- Email: [email protected]
Integrated Approach for Design of Machining Systems
9th IFAC Workshop on Intelligent Manufacturing Systems Szczecin, Poland, October 9-10, 2008
Integrated Approach for Design of Machining Systems A. Dolgui1, N. Guschinsky2, and G. Levin2 1
Industrial Engineering and Computer Science Centre Ecole des Mines de St Etienne, 158, cours Fauriel, 42023 Saint Etienne, France [email protected] 2
Operations Research Laboratory United Institute of Informatics Problems of the National Academy of Sciences Surganov St., 6, 220012 Minsk, Belarus [email protected], [email protected] Abstract. In this paper we present the prototype of a decision support system for logical layout design of machining systems. The approach and developed decision support system are focused on systems which are used in the mass production of a unique product or a family of similar products. In these lines, the machining operations are realized on working positions equipped by standard modular spindle heads. The part transportation from a working position to the next one is synchronized. The spindle heads selected and their layout define the system productivity and the final cost. The paper present a novel approach and depicts mathematical and decision-aid methods developed and implemented in the software tool for optimization of each design (or reconfiguration) stage of such a line, in particular, a method for finding the optimal logical layout. In this work we present the main principles and ideas of decision making by the example of decision and support soluton for machining systems used for mass production. The used approach is based on several techniques: powerful database of standard solutions and efficient mecanisms to search the existing elements; expert system to choose better solutions from database; line balancing model based on shortest path approach; set of problem oriented rules; user friendly software environment.
1. INTRODUCTION The design of manufacturing systems is a wide open area for development and application of decision making and decision support technologies. This domain is characterized by the necessity to combine the standard decision making methods, sophisticated operational research techniques and some specific rules based on expert knowledge to take into account principal technological constraints and criteria. A promising trend in this area deals with the development of integrated software tools (Brown, 2004; Grieves, 2005; Stark, 2005). Their main idea consists in integrating product and manufacturing data into a common database. This enables product designers to consider the manufacturing processes constraints at the early product design stage. At the same time, all data of product design should be used directly for optimizing the corresponding manufacturing system. That’s why the core of these software tools is a powerful extendable database, supported by a user friendly software environment. This database normally contains digital models of product and processes. In order to find an optimal manufacturing system configuration, a set of advanced decision making and decision support methods are used for data processing.
978-3-902661-40-1/09/$20.00 © 2008 IFAC
Now, these techniques are combined in the decision support software tool for optimal process planning, line balancing and equipement selection for optimal design of a transfer machines with rotary or mobile tables. 2. BACKGROUND The studing of design problems for mass production manufacturing systems began by considering the simple assembly line balancing problem (SALBP) (Baybars, 1986; Scholl and Klein, 1998). The SALBP consists in assigning a set of operations to identical consecutive stations minimizing the number of stations required, subject to precedence constraints between operations and cycle time constraints. Many exact and heuristic approaches for
302
10.3182/20081009-2-PL-4001.0051
SALBP were suggested in literature: Lagrange relaxation techniques (Aghezzaf and Artiba, 1995), Branch and Bound algorithms (Assche and Herroelen, 1998; Ugurdag et al., 1997; Scholl and Klein, 1998), and heuristics and metaheuristics (Arcus, 1966; Helgenson and Birnie, 1961; Rekiek et al., 2001). This list is not exhaustive. A state-ofthe-art can be found in (Baybars, 1986; Becker and Scholl, 2006; Erel and Sarin, 1998; Ghosh and Gagnon, 1989; Rekiek et al., 2002).
Stage 1. Input of data Step 1.1. Part modeling with features Step 1.2. Input of part and machine properties Step 1.3. Process planning using an expert system Step 1.4. Constraints generation based on machining data and user experience Stage 2. Optimization of logical layout Step 2.1. Finding all solutions minimizing the number of spindle heads and working positions while assigning operations to working positions and defining cutting modes for spindle heads Step 2.2. Choice of a solution among the optimal ones (solution to be applied) Stage 3. Definition of physical layout and machine parameters Step 3.1 Working plan documentation Step 3.2. Part positioning Step 3.3. Equipment selection Step 3.4. Preliminary 3D layout design Step 3.5. Control equipment and additional devices selection Step 3.6. Cost estimation
The problem where line balancing is combined with equipment selection is often called Simple Assembly Line Design Problem (SALDP) (Baybars, 1986; Becker and Scholl, 2006) or Single-Product Assembly System Design Problem (SPASDP) (Gadidov and Wilhelm, 2000). SALDP considers the “high-level” logical layout design with equipment selection (one per station) from a set of alternatives. There are several equipment alternatives for each operation, and often a particular piece of equipment is efficient for some operations, but not for others (Bukchin and Tzur, 2000; Bukchin and Rubinovich, 2003). There is a given set of equipment types; each type is associated with a specific cost. The equipment cost is assumed to include the purchasing and operational cost. The duration of an operation depends on the equipment selected. An operation can be performed at any station, provided that the equipment selected for this station is appropriate and that precedence relations are satisfied. The total station time should not exceed the predetermined cycle time. The problem consists of selecting equipment and assigning operations to each station. The objective is to minimize the total equipment cost.
