# Analytical synthesis model of the manufacturing task for design of flexible systems for the round shafts processing.

1. INTRODUCTION

Flexible manufacturing systems (FMS) are adapted to the manufacturing task. There is no "general" FMS, but only adapted FMS to the peculiarities of an item class or family--in this analyzed case, the flexible manufacturing system for round shafts processing.

In papers, especially in those technology, item family, variant or item oriented ones, this considered as technological entity, which can be processed by means of mechanical processes, having given configurative-geometrical and technological data, know from the lingvistic classification grounded on the morphological analysis method (Kusiak, 1993). It can't be used in this form in an analytical synthesis model of production task, which could be used as basis of the flexible manufacturing systems designing.

In the paper it is presented an analytical synthesis model of the production plan for any manufacturing systems comprising family, variant and specific individual features of all the items being parts of them, grounded on paper (Fota, 2004).

Laying on the grounds of flexible manufacturing systems designing for processing round shafts the generalized manufacturing task was fixed before, on grounds of the typological nucleus, which includes the whole typology of possible items belonging to an item class, family or variant, limited by constrictions to an imposed field.

The stages as below were covered: a. The synthesis method of the current manufacturing task was drawn up by the analysis and mathematical formalization of the items features (round shafts); b. On grounds of the generalized analytic and global synthesis model of the manufacturing task for designing any flexible system for the round shafts processing, generalized item models, hypothetical and representative items for the family (F) or variant (V) of particular real items ([I.sub.k]), were drawn up. The generalized item includes all constructive-geometrical elements of the multitude of real, factual items of the represented family or variant.

2. FAMILY, VARIANT AND INDIVIDUAL FEATURES OF THE SHAFTS CLASS

Family features are those which separate items of a class in item families. These are configurative-geometrical features, constructive functions, which allow their severance in different constructive families.

Item family is a relative item collection by geometrical configuration, dimensional and sequence processing attributes in their manufacturing. For example, the specific element of separation in families of the circular shafts is their outer and inner geometrical form, the specific of their external geometrical configuration.

Variant features are separing items of a family in item variants or sorts. For example, the main separating parameters in variants of the circular shafts are the bearing type, placing manner, transmission of the driving couple, place of disposition of the transmitting elements, type of transmitting elements of the couple.

Individual features are those specific peculiar features of an item which are representing constructive-technological entities by awarding a functional part. For example, for the circular shafts, these are: the supporting function, presence of screws, circular canals, bevel cants, conics, spacers, polygonals, eccentricities, cams, a.o.

In this paper the above features will be symbolized as follows: [F.sub.f]--family features, [F.sub.v]--variant features, [F.sub.id] individual features, [F.sub.m]--main features and [F.sub.s]--subordinated features. Acording to (Malta, 2005) setting up of item families and variants in a class comes to dividing a collection of goods in sub-multitudes and the item entity is determined by establishing an object's belonging to a given multitude / submultitude. These constructive-geometric components were ordered in a logic and natural sequence (Beno, 2003).

In this manner six types of generalized item models were drawn up, laying on the grounds of configuring and sizing the flexible manufacturing system for processing round shafts: the model of generalized item of compact, typical, asymmetrical, external configured round shafts family (RSF); the model of generalized item of round gap shafts family (GSF); the model of generalized item of polygonal/conic round shafts (PSF); the model of generalized item of axles and spindles family (ASF); the model of generalized item of threaded shafts family (TSF); the model of generalized item of spherical shafts family (SSF).

It is resulting that all above named partitions are exclusively disjointed by the family, variant and individual separation functions of the table and consequently, are disjointed entities (sub-multitudes).

The family features matrix [[F.sub.f]M] can be defined as a matrix having heuristic-factual elements, representing marks of the items, variants matrices. The variant feature matrix [[F.sub.v]M] being a matrix with heuristic-factual elements, representing marks of the individual items matrices. The individual item features matrix [[F.sub.id]M] being a matrix with heuristic-factual elements representing marking parts of the separation function [f.sub.i]([p.sub.j]) where [p.sub.j] are separation function which are determining the multitude of families, variants and individual guide-marks.

2.1 Synthesis of the circular shafts families and variants.

The selection coefficients (indexes) matrix can be defined as the same type matrix [[F.sub.f]M], having n x m dimensions, and elements [c.sub.ji], 1 [less than or equal to] j [less than or equal to] m, 1 [less than or equal to] i [less than or equal to] n; m = v, n = f (where f - family and v- variant), with [c.sub.ji] : B [right arrow] B = {0, 1}.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

Variant features and Individual Items matrices are treated similarly. For each [[F.sub.v]M] and [[F.sub.id]M] similarly can be written dependences between marks and variants, respectively individual items, marks conditions, specific functions, constrictions and matrices of selection coefficients [[F.sub.f]M].

