Optimization of hole-making operations: a tabu-search approach

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<ul><li><p>International Journal of Machine Tools &amp; Manufacture 40 (2000) 17351753</p><p>Optimization of hole-making operations: a tabu-searchapproach</p><p>Farhad Kolahan, Ming Liang *</p><p>Department of Mechanical Engineering, University of Ottawa, Ottawa, Ontario, CanadaReceived 10 May 1999; received in revised form 3 March 2000; accepted 17 March 2000</p><p>Abstract</p><p>This paper reports a tabu-search approach to minimize the total processing cost for hole-making oper-ations. Four issues, namely, tool travel scheduling, tool switch scheduling, tool selection, and machiningspeed specification have been simultaneously addressed in this study. The total processing cost consists oftooling cost, machining cost, non-productive tool travelling cost, and tool switching cost. This problemhas a structure similar to the Travelling Salesman Problem (TSP) and hence is NP-complete. In addition,the problem under consideration is more complex since the cost associated with each operation is bothsequence-dependent and position-dependent. To provide an efficient solution procedure, a tabu searchapproach is used. To improve the search performance two new neighbourhood generation and move selec-tion policies have been proposed and tested. The decisions on the above issues can be made simultaneouslybased on the output of the proposed algorithm. The results obtained from computational experiments showthat the total processing cost can be significantly reduced within a reasonable search time. The effects ofsome search parameters and diversification strategies on the search performance have also been investigated. 2000 Elsevier Science Ltd. All rights reserved.</p><p>Keywords: Hole-making; Optimization; Tabu search</p><p>1. Introduction</p><p>Hole-making operations such as drilling, reaming, and tapping account for a large portion ofmachining processes for many industrial parts such as dies and moulds. For instance, a typicalplastic injection mould could have over 100 holes of different diameters, depths, tolerance andsurface specifications, representing various tool requirements and a large number of tool switches.Due to the point-to-point machining feature in hole-making, tool travel takes a significant amount</p><p>* Corresponding author. Tel.: +1-613-5625800-6269; fax: +1-613-5625177.E-mail address: liang@eng.uottawa.ca (M. Liang).</p><p>0890-6955/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.PII: S0 890- 695 5(00 )000 24- 9</p></li><li><p>1736 F. Kolahan, M. Liang / International Journal of Machine Tools &amp; Manufacture 40 (2000) 17351753</p><p>Nomenclature</p><p>i tool type index in ascending order according to the tool diameters, i=1,...,Ij,k,l hole index, j=1,...,J k=1,...,J l=1,...,Jij index for the last tool to be used on hole js sequence index, denoting a specific permutation of operationsa cost per unit non-productive travelling distanceb cost per unit tool switch timeC machining cost per unit timeC ij combined tool and machining costs when tool type i is used on hole jdi diameter of tool iDj final size of hole jeij depth of cut when tool type i performing a cutting operation on hole jfi recommended feed rate for tool type iIj set of tools that can be used to drill hole j to its final sizeLj depth of hole j, including the clearanceNj number of tools in Ijpjk non-productive travelling distance between hole j and hole kqii0j tool switch time between current tool type, i0, and tool i required by hole jQi cost of tool type itij(s,l) optimum processing time of operation ij located in lth position of sequence stij machining time required by tool i for hole jTij life of tool type i associated with cutting operation on hole jT ij(s,l)) optimum life of tool type i associated with cutting operation on hole j in lth</p><p>position of sequence sU total number of possible operationsVij cutting speed of tool i associated with an operation on hole jVij optimum cutting speed for tool i operating on hole jWs a 0-1 integer variable, Ws =1 if sequence s is selected; 0, otherwisexii9i0ljk a 0-1 integer variable, xii9i0ljk=1 if tool i replaces tool i0 to drill hole j which is</p><p>located in the path between holes l and k and has been drilled by tool i9; 0,otherwise</p><p>G(s) total cost associated with operations in sequence sCbest the best objective function value found so farMmax maximum allowed number of moves for the entire search processNmax number of allowed moves in each search phaseMFctr a counter used to record total number of moves made so farNFctr a counter used to record number of moves made so far in a search phaseN(s) set of job sequences in the neighbourhood of sSFbest the best job sequence found so farTFlist tabu listTFsize size of tabu lists* the best sequence in the current neighbourhoods** the best sequence found in the immediate previous neighbourhood</p></li><li><p>1737F. Kolahan, M. Liang / International Journal of Machine Tools &amp; Manufacture 40 (2000) 17351753</p><p>of time. A considerable amount of the processing time is spent on switching tools and movingthe table from one drilling location to another. The survey by Merchant [1] has shown that tooland part movements take on average 70% of the total time in a manufacturing process. In addition,to drill a given hole to its final size, different sets of tools with different cutting speeds may beused which directly influences tooling and machining costs.