Modeling the Component Pickup and Placement Sequencing Problem with Nozzle Assignment in a Chip Mounting Machine Hiroaki Konishi, Hidenori Ohta and Mario Nakamori Department of Information and Computer Sciences, Faculty of Engineering Tokyo University of Agriculture and Technology Koganei, Tokyo, Japan Abstract - In the production of electronic circuit boards in industry, electronic components are placed onto the circuit board by component placement machines. The actions of multifunction placement machines are roughly divided into pick-up phase and placing phase. In the past, these two phases were typically optimized independently of each other to be combined, which do not necessarily lead to the overall optimization. Therefore, in this paper, the action of multifunction component placement machines is modeled in a different way than that in the conventional approach, and a method for comprehensive optimization of pick-up phase and placing phase is proposed. The proposed method, which takes into account nozzle allocation, can also be applied to the load balancing of component placement machine production lines. Keywords: component placement machine, line-balancing 1 Introduction Electronic circuit boards are produced through several processes (printing, placing, heat treatment, etc.), among which the process of placing the components onto the circuit boards is the most significant and often becomes the bottleneck. In this process, components are automatically placed onto the circuit boards by machines called component placement machines. Since the circuit board production efficiency is dependent on the performance of the component placement machines, a variety of research has been published on motion optimization and operation of each of the several types of component placement machines already developed. However, a relatively new type of component placement machines called multifunction component placement machines have a large degree of freedom of motion, and only a few researches are reported on optimization algorithms for this type of machines. In the present paper we consider multifunction component placement machines and call hereafter component placement machines in abbreviation. 1.1 Component placement machines At circuit board production sites in industry, production is usually carried out through production lines composed of multiple component placement machines connected in series. More specifically, it is determined in advance which components will be assigned to each component placement machine (machine allocation). When the placing of components allocated to one component placement machine is complete, the circuit board is carried to the next component placement machine by a conveyor. To place all of the components on a circuit board, it is necessary for the circuit board to pass through all component placement machines in the line. A simplified schematic of a component placement machine is shown in Figure 1. The component placement machine has a head which has multiple nozzles for picking up and placing components. Figure1 Component placement machine The component placement machine places components on a circuit board by repeating the following actions: (1) The head moves to a position above the component feeder and the nozzles pick up the required components from the appropriate feed slots; (2) The head moves to the camera which checks whether the components have been picked up correctly; (3) When it has been confirmed that the components have been picked up correctly, the head moves above the circuit board and travels around the board, placing the components in their respective places; (4) When all of the picked-up components have been placed, the head returns to the initial position above the component feeder.
The abovementioned sequence of actions is called a turn. Generally, multiple turns are carried out before all components allocated to one component placement machine have been placed. The required for placing components in a turn is approximately proportional to the travel distance of the head. The head travel distance is shorter if picking-up and placing positions are closer together. In order to optimize the picking up and placing actions, it is important to assign components to turns so that the total sum of travel distance of the head is the minimum. 