing o repositioning o a robot gripper must be inicate in avance. The grasping position an repositioning act as constraints, but they can also be use to reuce the search space rastically in accorance with hanling rules. The aspect o grasping an repositioning can be use as one o the riving orces to obtain easible bening sequences eiciently. The obtaine sequences were sorte in orer o election size. The total error accumulate in bening is calculate or each sequence, an the easibility with respect to accuracy aspect is veriie. This metho has been applie or many sheet metal examples an its eectiveness is veriie. REFERENCES 1. Homann, M., Geissler, U., an Geiger, M., Computer-aie generation o bening sequences or ie-bening machines, Journal o Materials Processing Technology, Vol.30, 1992, Fukua, T., Trajectory control o lexible boar using neural network, IFToMM-jc, International Symposium on Theory o Machines an Mechanisms, Stamp, R. J., an Earl, C. F., Prouction o Sheet Metal Components by an Automatically Planne Robot Assiste Press Brake, Proceeings o the International SheMet 92 Conerence, Birmingham, 1992, Zussman, E., an Horsch, T., A planning approach or robot-assiste multiple-bent proile hanling, Robotics & Computer-Integrate Manuacturing, Vol.11, No.1, 1994, Wang, C.H., an Bourne, D. A., Design an manuacturing o Sheet-metal parts: Using eatures to ai process planning an resolve manuacturability problems, Robotics & Computer-Integrate Manuacturing, Vol.13, No.3, 1997, Wang, C.H., an Bourne, D. A., Carnegie Melon University RI Technical Report 97-35, e Vin, L.J., e Vries, J., Streppel, A.H., Klaassen. E.J.W., an Kals, H.J.J., The Generation o Bening Sequences in a CAPP System or Sheet-metal Components, Journal o Materials Processing Technology, Vol.42, 1994, e Vin, L.J., Streppel, A.H., an Kals, H.J.J., Tolerancing an Sheet Bening in Small Batch Part Manuacturing, Annals o the CIRP, Singapore Vol.43, No.1, 1994, Streppel, A.H., Lutters, D.H., an Kals, J.J., Process Planning in Small Batch Sheet Metal Part Manuacturing, In proceeings o the Secon Worl Congress on Intelligent Manuacturing Process & Systems, Aomura, S., Koguchi, A., an Niwa, Y., Automate an optimize process planning in sheet metal bening by a robot, International Conerence on Inustrial Tools ICIT 99, 1999,
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