</p><p>For a part with many holes, a particular tool may be required by several holes and also toolsof different diameters may be used to drill a single hole to its final size. To reduce tool traverse,it may be suggested that the spindle should not be moved until a hole is completely drilled usingseveral tools of different diameters. This however will lead to excessive tool switches. By thesame token, though tool switches can be reduced by completing all operations on all the holesthat require the current tool, the travel time will be increased. Furthermore, the amount of toolmovement and the number of tool switches will depend on which set of tools are to be used todrill each hole to its final size. The machining cost and tool cost are affected by the selection oftool combination for each hole and the machining speeds. Hence, the proper determination of theoperations sequence and the corresponding machining speed used to perform each operation arecrucial in reducing the total cost of production.</p><p>Surprisingly the above problem has not been addressed directly in literature. The studies onsimilar problems in punching operations are also scarce. In this direction, Walas and Askin [2]and Chauney et al. [3] proposed heuristic algorithms based on the travelling salesman problemto minimize total tool travel distance in punching operations. Using an artificial intelligenceapproach, Ssemakula and Rangachar [4] proposed a method to generate an operation sequenceapplicable to a variety of manufacturing processes. Roychoudhury and Muth [5] examined severalheuristic techniques for NC punch press operation sequencing.</p><p>Luong and Spedding [6] are among the few who addressed process planning in hole makingoperations. They developed a generic knowledge based system for process planning and costestimation in hole making. Based on input data, the proposed system can recommend the appropri-ate tools, tool sequence, and machining conditions for each individual hole. The manufacturingcost is then calculated based on the recommended process plan. A similar approach was takenby Khoshnevis and Tan [7] to develop rule-base modules for hole making. Their system can beused to provide a process plan found from all possible operation sequences for a given feature.Taiber [8] presented a search procedure to minimize the number of tool changes, non-cutting toolpath, machining time, and tool cost for prismatic workpieces. At each iteration, a good solutionis found for each of these criteria using different algorithms. A threshold accepting heuristicmethod is then used to navigate the search through the solution space. His computational experi-ments showed a 15% cost reduction over 25 min of search time for a workpiece consisting of48 manufacturing features and 31 tool types. Usher et al. [9] presented an object-oriented approachto generate and rank alternative tool sets for the part process plan. The system is designed as apart of a dynamic process planning system and is able to extract the required data from CAD files.</p><p>Nevertheless, there are two main drawbacks in existing literature on this type of the optimiz-ation problem. First, in punching operations the main concern is to minimize those costs relatedto non-cutting tool travel only. It was also assumed that for each operation the cutting speed isfixed and the problems of tool selection and tool assignment do not arise [5]. Second, every feature(hole) is treated separately and global optimization of the overall process plan is considered.</p><p>In reality, the planning decisions in hole making operations involve several issues. They are:</p></li><li><p>1738 F. Kolahan, M. Liang / International Journal of Machine Tools &amp; Manufacture 40 (2000) 17351753</p><p>(a) tool travel routing; (b) tool switch scheduling; (c) tool-hole grouping; and (d) selection ofcutting speed for each tool-hole combination (operation). These issues are interlocked and concur-rently contribute to the total processing cost. For these reasons, we suggest that the above fourissues be addressed concurrently. The objective is to minimize production cost which consists ofmachining cost, tool cost, tool travel cost, and tool switch cost.</p><p>2. Problem statement</p><p>2.1. Problem description</p><p>As mentioned earlier, this paper attempts at developing an efficient solution method to deter-mine the best sequence of operations and associated machining speeds in hole-making operationsso that the total processing cost is minimized. Generally, a part, e.g. a plastic injection mould,may have many holes of various diameters, surface finishes, tolerances, and possibly differentdepths. Depending on the hole diameter, tool geometry, and surface quality specifications, a holemay or may not be completed using a single tool. If the diameter of hole is relatively large, apilot hole may have to be drilled using a tool of smaller diameter and then enlarge to its finalsize with a larger tool, possibly followed by reaming or tapping when necessary. A hole can bemade using alternative sets (or combinations) of tools. Each set of tools could include a pilottool, a final tool (a tool with the same diameter as that of the final hole), and one or moreintermediate tools. Fig. 1 shows a schematic representation of different set of tools that could beused to drill three holes on a part.