1.2 Mounting method of component placement machines There are two typical methods of mounting for component placement machines; alternating mounting and separate mounting. In the alternating mounting method, two heads positioned opposite each other alternately place components onto a central circuit board, and while one head is performing a component placing action, the other head performs a component picking-up action. Since placing usually requires more than picking up, the motion of the component placement machine is determined only by the component placing action. In the separate mounting method, on the contrary, only one head places the components onto one circuit board; there are two conveyors, which carry two boards independently on each other. Unlike the alternating mounting method, the component placement machine s motion in the separate mounting method is determined by both the component placing action and the pick-up action. Most component placement machines are equipped with two conveyors, and it is possible to carry out separate mounting using two conveyors as well as alternating mounting using only one conveyor; recently, however, the most common placing method used at circuit board production sites has been shifting from alternating mounting to separate mounting. Figure 2 shows a simplified schematic of each mounting method. one machine refers to one side of a machine that uses the separate mounting method (upper or lower half). 1.3 Problems concerning motion optimization of component placement machines In both the pick-up action and the placing action, the travel distance of the head may vary greatly depending on which components are allocated to which nozzle (nozzle allocation), because the size of the head is not negligible compared to the size of the circuit board and the component feeder. Figure 3 shows how the travel distance of the head when placing components varies by nozzle allocation. (a) (b) Figure3 Difference of travel distance by nozzle allocation Also, to increase the speed of the pick-up action, recent component placement machines are capable of picking up multiple components at the same (gang pick), if the interval of nozzle positions and that of slot positions of the concerning components are the same. For example, with the arrangement of the component feeder shown in Figure 4, it is possible for the two components supplied from slots 5 and 7 to be picked up simultaneously by nozzles B and D, respectively. Gang pick reduces the number of component picking-ups and accelerates the picking-up action. Figure4 Gang pick (a) (b) Figure 2 Separate mounting (a) and alternate mounting (b) The component placement machine shown in Figure 1 is just one side of the component placement machine shown in Figure 2 (i.e., lower half of Figure 2). In the following, Thus, considering the problem of nozzle allocation is very important. In the former research, however, nozzle allocation was not often given sufficient consideration. Yamamoto et al. [3] proposed a method for optimizing the placing action taking the nozzle allocation into account and achieved a reduction in head travel distance of approximately 20% compared to conventional methods. This research, however,
considered the placing action only and neglected the pickup action. When the placing is longer than the pick-up in the alternating mounting method, this approach is adequate. On the contrary, in the separate mounting method, both placing and pick-up are reflected in the circuit board production, and so the assumption of the above approach does not hold. At actual circuit board production sites in industry, when motion optimization of component placement machines under the separate mounting method is performed, nozzle allocation is determined from the point of view of optimization of the picking-up action first and optimization of the placing action is carried out next. The method proposed by Yamamoto et al. can cope with the alternating mounting method, but it cannot sufficiently optimize component placement machines under the separate mounting method. In this paper, we propose first a model for simultaneous optimization of picking-up action and placing action by considering nozzle allocation in one component placement machine under the separate mounting method. At actual sites where component placement machines are in operation, multiple machines are connected to form a production line. Machine allocation, turn allocation, nozzle allocation, component pick-up action, and component placing action should really be optimized in a comprehensive way that also takes into account line balancing. As for line balancing, a method for allocating components by finding placing paths in component placement machines has been proposed, but this method does not consider nozzle allocation or component pick-up action [2]. The model proposed in this paper is basically intended for motion optimization of one machine, but line balancing can be carried out at the same by using a simple extension. 2 Formulation of the problem In this paper, we consider the following two problems. 