Description of flexible assembly systems by means of Coloured Object Observable Petri Net.

Cyklis, J. ; Zajac, J. ; Slota, A. 等

Abstract: In the paper Flexible Assembly Systems (FAS) are considered. Authors specify information which is necessary to build FAS model. The information is divided into three groups: system definition, products' structure description and products' specification. Then a procedure of creation FAS model, with the use of Coloured Observable Petri Nets (COPN), is presented.

Key words: flexible assembly, modelling, Petri Nets

1. INTRODUCTION

Flexibility allows manufacturing system to a fast and cost effective reconfiguration so it can adapt to changes inside the system structure and also variable production orders. Flexible Assembly Systems (FAS) should enable assembling different products and different versions of a product according to specifications demanded by customers. Analysis and control of such systems require a model describing the system's operation. The goal of the authors is to work out a method for modelling flexible assembly systems. Authors point out how information describing assembly system may be structured and then propose a procedure--how this information may be converted into a model.

Information concerning FAS operation may be divided into two groups: description of the system and description of products' structure assembled in the system.

2. FAS DESCRIPTION

Description of the system consists of:

--a list of the system components: assembly stations (AS), transport devices (AGV), automated storage/retrieval system (AS/RS) and input/output buffers (BUF),

--structure of FAS components connections,

--definition of components operation.

Structure of FAS components defines possible flow of assembled elements and sub-assemblies through the system. A sample of the diagram showing connections of an assembly station AS, two input buffers BUF1, BUF2 and output buffer BUF3 is presented in figure 1. FAS components' connections may also be defined in the matrix form.

[FIGURE 1 OMITTED]

Definition of components operation comprises the list of activities executed by the component and permissible sequence of activities execution. To unify components description three general activities for each component are defined:

--[A.sub.IN]--taking elements/sub-assemblies from the preceding component,

--[A.sub.PROC]--processing elements/sub-assemblies (for AS it is an assembly operation, for AGV it is a transport activity),

--[A.sub.OUT]--transferring elements/sub-assemblies to the subsequent component.

All the components work in a repetitive cycle executing activities [A.sub.IN], [A.sub.PROC], [A.sub.OUT], however for selected components some activities may be excluded from the cycle. For example BUF does not perform any processing so it can not execute the activity [A.sub.PROC], AS/RS which acts both as a source and destination of components in the system, can only execute activities [A.sub.IN] and [A.sub.OUT].

3. PRODUCT DESCRIPTION

3.1 Product structure

Product structure definition describes what elements/subassemblies it consists of and in what quantities:

[P.sub.j] = [n.sub.1] * [SA.sub.1] + [n.sub.2] * [SA.sub.2] + ... + [n.sub.n] * [SA.sub.n] where:

[P.sub.j]--identifier of jth product,

[SA.sub.i]--identifier of ith element/sub-assembly,

[n.sub.i]--number of sub-assemblies [SA.sub.i] in product [P.sub.j].

Any sub-assembly [SA.sub.i] is defined in the same way. It leads to a hierarchical recursive product structure description (Biswas et al., 1995). Each sub-assembly is created during one assembly operation. For each sub-assembly there is a list of assembly stations where the operation may be executed and list of buffers where it may be stored.

3.2 Product specification

To manufacture customized products assembling some elements/sub-assemblies to the product may be optional. Moreover products/sub-assemblies may be assembled using different versions of elements. Specification which elements should be assembled and what versions of elements should be used is built on the basis of customers' orders.

4. MODEL CREATION

Permissible operation of the assembly system components is defined by information included in section 2. This information together with information from section 3.1 defines how the system works while assembling products of the defined structure. The above information is used for building model of the assembly system.

For modelling discrete assembly systems different tools are used: (Zurek & Knast, 1998; Zha et al., 1998) propose modelling assembly processes with the use of Petri Nets, (Su & Smith, 2003) uses IDEF0 language for simulation and optimization of FAS. In the paper, Coloured Object Observable Petri Net (COPN) is chosen as a modelling tool. So far, COPN has been used, with good results, in modelling of machining systems because of their observability features: states of systems' objects may be directly determined on the basis of the current state of the model (Cyklis & Slota, 2000 and 2002).

Using COPN a model template for each component of FAS is built. Such the model of an assembly station is presented in figure 2.