</p><p>Fig. 1. A schematic representation of alternative sets of tools for hole making.</p></li><li><p>1739F. Kolahan, M. Liang / International Journal of Machine Tools &amp; Manufacture 40 (2000) 17351753</p><p>For each hole in Fig. 1 the largest tool, shown by solid lines, has to be used to drill the holeto its final size. Some pilot or intermediate tools, shown by dashed lines, may also be used. Forinstance, for hole A, there could be four different sets of tools; {1,2,3}, {2,3}, {1,3}, and {3}.The selection of tool set for each hole directly affects the optimum cutting speeds, required numberof tools switches, and tool travel distance.</p><p>The problem under consideration is similar to the Travelling Salesman Problem (TSP) in whicheach node (operation) in a tour (sequence of all operations) must be visited only once. However,unlike the TSP, the cost of visiting each node is determined by its position in the sequence ofoperations (constructed tour), i.e. certain tools may not be used for some holes even though suchoperations are feasible (such nodes are visited at no cost). This adds more complexity to theproblem as the cost involved in performing a cutting operation in a drilling site is affected bythe historical background pertaining to that particular site. That is, the selection of cutting speedand the schedule of tool switches depend upon the depth of cut and hence the current status ofthe concerned hole which, in turn, is determined by whether or not other tools have already beenused on that hole.</p><p>The problem is now to select a set of operations along with the optimum cutting speed andsequence those operations in such a way that the total processing cost is minimized. The costcomponents considered in this paper include:</p><p>a) Tool travel cost: This is the cost of moving the tool from its previous location to the currentdrilling position. Tool travel cost is proportional to the distance required for the spindle to movebetween two consecutive drilling locations, pjk. The cost per unit time is usually lower for non-cutting motions than for the actual cutting processes due to the lower power consumption.</p><p>b) Tool switch cost: This cost occurs whenever a different tool is used for the next operation.If for operation ij tool type i is not available on the spindle, then the required tool must be loadedon the spindle prior to performing operation ij. In CNC machining each tool is usually mountedon the tool magazine with its own collet. For any tool switch, the tool magazine has to rotate sothat the tool changing device can reach the required tool. The tool switch time depends on thelocation of the required tool on the magazine. If for operation ij the location of replacing tool ion the tool magazine is far from the current tool, i9, then the magazine has to rotate a longerdistance before the tool switch can take place. This causes a longer tool switch time, tii9, andhence a higher tool switch cost.</p><p>c) Tool and machining costs: The tool cost consists of the new tool cost and the cost of machinedown time required to replace the tool. The operating cost and the machine overhead cost arethe major components of machining cost. Both tool and machining costs are affected by machiningparameters such as depth of cut, feed rate, and cutting speed. The combined tool and machiningcosts when tool type i is used on hole j can be written as:</p><p>C ij5tijTij</p><p>Qi1Ctij (1)</p><p>where the machining time, tij, is calculated by:</p><p>tij5pdiLj</p><p>1000Vijfi (2)</p><p>and the general tool life expression, Tij, is as follows [10]:</p></li><li><p>1740 F. Kolahan, M. Liang / International Journal of Machine Tools &amp; Manufacture 40 (2000) 17351753</p><p>Tij5S A1d A2iVijeA3ij f A4i DA5 (3)</p><p>The above expression is an empirical formula in which Tij is the life of tool type i performing acutting operation on hole j with the speed of Vij, di is the tool diameter, and fi is the recommendedfeed rate for tool type i which is determined by tool and part materials, required surface finish,and tool geometry. In the case where an existing hole is enlarged by drilling, reaming, or tapping,the depth of cut, eij, is the difference between the tool radius and the current hole radius. Thevalues of A1, A2, A3, A4 and A5 will depend on the type of operation (drilling, reaming, tap-ping, etc.).</p><p>There is a set of machining parameters with which the total tooling and machining costs canbe minimized. In drilling operations the depth of cut is fixed. It is also a...</p></li></ul>

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