2.1 Problem of motion optimization of one machine This is the problem of finding turn allocation, nozzle allocation, pick-up order, and placing order for given components, with the aim of carrying out motion optimization of one component placement machine on a production line, where components are already allocated to machines. In this paper, the arrangement of the slots in the component feeder is given, and it is assumed that one type of component is supplied from exactly one feed slot and the same type of component is not placed in multiple slots. Also, in real component placement machines, the type of component that can be picked up and placed may be limited according to the type of nozzle, but, here, it is assumed that all types of components can be picked up and placed by any nozzle. The motion spent on each circuit board by the component placement machine is approximately proportional to the travel distance of the head, and so the head travel distance is used to uate the solution. However, to take into account the number of component pick-ups, the spent for picking up is converted to head travel distance and added to the uation value. Furthermore, because the head is driven by motors operating independently in the x- and y-directions, the head travel distance is defined as the Chebyshev distance. 2.2 Problem of motion optimization of multiple machines and line balancing This is the problem of load balancing between machines on a production line composed of multiple machines. This is an extension of the problem of motion optimization of a single machine. In this problem, it is necessary to find the machine allocation of components as well as turn allocation, nozzle allocation, pick-up order, and placing order for each machine. The amount of spent per circuit board in the production line is the motion of the machine that causes bottlenecking, so the solution is uated by using the head travel distance of the bottleneck machine. In the same way as the problem of motion optimization of one machine, the spent picking up is converted to distance and added to the uation value. 3 The algorithm In our proposed algorithm, component turn allocation is sought in combination with nozzle allocation using a local search technique. Also, these allocations are uated by finding the pick-up and placing paths for each allocation and calculating the respective head travel distance and the number of pick-ups. A flowchart of the proposed algorithm is shown in Figure 5. Figure5 Flowchart of the proposed algorithm
3.1 Method of expression of nozzle allocation 3.1.1 Expression of nozzle allocation for a single machine Individual numbers are assigned to the components, and nozzle allocation is expressed together with component turn allocation by arranging the assigned component numbers, as shown in Figure 6. Component turn allocation is obtained by dividing up the arranged components based on the number of nozzles in the head, starting from the leftmost component. Also, the sequence of component numbers within a turn indicates the nozzle picking them up. Figure 6 shows an example of nozzle allocation in a component placement machine with four nozzles. The character e is inserted instead of a component number when the nozzle does not pick up a component. Figure6 Nozzle allocation in a placement machine 3.1.2 Expression of nozzle allocation for multiple machines and line balancing As in the expression of turn allocation and nozzle allocation in the problem of motion optimization of a single machine, individual numbers are assigned to the components, where nozzle allocation is expressed together with component machine allocation, and turn allocation is performed by arranging the assigned component numbers. Machine allocation consists of several turns. Also, the sequence of component numbers within a turn indicate the nozzle picking them up. Figure 7 shows an example of nozzle allocation in component placement machines with four nozzles. Figure7 Nozzle allocation in component placement machines 3.2 Determination of component picking-up and placing order To uate a solution corresponding to a certain nozzle allocation, the component pick-up order and the component placing order are determined as described below, and the respective head travel distances and number of pickups are calculated. 3.2.1 Determination of the order of component picking-up order When the nozzle allocation is given, the position of the head above the component feeder is settled. It is possible to pick up components in the shortest head travel distance by picking them up in order from the left or right of the head position. Also, the head position during pick-up may overlap for several components and, in this case, the components can be picked up at the same with one up-down motion (gang pick mentioned before). 