This methodology will be illustrated in the next section using the case of the design of transfer machines with rotary or mobile tables. 4. PRODUCT/PROCESS MODELING
The balancing of dedicated transfer lines (Dolgui et al., 2000) in machining environments deals with grouping operations into a number of blocks (sets of operations performed by a spindle head) and assigning these blocks to stations. Each block requires a piece of equipment (a multispindle head), which incurs a purchase cost. Therefore, it is necessary to minimize both the number of stations and the number of blocks. To do it, all possible operations assignments to blocks and stations must be considered; otherwise the optimality of a solution cannot be guaranteed. The set of alternative blocks is not known in advance and the parameters of a block depend on the set of operations assigned to it. Therefore, the balancing of dedicated machining systems of mass production, as it was demonstrated in (Dolgui et al., 2006), is more complex than SALBP and SALDP.
4.1. Part modeling The first step deals with the modeling of a part to be machined. The clients provide the machine tool manufacturer with the specifications of a part already designed, which they want to produce using a transfer machine. Usually, the manufacturing process includes milling, drilling, boring, etc. a set of part elements such as planes, facets, holes of different types (cylindrical, bevel, threaded, etc). Each element concerns a certain side (or surface) of the part and is characterized by a set of technological parameters, like required tolerances and surface conditions. In order to use the same format for the geometric and technological data, the part is modeled with machining features. The concept of feature associates the technological characteristics of a machining element with its geometric parameters. Therefore, the part modeling step demands analyzing the part to be machined and identifying features, their geometric and topological relations.
3. DECISION MAKING METHODOLOGY A design methodology for manufacturing systems can be defined as a set of procedures that analyzes and segregates a complex manufacturing system design task into simpler manageable sub-design tasks while still maintaining their links and interdependencies (Wilhelm et al., 1995). An illustration of decision support system is given in (Dolgui et al., 2005). It is composed of the following steps:
When the part has been modeled, some additional characteristics of the part (for example, the material and its properties, the properties of the billet, etc.), and of the
303
machine (for example, the desired productivity, the cooling method, the type of cooling liquid, etc.) must be defined as well as a desired type of machine (with rotary or mobile table) must be selected.
technological factors (fixed sequences of operations for machining features, the presence of roughing, semifinishing and finishing operations, etc.). b) Inclusion constrains reflect the necessity to perform some operations on the same working position or even by the same spindle head. They are implied by the required precision (tolerance) of mutual disposition of machined features as well as a number of additional factors.
4.2. Process planning At this stage, the machining operations, required tools and their parameters for each part feature are determined. The process plan of a part feature, i.e. a set of operations to be performed in order to provide the required geometric and technological characteristics is chosen using the following: •
condition of surface before machining,
•
diameter of machining holes,
•
required precision for each machining element.
c) Exclusion constrains are used in the cases when it is impossible to assign some pairs of operations to the same working position (or to the same spindle head). It can be caused by a number of constructional and technological constraints: mutual influence of these operations, a forbidden tool location, etc. This type of constraint must be fulfilled also for operations executed on the different sides of the part because they cannot be performed by the same spindle head.
These parameters are stored in the data fields associated with the features. Analyzing their values and using the expert system, all possible process plans for each feature can be chosen from the process plans database. This database contains also dependences between the feature parameters and the set of all possible operations that a machine equipped by standard spindle heads can process. Then, for each feature and each possible process plan the corresponding tolerances are calculated. The obtained values of tolerances are compared with those required and the plan providing the values nearest to the required is chosen. For this chosen plan, the parameters of operations (like cutting depth, machining length, type and material of cutting tool, working stroke, and cutting mode) are determined automatically.
The overall equipment dimensions limit the total number of working positions and the number of blocks at each working position by the values of the parameters m and n respectively. The values of m and n are obtained taking into account the available machine configuration and economical constraints. The objective production rate is obtained, if the machine cycle time T(P) does not exceed the maximum authorized value T0. 4.4. Logical layout optimization The manufacturing information as well as diverse constraints related to the design of spindle heads and working positions are used as input data for the second design stage, i.e. logical layout design (Wilheim et al., 1995; Zhang et al., 2002). The quantity of equipment (spindle heads, working positions) required to produce a part with the given productivity rate defines the final cost of the transfer machine. Therefore, the goal of the logical layout optimization is to find a design variant that minimizes the number of working positions and the total number of spindle heads while satisfying all given technological and economical constraints (Dolgui et al., 2006).