[FIGURE 2 OMITTED]

Transitions [t.sub.IN], [t.sub.PROC], [t.sub.OUT] represent activities [A.sub.IN], [A.sub.PROC], [A.sub.OUT] respectively.

Such template is used for creation model of AS. For each sub-assembly type assembled on a given assembly station (described by product structure definition) one copy of model template is built.

The process of model creation will be illustrated for the part of FAS presented in figure 1. Let's assume that the assembly station assemblies two different products:

--the first product consists of two elements

[P.sub.1] = [SA.sub.1] + 2 * [SA.sub.2]

--the second one consists of three elements

[P.sub.2] = 2 * [SA.sub.3] + [SA.sub.4] + 2 * [SA.sub.5]

Elements for [P.sub.1] are stored in BUF1, elements for [P.sub.2] are stored in BUF2 and final products are stored in BUF3. There are three different versions of any element used in assembly operations ([SA.sub.1,i] are versions of SA1, for i=1,2,3). Figure 3 presents a model of the assembly station which assembles these two products.

[FIGURE 3 OMITTED]

In COPN places represent states of the system's objects. In case of FAS these are components of the system and elements/sub-assemblies/products. Objects are represented in the model by tokens. Different versions of elements are represented by tokens of different colours. During simulation/control tokens are moved between places what corresponds to change of objects' state. Execution of an assembly operation (in the presented example firing transitions [t.sub.PROC]) means that a set of elements is "transformed" into a new element: sub-assembly/product. This fact is included in the model by assigning sub-assembly/product specification to the transition representing the assembly operation. Firing such a transition changes elements' representation in the model: set of tokens representing separate elements is replaced by a token representing the sub-assembly/product according to the subassembly/ product specification.

[FIGURE 4 OMITTED]

Sample COPN models of other configurations of buffers, transport and storage devices are presented in (Cyklis et al., 2005). Models of FAS components are integrated on the basis of structure of FAS components connections (section 2). If assembly station takes elements for product P1 from BUF1 transition tOUT1 in model of BUF1 is equivalent to transition tIN1 in model of AS. Other transitions are merged in the same way. To perform a simulation experiment specification of products that are to be assembled is necessary. For example there may be an order for product [P.sub.1] composed of element [SA.sub.1] version 2 and element [SA.sub.2] version 3 ([P.sub.1]=[SA.sub.1,2] + 2 * [SA.sub.2,3]). Such specification is attached to the model dynamically and it defines colours of tokens to be used for firing transitions.

5. CONCLUSION

Structure of FAS description presented in the paper allows separation of two kinds of information: description of the system behaviour and specification of products to be assembled in the system. The first one is used for creation COPN model of FAS, the second one is attached to the model to make a simulation experiment or for control purposes. Proposed procedure of model creation is a base for further work. It will concern developing an algorithm for automatic creation COPN model of FAS.

6. REFERENCES

Biswas, G., Bagchi, S. & Saad A. (1995). Holonic Planning and Scheduling for Assembly Tasks. TR CIS-95-01, Center for Intelligent Systems, Vanderbilt University

Cyklis, J. & Slota, A. (2000). FMS model based on Coloured Object Observable Petri Nets, Proceedings of DAAAM 2000, Katalinic, B. (Ed.), pp. 105-106, ISBN 3-901509-13-5, Opatia, October 2000, DAAM International, Viena

Cyklis, J. & Slota, A. (2002). Hierarchical Coloured Object Observable Petri Net applied for FMS modelling. Proceedings of the 13th International DAAAM Symposium, Katalinic, B. (Ed.), DAAM International, Vienna

Cyklis, J., Zajac, J. & Slota, A. (2005). Modelling components of flexible assembly system by means of Coloured Object Observable Petri Nets, Proceedings of 6th ICCC, Miskolc

Su, Q. & Smith, S. (2003). An Integrated Framework for Assembly-Oriented Product Design and Optimization. Journal of Industrial Technology, Vol. 19, No. 2

Zha, X., Lim, S. & Fok, S. (1998). Integrated knowledge-based Petri net intelligent flexible assembly planning. Journal of Intelligent Manufacturing, Vol. 9, No. 3, pp. 235-250

Zurek, J. & Knast, P. (1998). Modelowanie procesow technologicznych montazu za pomoca sieci Petriego, Wydawnictwo Politechniki Poznanskiej, ISBN 83-7143-078-7, Poznan