3.2.2 Determination of component placing order When the nozzle allocation is given, the center of the head above the circuit board when placing each component, as shown in Figure 8, is settled. Here, the shortest path when traveling around the head centers can be regarded as a type of traveling salesman problem (TSP). Therefore, the placing order is determined using the nearest neighbor (NN) method, which is often used as the initial solution to the TSP. The NN method is a typical greedy method, and it generates a solution by repeating the operation of moving from the current point to the nearest point until all points have been visited. Figure8 Location of the center of the head 3.3 Improvement of component placing order After component nozzle allocation has been improved, improvement of the placing path of each turn is carried out. A local search technique based on the first admissible move strategy using a 2-opt neighborhood is used to improve the placing path. A 2-opt neighborhood is a set of solutions generated by swapping two branches on a path, and it is often used to solve problems such as the TSP. 4 Computational experiment A computational experiment was carried out to uate the effectiveness of the proposed method. The experiment environment consisted of an Intel Pentium CPU B940 2.00 GHz with 4.00 GB of memory, and the language used was C. The number of slots in the component feeder was set at 30 and the distance between slots at 10 mm. The positional relationship of the circuit board and the component feeder and camera is set as shown in Figure 9. Also, the number of
nozzles was 16, and these nozzles were arranged on the head as shown in Figure 10. These settings were determined with reference to real component placement machines. The experiment was done for 27 types of circuit boards randomly generated. uation value 25000 24000 23000 22000 21000 20000 19000 18000 17000 16000 15000 14000 proposed pick-up first placing first Figure9 Location of the circuit board and the component feeder and camera a = b = 10mm Figure10 Location of the nozzles on the head 4.1 Comparison with the conventional methods in the case of a single machine An experiment comparing the proposed algorithm and conventional methods was carried out with regard to optimization of the pick-up and placing actions of one machine. As for conventional methods, we tried two types of methods; pick-up first and placing first. In the former (pickup first) method, picking-up action, turn allocation and nozzle allocation are determined before placing, which is determined by NN and 2-opt methods. This method reflects the actual process of optimization in the production of electronic circuit boards in industry. In the latter (placing first) method, the order of placing, turn allocaton and nozzle allocation are fully optimized before picking-up. Although this latter method is rather imaginary and not used in real industry, we conceived it in order to explore the superiority of picking-up first and placing first. Figure 11 shows the relationship between the computation and the uation value for the proposed algorithm and the conventional method (both 2 types) with regard to Data 14. It can be seen that the proposed algorithm converges to a better solution than those by the conventional methods. 13000 0 3000 6000 9000 12000 15000 computing (ms) Figure11 Relationship between the computation and the uation value (Data 14) Table 1 gives the uation values obtained after a sufficient length of using the algorithm of the conventional methods and the uation values obtained after an equivalent length of using the proposed algorithm. The algorithm of the proposed method gives better solutions for all data than those by the algorithms of the conventional method. As for the conventional method with pick-up first, Table 1 shows that the gap increases as the circuit board size increases. This is presumed to be because the cost of the placing action increases in proportion to the circuit board size, and so the proposed method, in which searching progresses while taking account of placing, becomes more advantageous. Table 1 shows also that the gap decreases as the number of component types increases. This is presumed to be because the greater the number of component types, the greater the cost of the pick-up action, and so improvement progresses easily, even in the conventional method. As for the conventional method with placing first, Table 1 shows that the gap decreases as the circuit board size increases. This is presumed to be because the cost of the picking up action becomes more significant than the placing action as the circuit board size increases. Table 2 gives the uation values obtained by the proposed method and the modified version of the proposed method where SA (simulated annealing) is used instead of local search with sufficient length of. Parameters of SA have been adequately by preparatory test. Table 2 shows that local search gives relatively good solution in short of computation, although the uated value itself is rather inferior to SA. In addition, the gap between SA and local search grows as the number of components increases; 3.71% for 64 components, 5.96% for 256 components, 13.98% for 512 components, and so on. This is presumed to be because when the number of components increases, the search space grows wide and LS tends to fall into a local optimal solution.