Cutting mode is defined by minimal, maximum and recommended values of the following parameters: •
cutting speed,
•
feed rate per minute,
•
feed rate per revolution.
Then, the user, who can replace or modify automatically chosen plans, analyzes the plans suggested by the decision support tool. New process plans can be stored in the database. In order to establish a total process plan, the individual machining plans selected for the features must be completed by introducing the existing relations between the operations of different features. These relations are introduced using different types of constraints.
5. OPTIMIZATION 5.1. Problem statement If the machining is organized on m working positions, then at the k-th working position k=1, ..., m, a subset Nk of the given set N of operations is performed. Each set Nk is uniquely partitioned into nk subsets (Nkl, l=1,...,nk), where the operations of each subset Nkl are performed by the same spindle head. Such a partition is unique due to the fact that each operation corresponds to one “side” of the part, and only the operations of the same side can be performed by one spindle head. Parameters of the kl-th spindle head and
4.3. Generation of constraints The proposed decision methodology and models consider the following types of relations between machining operations: a) Precedence constraints which define possible sequences of operations and are determined by a number of known
304
its execution time depend both on the set of operations Nkl and their cutting modes.
x0(i)= s0(i)v0(i),
The logical layout optimization consist in determining simultaneously:
x1(i)= s1(i)v1(i), x2(i)= s2(i)v2(i).
a) the number m of working positions;
The interval of possible values of the feed per minute for the spindle head which executes the set N of operations X(N)= [ X ( N ), X ( N )] is calculated as follows:
b) the partitioning of the given set N of operations into subsets Nk, k= 1,...,m; c) the feed per minute Xkl for each Nkl, l=1,…, nk. Let P= is a design solution with Pk= (Pk1, ..., Pkl ,..., Pknk ) and Pkl = (Nkl, Xkl). Let C1 and C2 be the relative costs for one working position and one block, respectively. Then, the objective function of the considered design problem can be formulated as follows: m
Min Q( P ) = C1m + C2 ∑ nk .
(1)
Let λ(i) be the given length of the working stroke for operation i∈N. The execution time τb(Nkl, Xkl) of the set Nkl of operations performing by the kl-th spindle head working with the feed per minute Xkl is equal to: (2)
k =1
(10)
x(N)= min{x**, X (N ) }.
(11)
m
(12)
k =1
subject to: T(P) ≤ T0;
(4)
m
U N k =N;
(13) (14)
k =1
The cycle time for machines with a mobile table is defined by the sum of the machining times of the working positions:
τp(Pk).
x**(N)= max{ X (N ) , x*},
Minimize Q ( P ) = C1m + C2 ∑ O ( N k ) ,
(3)
where τ″ is a given constant, an additional time for loading the billet and unloading the part after machining.
T(P)=τ″ + ∑
(9)
The optimization model of the considered decision making problem for logical layout design can be formulated as follows:
The cycle time for machines with a rotary table is defined by the maximum value among the execution times of the working positions:
m
(8)
5.3. Optimization model
The execution time for all operations of the k-th working position (k=1,…,m) is equal to:
T(P)=τ″ + max{τ (Nk) | k= 1, 2..., m},
X (N ) = min{x2(i)|i∈N}.
In this case, the feed per revolution for operation i is equal to s(i,x)= min[s2(i),x/v1(i)], and the cutting speed is equal to v(i,x)= x/s(i,x).
where L(Nkl) = max{ λ(i) | i∈ Nkl }.
p
(7)
x*(N)= min{(L(N)/λ(i))μ(i)x0(i)|i∈N},
5.2. Cycle time calculation
τp(Pk) = max { τ b(Nkl, Xkl) | l=1,…,nk }.
X ( N ) = max(max{x1(i)|i∈N}, L(N)/T),
If the set X(N) is empty, then operations of the set N cannot be executed by one spindle head. Otherwise, a preliminary value x∈X(N) might be chosen in the following way:
k =1
τb(Nkl, Xkl)= L(Nkl)/ Xkl,
(6)
(5)
Let μ(i) be a constant that characterizes the tool life rate, [s1(i),s2(i)] and [v1(i),v2(i)] the ranges of the feasible values of feed per revolution s(i) and spindle speed (cutting speeds) v(i), respectively for each operation i∈N, s0(i), v0(i) their “recommended” values:
Nk’ ∩Nk”=∅, ∀ k', k"=1,…,m such that k '≠ k";
(15)
O(Nk) ≤ n , for all k=1,…,m;
(16)
Xkl∈X(Nkl), for all k=1,…,m, l=1,…,nk;
(17)
m=m(P) ≤ m .