Structural matrix of family, variant and of individual items can be defined as being outcome of matrices:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Resulting matrices:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Similar to write the other two structural matrices of variant (SMV) and individual items ([SMI.sub.k]). Matrix expressions (3) afford the logic engineering model of family (F), variants (V) and individual items ([I.sub.k]) composing. From the above matrix relations, characteristic logical models of any (F, V, [I.sub.k]) can be derived. For example is writing the relation (4).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The above logical relations afford only constructive-functional composing of F, V, [I.sub.k], not its geometric-constructive configuration. Content of the assigned [f.sub.ij] functions represents a data basis problem, which will be presented later. The model presented hereby can be integrated in a generalized and global synthesis model of the manufacturing task for any FMS designing, (Shlvanand, & all., 2006).

On grounds of the manufacturing task synthesis model for the class of circular shafts elaborated in the paper stay structural synthesis matrices of the class features [SMCL], general features [SMG], family features [SMF], variant features [SMV] and the item's individual features [[SMI.sub.k]]. Using the notation [M.sub.a][T.sub.a] ([I.sub.k]) for the manufacturing task [3] depending on individual items [I.sub.k], 1 [less than or equal to] k [less than or equal to] r and noting with [[SMM.sub.a][T.sub.a]] - the synthesis matrix of the manufacturing task for circular shafts, the last matrix shall be expressed as:

[[sMM.sub.a][T.sub.a]] = [SMCL] x [SMG] x ([SMF] + [SMV] + [[SMI.sub.k]]) (5)

2.2 The graphical model of the generalized item

The generalized item is a hypothetical and representative item of a family (F) or variant (V) of real, peculiar items ([I.sub.k]). It includes all the geometrical-constructive component parts of the factual item multitude from F or V, by means of the [f.sub.ij] assigned functions and is described by the characteristic function ([f.sub.c]). Its composing is given by matrix relations (3). The geometrical-constructive configuration of any items ([I.sub.k]) is given by an ordering rule of the [f.sub.ij] assigned functions in the characteristic function ([f.sub.c]). The ordering rule is established by an engineering heuristic by using features of ordered sequence. This ordered sequence leads to the construction of a specific, filled, increment shaft, with external configuration, radial-axial bearing at both ends one--piece cog wheel in the center and right remate grooves. The real and peculiar item construction is shown in figure 1.

[FIGURE 1 OMITTED]

3. CONCLUSION

There will be created a data base for the synthesis of the geometric representation from the manufacturing task references, and by the applicative research there will be performed the simulation on the computer for real manufacturing items. The simulating program realized has as objective the application of flexible manufacturing systems for processing round shafts. Conclusion regarding time and working station number of FMS selection as well as machine number of each working station are resulting. These conclusions will be used in elaborating general flexible manufacturing systems strategies of round shafts processing.

Acknowledgement: This paper is a result of the research from the scientific project CNCSIS, code PCE_756 / 2008.

4. REFERENCES

Beno, B. (2003). Manufacturing: Design, Production, Automation and Integration, Marcel Dekker, ISBN: 08247-4273-7, New York, NY, USA

Fota, A. (2004). Machine systems design. Modelling and simulation, Transilvania University Publishing House, Brasov, Romania

Kusiak, A. (1993). Part families selection model for flexible manufacturing systems, proc. Annual IIE Conf., Louisville, KY, 1993, p. 575

Malta, A. & Semeraro, Q. (2005). Design of Advanced Manufacturing Systems, Springer Verlag, Berlin

Shivanand, M. K., Benal, M. M. & Koti, V. (2006). Flexible Manufacturing Systems, Editor: New Age International, ISBN 8122418708, 9788122418705

Flexible manufacturing systems (FMS) are adapted to the manufacturing task. There is no "general" FMS, but only adapted FMS to the peculiarities of an item class or family--in this analyzed case, the flexible manufacturing system for round shafts processing.

In papers, especially in those technology, item family, variant or item oriented ones, this considered as technological entity, which can be processed by means of mechanical processes, having given configurative-geometrical and technological data, know from the lingvistic classification grounded on the morphological analysis method (Kusiak, 1993). It can't be used in this form in an analytical synthesis model of production task, which could be used as basis of the flexible manufacturing systems designing.

In the paper it is presented an analytical synthesis model of the production plan for any manufacturing systems comprising family, variant and specific individual features of all the items being parts of them, grounded on paper (Fota, 2004).

Laying on the grounds of flexible manufacturing systems designing for processing round shafts the generalized manufacturing task was fixed before, on grounds of the typological nucleus, which includes the whole typology of possible items belonging to an item class, family or variant, limited by constrictions to an imposed field.

The stages as below were covered: a. The synthesis method of the current manufacturing task was drawn up by the analysis and mathematical formalization of the items features (round shafts); b. On grounds of the generalized analytic and global synthesis model of the manufacturing task for designing any flexible system for the round shafts processing, generalized item models, hypothetical and representative items for the family (F) or variant (V) of particular real items ([I.sub.k]), were drawn up. The generalized item includes all constructive-geometrical elements of the multitude of real, factual items of the represented family or variant.