Data No. Table1 Comparison of conventional procedure and our algorithm chip num Data details pick-up first (A) placement first (B) proposed board variety size of chips (ms) (ms) (mm) (ms) gap A-proposed (%) gap B-proposed (%) 1 64 10 100 3279 3621 3860 3633 2912 3486 11.19 24.56 2 64 10 200 4496 3590 4403 3552 3615 3445 19.60 17.90 3 64 10 300 5739 3585 5038 3571 4789 3482 16.55 4.94 4 64 20 100 3305 3551 4144 3593 3042 3450 7.96 26.59 5 64 20 200 4436 3553 4538 3663 3803 3428 14.27 16.20 6 64 20 300 5368 3538 5289 3584 4594 3454 14.42 13.14 7 64 30 100 3218 3545 4022 3731 3089 3409 4.01 23.20 8 64 30 200 4341 3550 4773 3594 3849 3426 11.33 19.36 9 64 30 300 5428 3578 5352 3596 4857 3416 10.52 9.25 10 256 10 100 13250 15162 15343 15382 11149 13765 15.86 27.33 11 256 10 200 17711 15108 18227 15269 14387 13771 18.77 21.07 12 256 10 300 22936 14906 20221 15191 17507 13750 23.67 13.42 13 256 20 100 12976 15057 16006 15227 11321 13739 12.75 29.27 14 256 20 200 17290 15150 18754 15348 14620 13703 15.44 22.04 15 256 20 300 23071 15077 21562 15198 18597 13783 19.39 13.75 16 256 30 100 12821 14990 16651 15430 11667 13399 9.00 29.93 17 256 30 200 18326 15040 19356 15327 14798 13515 19.25 23.55 18 256 30 300 22594 15250 20998 15172 18050 13414 20.11 14.04 19 512 10 100 25547 33652 31170 34465 22592 28267 11.57 27.52 20 512 10 200 35156 33541 36402 34650 29271 28339 16.74 19.59 21 512 10 300 46162 33597 41730 34815 35168 28471 23.82 15.72 22 512 20 100 25928 33615 32683 34447 23648 28417 8.79 27.64 23 512 20 200 35660 33793 38029 34775 30260 28362 15.14 20.43 24 512 20 300 46414 34120 43257 34792 37356 28401 19.52 13.64 25 512 30 100 26390 34966 33271 34690 24313 27824 7.87 26.92 26 512 30 200 35682 34083 38552 34977 30995 27958 13.14 19.60 27 512 30 300 46360 33938 43797 34731 37784 27672 18.50 13.73 Table2 Comparison of LS and SA LS SA gap Data LS-SA No. (s) (s) (%) 1 2912 3.49 2789 695.05 4.22 2 3615 3.45 3583 633.20 0.89 3 4789 3.48 4646 626.12 2.99 4 3042 3.45 2935 623.42 3.52 5 3803 3.43 3686 681.97 3.08 6 4594 3.45 4348 613.21 5.35 7 3089 3.41 2893 623.50 6.35 8 3849 3.43 3790 757.92 1.53 9 4857 3.42 4590 627.47 5.50 10 11149 13.77 10678 2920.29 4.22 11 14387 13.77 13085 2870.90 9.05 12 17507 13.75 16065 2855.21 8.24 13 11321 13.74 10650 2942.82 5.93 14 14620 13.70 13659 2892.42 6.57 15 18597 13.78 17375 2937.27 6.57 16 11667 13.40 11070 3018.16 5.12 17 14798 13.52 14551 3102.37 1.67 18 18050 13.41 16918 2891.23 6.27 19 22592 28.27 19440 6400.85 13.95 20 29271 28.34 24483 6408.74 16.36 21 35168 28.47 30143 6286.78 14.29 22 23648 28.42 20648 6363.88 12.69 23 30260 28.36 25890 6383.37 14.44 24 37356 28.40 31791 6386.61 14.90 25 24313 27.82 21273 6323.90 12.50 26 30995 27.96 26685 6473.63 13.91 27 37784 27.67 32959 6417.25 12.77 4.2 Line balancing An example of line balancing using the proposed algorithm is given. Figure 12 shows the relationship between the head travel distance and the computation when placing is done by 1, 2, 4, and 8 component placement machines using Data 14. Under the computation within 2 seconds, multiple searches were performed while gradually increasing the computation. By using the algorithm of the proposed method, it can be seen that the uation value improves in all of the cases using different numbers of machines. Also, the rate of improvement from the respective initial solution is 27.8% for 1 machine, 27.7% for 2 machines, 25.0% for 4 machines, and 26.5% for 8 machines. 100000 uation value 10000 1000 400 800 1200 1600 2000 computing (ms) 1 machine 2 machines 4 machines 8 machines Figure12 Line-balancing of 1, 2, 4, and 8 component placement machines (Data 14) 5 Conclusions We have discussed in this paper the motion optimization of multifunction component placement machines and proposed a model for comprehensive optimization of machine allocation, turn allocation, nozzle allocation, placing order, and pick-up order. Also, it has been confirmed by computer experiment that performing motion optimization using this model gives a sufficiently good solution compared to that of a conventional method. Future work includes new algorithm of obtaining good solution as SA in a short of computation even if the number of components increases. Also, it is desired to formulate the problem as an integer programming problem and obtain an exact optimal solution by IP solver and compare with the proposed method. Finally, it is hoped to create a model that can also handle cases in which some constraints for nozzle allocation is imposed, cases that also take the arrangement of components in the component feeder into account, and cases in which several types of circuit boards are produced. 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