(18)
The objective function (12) is the estimation of the equipment cost; constraint (13) provides the required productivity rate; constraints (14-15) ensure the assignment of all the operations from N, each operation to one and only
305
one working position; (16) provides precedence constraints for operations, inclusion and exclusion constraints for spindle heads and working positions; (17) chooses feasible values of the feed per minute for each spindle head; (18) is the constraint on the number of working positions.
manufacturing plan. At this stage more detailed analysis of machine properties is needed, the manufacturability of parts can be verified using, for example, the finite elements model and simulation (Daschenko, 2003).
The values m and n are defined by the type of the
6. CONCLUSION
machine: for machines with rotary table m ≤ 15 and n = 2,
A novel and promising applied area for decision making methods and decision support technologies is the development of decision-aid software tools for manufacturing system design. It is necessary to use conjointly advanced operational research methods, standard decision making approaches, decision support technologies and problem oriented specific rules. We have presented an example of such a decision support system for preliminary design of machining systems for mass production.
for machines with mobile table m ≤ 3 and n ≤ 3. For machines with mobile table the expression (16) is replaced by (16'): O(Nk) ≤ 2, k=1,…, m-1; O(Nm) ≤ 3 .
(16')
Optimization algorithms are based on the shortest path approach (Dolgui et al., 2000; Dolgui et al., 2008). They find all optimal solutions corresponding to the different machine configurations with different operations’ assignment or allocation of spindle heads to working positions. In order to choose a solution to be applied, these solutions can be evaluated by user with other criteria and user’s preferences. If the results of the optimization do not satisfy user, it is possible to return to previous stages and make the necessary modifications of constraints and input data.
The integrated decision support system was developed to help machine tool designers to obtain a high-quality (and if possible optimal) architecture of transfer machines. The system supports the different stages of the logical layout design of a transfer machine: modeling of a part to be machined, process planning, optimization of the machine configuration, its preliminary 3D layout and cost estimation. The optimization problem of the logical layout is to minimize the number of working positions and the number of spindle heads by assigning the manufacturing operations to positions and choosing adequate cutting modes for each spindle head.
5.4. 3D-model and cost estimation The obtained logical layout defines the general configuration of a transfer machine and enables designers to complete this logical architecture by selecting the corresponding modular equipment from the library of standard units of the proposed decision support system. At first, designers specify the overall dimensions of the movable table and place the part to be machined on it. The part position defines the angles and positions of the spindle heads.
The perspectives of this research consist in the improvement and extension of the suggested approach for a larger class of manufacturing systems: linear transfer machines, transfer lines with buffers, multi-flow transfer lines, assembly lines etc. Another promising approach is the integration of the process planning and logical layout steps in a common optimization model using heuristics and meta-heuristics.
Then, designers define the dimensions and the specifications of the required equipment that will automatically be designed using the graphical library of standard units. Finally, designers can obtain a preliminary 3D-model of the machine.
Acknowledgements: The authors thank Chris Yukna for the help in checking the English. REFERENCES
In order to estimate the total machine cost, additional devices are to be selected, like control, tool storage, loadingunloading systems. This choice is guided by some automatically generated suggestions and accompanied by the verification of compatibility with all previous decisions. The costs of all selected devices are obtained from the database which contains market prices of standard units (spindle heads and other machine elements). The total cost estimation enables designers to formulate a commercial offer for customers. Therefore, using the decision support system, machine tools manufacturers can provide their clients with technological plans and a commercial offer in really short times. If clients accept this offer then the detailed design of the machine with the chosen configuration is to be prepared in order to establish a
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Becker, C., and Scholl A. (2006). A survey on problems and methods in generalized assembly line balancing. European Journal of Operational Research, 168, 694715. Bukchin, J., and Tzur, M. (2000). Design of flexible assembly line to minimize equipment cost. IIE Transactions, 32, 585-598.
Rekiek, B., Dolgui, A., Delchambre, A., and Bratcu, A. (2002). State of art of assembly lines design optimisation. Annual Reviews in Control, 26(2), 163174.
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Dolgui, A., Guschinsky, N. and Levin, G. (2000). Approaches to balancing of transfer line with block of parallel operations, Institute of Engineering Cybernetics, Minsk, Preprint No. 8, 42 pages.
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Dolgui, A., Guschinskaya O., Guschinsky N., Levin G., (2005). Conception de systèmes de fabrication: prototype d’un logiciel d’aide à la décision. Journal of Decision Systems, 14(4), 489-516.
Zhang G. W., Zhang S.C., Xu Y.S., (2002). Research on fl,exible transfer line schematic design using hierarchical process planning. Journal of Materials Processing Technology, 129, 629-633.
Dolgui, A., Finel B., Guschinsky N., Levin G., and Vernadat F. (2006). MIP approach to balancing transfer lines with blocks of parallel operations. IIE Transactions, 38, 869– 882. (Best paper award 2008) Dolgui, A., Guschinsky N., Levin G., and Proth J.-M. (2008). Optimisation of multi-position machines and transfer lines. European Journal of Operational Research, 185 (3), 1375–1389. Erel, E., and Sarin, S.C. (1998). A survey of the assembly line balancing procedures. Production Planning and Control, 9(5), 414-434. Gadidov, R., and Wilhelm W. (2000). A cutting plane approach for the single-product assembly system design problem. International Journal of Production Research, 38 (8), 2000, 1731–1754. Ghosh, S., and Gagnon, R. (1989). A comprehensive literature review and analysis of the design, balancing and scheduling of assembly lines. International Journal Production Research, 27(4), 637-670. Grieves, M., (2005). Product Lifecycle Management: Driving the Next Generation of Lean Thinking, McGraw Hill.
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Integrated Approach for Design of Machining Systems A. Dolgui1, N. Guschinsky2, and G. Levin2 1
Industrial Engineering and Computer Science Centre Ecole des Mines de St Etienne, 158, cours Fauriel, 42023 Saint Etienne, France [email protected] 2
Operations Research Laboratory United Institute of Informatics Problems of the National Academy of Sciences Surganov St., 6, 220012 Minsk, Belarus [email protected], [email protected] Abstract. In this paper we present the prototype of a decision support system for logical layout design of machining systems. The approach and developed decision support system are focused on systems which are used in the mass production of a unique product or a family of similar products. In these lines, the machining operations are realized on working positions equipped by standard modular spindle heads. The part transportation from a working position to the next one is synchronized. The spindle heads selected and their layout define the system productivity and the final cost. The paper present a novel approach and depicts mathematical and decision-aid methods developed and implemented in the software tool for optimization of each design (or reconfiguration) stage of such a line, in particular, a method for finding the optimal logical layout. In this work we present the main principles and ideas of decision making by the example of decision and support soluton for machining systems used for mass production. The used approach is based on several techniques: powerful database of standard solutions and efficient mecanisms to search the existing elements; expert system to choose better solutions from database; line balancing model based on shortest path approach; set of problem oriented rules; user friendly software environment.
1. INTRODUCTION The design of manufacturing systems is a wide open area for development and application of decision making and decision support technologies. This domain is characterized by the necessity to combine the standard decision making methods, sophisticated operational research techniques and some specific rules based on expert knowledge to take into account principal technological constraints and criteria. A promising trend in this area deals with the development of integrated software tools (Brown, 2004; Grieves, 2005; Stark, 2005). Their main idea consists in integrating product and manufacturing data into a common database. This enables product designers to consider the manufacturing processes constraints at the early product design stage. At the same time, all data of product design should be used directly for optimizing the corresponding manufacturing system. That’s why the core of these software tools is a powerful extendable database, supported by a user friendly software environment. This database normally contains digital models of product and processes. In order to find an optimal manufacturing system configuration, a set of advanced decision making and decision support methods are used for data processing.
978-3-902661-40-1/09/$20.00 © 2008 IFAC
Now, these techniques are combined in the decision support software tool for optimal process planning, line balancing and equipement selection for optimal design of a transfer machines with rotary or mobile tables. 2. BACKGROUND The studing of design problems for mass production manufacturing systems began by considering the simple assembly line balancing problem (SALBP) (Baybars, 1986; Scholl and Klein, 1998). The SALBP consists in assigning a set of operations to identical consecutive stations minimizing the number of stations required, subject to precedence constraints between operations and cycle time constraints. Many exact and heuristic approaches for
302
10.3182/20081009-2-PL-4001.0051
SALBP were suggested in literature: Lagrange relaxation techniques (Aghezzaf and Artiba, 1995), Branch and Bound algorithms (Assche and Herroelen, 1998; Ugurdag et al., 1997; Scholl and Klein, 1998), and heuristics and metaheuristics (Arcus, 1966; Helgenson and Birnie, 1961; Rekiek et al., 2001). This list is not exhaustive. A state-ofthe-art can be found in (Baybars, 1986; Becker and Scholl, 2006; Erel and Sarin, 1998; Ghosh and Gagnon, 1989; Rekiek et al., 2002).
Stage 1. Input of data Step 1.1. Part modeling with features Step 1.2. Input of part and machine properties Step 1.3. Process planning using an expert system Step 1.4. Constraints generation based on machining data and user experience Stage 2. Optimization of logical layout Step 2.1. Finding all solutions minimizing the number of spindle heads and working positions while assigning operations to working positions and defining cutting modes for spindle heads Step 2.2. Choice of a solution among the optimal ones (solution to be applied) Stage 3. Definition of physical layout and machine parameters Step 3.1 Working plan documentation Step 3.2. Part positioning Step 3.3. Equipment selection Step 3.4. Preliminary 3D layout design Step 3.5. Control equipment and additional devices selection Step 3.6. Cost estimation
The problem where line balancing is combined with equipment selection is often called Simple Assembly Line Design Problem (SALDP) (Baybars, 1986; Becker and Scholl, 2006) or Single-Product Assembly System Design Problem (SPASDP) (Gadidov and Wilhelm, 2000). SALDP considers the “high-level” logical layout design with equipment selection (one per station) from a set of alternatives. There are several equipment alternatives for each operation, and often a particular piece of equipment is efficient for some operations, but not for others (Bukchin and Tzur, 2000; Bukchin and Rubinovich, 2003). There is a given set of equipment types; each type is associated with a specific cost. The equipment cost is assumed to include the purchasing and operational cost. The duration of an operation depends on the equipment selected. An operation can be performed at any station, provided that the equipment selected for this station is appropriate and that precedence relations are satisfied. The total station time should not exceed the predetermined cycle time. The problem consists of selecting equipment and assigning operations to each station. The objective is to minimize the total equipment cost.
This methodology will be illustrated in the next section using the case of the design of transfer machines with rotary or mobile tables. 4. PRODUCT/PROCESS MODELING
The balancing of dedicated transfer lines (Dolgui et al., 2000) in machining environments deals with grouping operations into a number of blocks (sets of operations performed by a spindle head) and assigning these blocks to stations. Each block requires a piece of equipment (a multispindle head), which incurs a purchase cost. Therefore, it is necessary to minimize both the number of stations and the number of blocks. To do it, all possible operations assignments to blocks and stations must be considered; otherwise the optimality of a solution cannot be guaranteed. The set of alternative blocks is not known in advance and the parameters of a block depend on the set of operations assigned to it. Therefore, the balancing of dedicated machining systems of mass production, as it was demonstrated in (Dolgui et al., 2006), is more complex than SALBP and SALDP.
4.1. Part modeling The first step deals with the modeling of a part to be machined. The clients provide the machine tool manufacturer with the specifications of a part already designed, which they want to produce using a transfer machine. Usually, the manufacturing process includes milling, drilling, boring, etc. a set of part elements such as planes, facets, holes of different types (cylindrical, bevel, threaded, etc). Each element concerns a certain side (or surface) of the part and is characterized by a set of technological parameters, like required tolerances and surface conditions. In order to use the same format for the geometric and technological data, the part is modeled with machining features. The concept of feature associates the technological characteristics of a machining element with its geometric parameters. Therefore, the part modeling step demands analyzing the part to be machined and identifying features, their geometric and topological relations.
3. DECISION MAKING METHODOLOGY A design methodology for manufacturing systems can be defined as a set of procedures that analyzes and segregates a complex manufacturing system design task into simpler manageable sub-design tasks while still maintaining their links and interdependencies (Wilhelm et al., 1995). An illustration of decision support system is given in (Dolgui et al., 2005). It is composed of the following steps:
When the part has been modeled, some additional characteristics of the part (for example, the material and its properties, the properties of the billet, etc.), and of the
303
machine (for example, the desired productivity, the cooling method, the type of cooling liquid, etc.) must be defined as well as a desired type of machine (with rotary or mobile table) must be selected.
technological factors (fixed sequences of operations for machining features, the presence of roughing, semifinishing and finishing operations, etc.). b) Inclusion constrains reflect the necessity to perform some operations on the same working position or even by the same spindle head. They are implied by the required precision (tolerance) of mutual disposition of machined features as well as a number of additional factors.
4.2. Process planning At this stage, the machining operations, required tools and their parameters for each part feature are determined. The process plan of a part feature, i.e. a set of operations to be performed in order to provide the required geometric and technological characteristics is chosen using the following: •
condition of surface before machining,
•
diameter of machining holes,
•
required precision for each machining element.
c) Exclusion constrains are used in the cases when it is impossible to assign some pairs of operations to the same working position (or to the same spindle head). It can be caused by a number of constructional and technological constraints: mutual influence of these operations, a forbidden tool location, etc. This type of constraint must be fulfilled also for operations executed on the different sides of the part because they cannot be performed by the same spindle head.
These parameters are stored in the data fields associated with the features. Analyzing their values and using the expert system, all possible process plans for each feature can be chosen from the process plans database. This database contains also dependences between the feature parameters and the set of all possible operations that a machine equipped by standard spindle heads can process. Then, for each feature and each possible process plan the corresponding tolerances are calculated. The obtained values of tolerances are compared with those required and the plan providing the values nearest to the required is chosen. For this chosen plan, the parameters of operations (like cutting depth, machining length, type and material of cutting tool, working stroke, and cutting mode) are determined automatically.
The overall equipment dimensions limit the total number of working positions and the number of blocks at each working position by the values of the parameters m and n respectively. The values of m and n are obtained taking into account the available machine configuration and economical constraints. The objective production rate is obtained, if the machine cycle time T(P) does not exceed the maximum authorized value T0. 4.4. Logical layout optimization The manufacturing information as well as diverse constraints related to the design of spindle heads and working positions are used as input data for the second design stage, i.e. logical layout design (Wilheim et al., 1995; Zhang et al., 2002). The quantity of equipment (spindle heads, working positions) required to produce a part with the given productivity rate defines the final cost of the transfer machine. Therefore, the goal of the logical layout optimization is to find a design variant that minimizes the number of working positions and the total number of spindle heads while satisfying all given technological and economical constraints (Dolgui et al., 2006).
Cutting mode is defined by minimal, maximum and recommended values of the following parameters: •
cutting speed,
•
feed rate per minute,
•
feed rate per revolution.
Then, the user, who can replace or modify automatically chosen plans, analyzes the plans suggested by the decision support tool. New process plans can be stored in the database. In order to establish a total process plan, the individual machining plans selected for the features must be completed by introducing the existing relations between the operations of different features. These relations are introduced using different types of constraints.
5. OPTIMIZATION 5.1. Problem statement If the machining is organized on m working positions, then at the k-th working position k=1, ..., m, a subset Nk of the given set N of operations is performed. Each set Nk is uniquely partitioned into nk subsets (Nkl, l=1,...,nk), where the operations of each subset Nkl are performed by the same spindle head. Such a partition is unique due to the fact that each operation corresponds to one “side” of the part, and only the operations of the same side can be performed by one spindle head. Parameters of the kl-th spindle head and
4.3. Generation of constraints The proposed decision methodology and models consider the following types of relations between machining operations: a) Precedence constraints which define possible sequences of operations and are determined by a number of known
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its execution time depend both on the set of operations Nkl and their cutting modes.
x0(i)= s0(i)v0(i),
The logical layout optimization consist in determining simultaneously:
x1(i)= s1(i)v1(i), x2(i)= s2(i)v2(i).
a) the number m of working positions;
The interval of possible values of the feed per minute for the spindle head which executes the set N of operations X(N)= [ X ( N ), X ( N )] is calculated as follows:
b) the partitioning of the given set N of operations into subsets Nk, k= 1,...,m; c) the feed per minute Xkl for each Nkl, l=1,…, nk. Let P=
Min Q( P ) = C1m + C2 ∑ nk .
(1)
Let λ(i) be the given length of the working stroke for operation i∈N. The execution time τb(Nkl, Xkl) of the set Nkl of operations performing by the kl-th spindle head working with the feed per minute Xkl is equal to: (2)
k =1
(10)
x(N)= min{x**, X (N ) }.
(11)
m
(12)
k =1
subject to: T(P) ≤ T0;
(4)
m
U N k =N;
(13) (14)
k =1
The cycle time for machines with a mobile table is defined by the sum of the machining times of the working positions:
τp(Pk).
x**(N)= max{ X (N ) , x*},
Minimize Q ( P ) = C1m + C2 ∑ O ( N k ) ,
(3)
where τ″ is a given constant, an additional time for loading the billet and unloading the part after machining.
T(P)=τ″ + ∑
(9)
The optimization model of the considered decision making problem for logical layout design can be formulated as follows:
The cycle time for machines with a rotary table is defined by the maximum value among the execution times of the working positions:
m
(8)
5.3. Optimization model
The execution time for all operations of the k-th working position (k=1,…,m) is equal to:
T(P)=τ″ + max{τ (Nk) | k= 1, 2..., m},
X (N ) = min{x2(i)|i∈N}.
In this case, the feed per revolution for operation i is equal to s(i,x)= min[s2(i),x/v1(i)], and the cutting speed is equal to v(i,x)= x/s(i,x).
where L(Nkl) = max{ λ(i) | i∈ Nkl }.
p
(7)
x*(N)= min{(L(N)/λ(i))μ(i)x0(i)|i∈N},
5.2. Cycle time calculation
τp(Pk) = max { τ b(Nkl, Xkl) | l=1,…,nk }.
X ( N ) = max(max{x1(i)|i∈N}, L(N)/T),
If the set X(N) is empty, then operations of the set N cannot be executed by one spindle head. Otherwise, a preliminary value x∈X(N) might be chosen in the following way:
k =1
τb(Nkl, Xkl)= L(Nkl)/ Xkl,
(6)
(5)
Let μ(i) be a constant that characterizes the tool life rate, [s1(i),s2(i)] and [v1(i),v2(i)] the ranges of the feasible values of feed per revolution s(i) and spindle speed (cutting speeds) v(i), respectively for each operation i∈N, s0(i), v0(i) their “recommended” values:
Nk’ ∩Nk”=∅, ∀ k', k"=1,…,m such that k '≠ k";
(15)
O(Nk) ≤ n , for all k=1,…,m;
(16)
Xkl∈X(Nkl), for all k=1,…,m, l=1,…,nk;
(17)
m=m(P) ≤ m .
(18)
The objective function (12) is the estimation of the equipment cost; constraint (13) provides the required productivity rate; constraints (14-15) ensure the assignment of all the operations from N, each operation to one and only
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one working position; (16) provides precedence constraints for operations, inclusion and exclusion constraints for spindle heads and working positions; (17) chooses feasible values of the feed per minute for each spindle head; (18) is the constraint on the number of working positions.
manufacturing plan. At this stage more detailed analysis of machine properties is needed, the manufacturability of parts can be verified using, for example, the finite elements model and simulation (Daschenko, 2003).
The values m and n are defined by the type of the
6. CONCLUSION
machine: for machines with rotary table m ≤ 15 and n = 2,
A novel and promising applied area for decision making methods and decision support technologies is the development of decision-aid software tools for manufacturing system design. It is necessary to use conjointly advanced operational research methods, standard decision making approaches, decision support technologies and problem oriented specific rules. We have presented an example of such a decision support system for preliminary design of machining systems for mass production.
for machines with mobile table m ≤ 3 and n ≤ 3. For machines with mobile table the expression (16) is replaced by (16'): O(Nk) ≤ 2, k=1,…, m-1; O(Nm) ≤ 3 .
(16')
Optimization algorithms are based on the shortest path approach (Dolgui et al., 2000; Dolgui et al., 2008). They find all optimal solutions corresponding to the different machine configurations with different operations’ assignment or allocation of spindle heads to working positions. In order to choose a solution to be applied, these solutions can be evaluated by user with other criteria and user’s preferences. If the results of the optimization do not satisfy user, it is possible to return to previous stages and make the necessary modifications of constraints and input data.
The integrated decision support system was developed to help machine tool designers to obtain a high-quality (and if possible optimal) architecture of transfer machines. The system supports the different stages of the logical layout design of a transfer machine: modeling of a part to be machined, process planning, optimization of the machine configuration, its preliminary 3D layout and cost estimation. The optimization problem of the logical layout is to minimize the number of working positions and the number of spindle heads by assigning the manufacturing operations to positions and choosing adequate cutting modes for each spindle head.
5.4. 3D-model and cost estimation The obtained logical layout defines the general configuration of a transfer machine and enables designers to complete this logical architecture by selecting the corresponding modular equipment from the library of standard units of the proposed decision support system. At first, designers specify the overall dimensions of the movable table and place the part to be machined on it. The part position defines the angles and positions of the spindle heads.
The perspectives of this research consist in the improvement and extension of the suggested approach for a larger class of manufacturing systems: linear transfer machines, transfer lines with buffers, multi-flow transfer lines, assembly lines etc. Another promising approach is the integration of the process planning and logical layout steps in a common optimization model using heuristics and meta-heuristics.
Then, designers define the dimensions and the specifications of the required equipment that will automatically be designed using the graphical library of standard units. Finally, designers can obtain a preliminary 3D-model of the machine.
Acknowledgements: The authors thank Chris Yukna for the help in checking the English. REFERENCES
In order to estimate the total machine cost, additional devices are to be selected, like control, tool storage, loadingunloading systems. This choice is guided by some automatically generated suggestions and accompanied by the verification of compatibility with all previous decisions. The costs of all selected devices are obtained from the database which contains market prices of standard units (spindle heads and other machine elements). The total cost estimation enables designers to formulate a commercial offer for customers. Therefore, using the decision support system, machine tools manufacturers can provide their clients with technological plans and a commercial offer in really short times. If clients accept this offer then the detailed design of the machine with the chosen configuration is to be prepared in order to establish a
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