2. FAMILY, VARIANT AND INDIVIDUAL FEATURES OF THE SHAFTS CLASS

Family features are those which separate items of a class in item families. These are configurative-geometrical features, constructive functions, which allow their severance in different constructive families.

Item family is a relative item collection by geometrical configuration, dimensional and sequence processing attributes in their manufacturing. For example, the specific element of separation in families of the circular shafts is their outer and inner geometrical form, the specific of their external geometrical configuration.

Variant features are separing items of a family in item variants or sorts. For example, the main separating parameters in variants of the circular shafts are the bearing type, placing manner, transmission of the driving couple, place of disposition of the transmitting elements, type of transmitting elements of the couple.

Individual features are those specific peculiar features of an item which are representing constructive-technological entities by awarding a functional part. For example, for the circular shafts, these are: the supporting function, presence of screws, circular canals, bevel cants, conics, spacers, polygonals, eccentricities, cams, a.o.

In this paper the above features will be symbolized as follows: [F.sub.f]--family features, [F.sub.v]--variant features, [F.sub.id] individual features, [F.sub.m]--main features and [F.sub.s]--subordinated features. Acording to (Malta, 2005) setting up of item families and variants in a class comes to dividing a collection of goods in sub-multitudes and the item entity is determined by establishing an object's belonging to a given multitude / submultitude. These constructive-geometric components were ordered in a logic and natural sequence (Beno, 2003).

In this manner six types of generalized item models were drawn up, laying on the grounds of configuring and sizing the flexible manufacturing system for processing round shafts: the model of generalized item of compact, typical, asymmetrical, external configured round shafts family (RSF); the model of generalized item of round gap shafts family (GSF); the model of generalized item of polygonal/conic round shafts (PSF); the model of generalized item of axles and spindles family (ASF); the model of generalized item of threaded shafts family (TSF); the model of generalized item of spherical shafts family (SSF).

It is resulting that all above named partitions are exclusively disjointed by the family, variant and individual separation functions of the table and consequently, are disjointed entities (sub-multitudes).

The family features matrix [[F.sub.f]M] can be defined as a matrix having heuristic-factual elements, representing marks of the items, variants matrices. The variant feature matrix [[F.sub.v]M] being a matrix with heuristic-factual elements, representing marks of the individual items matrices. The individual item features matrix [[F.sub.id]M] being a matrix with heuristic-factual elements representing marking parts of the separation function [f.sub.i]([p.sub.j]) where [p.sub.j] are separation function which are determining the multitude of families, variants and individual guide-marks.

2.1 Synthesis of the circular shafts families and variants.

The selection coefficients (indexes) matrix can be defined as the same type matrix [[F.sub.f]M], having n x m dimensions, and elements [c.sub.ji], 1 [less than or equal to] j [less than or equal to] m, 1 [less than or equal to] i [less than or equal to] n; m = v, n = f (where f - family and v- variant), with [c.sub.ji] : B [right arrow] B = {0, 1}.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)

Variant features and Individual Items matrices are treated similarly. For each [[F.sub.v]M] and [[F.sub.id]M] similarly can be written dependences between marks and variants, respectively individual items, marks conditions, specific functions, constrictions and matrices of selection coefficients [[F.sub.f]M].

Structural matrix of family, variant and of individual items can be defined as being outcome of matrices:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Resulting matrices:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Similar to write the other two structural matrices of variant (SMV) and individual items ([SMI.sub.k]). Matrix expressions (3) afford the logic engineering model of family (F), variants (V) and individual items ([I.sub.k]) composing. From the above matrix relations, characteristic logical models of any (F, V, [I.sub.k]) can be derived. For example is writing the relation (4).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The above logical relations afford only constructive-functional composing of F, V, [I.sub.k], not its geometric-constructive configuration. Content of the assigned [f.sub.ij] functions represents a data basis problem, which will be presented later. The model presented hereby can be integrated in a generalized and global synthesis model of the manufacturing task for any FMS designing, (Shlvanand, & all., 2006).

On grounds of the manufacturing task synthesis model for the class of circular shafts elaborated in the paper stay structural synthesis matrices of the class features [SMCL], general features [SMG], family features [SMF], variant features [SMV] and the item's individual features [[SMI.sub.k]]. Using the notation [M.sub.a][T.sub.a] ([I.sub.k]) for the manufacturing task [3] depending on individual items [I.sub.k], 1 [less than or equal to] k [less than or equal to] r and noting with [[SMM.sub.a][T.sub.a]] - the synthesis matrix of the manufacturing task for circular shafts, the last matrix shall be expressed as:

[[sMM.sub.a][T.sub.a]] = [SMCL] x [SMG] x ([SMF] + [SMV] + [[SMI.sub.k]]) (5)

2.2 The graphical model of the generalized item

The generalized item is a hypothetical and representative item of a family (F) or variant (V) of real, peculiar items ([I.sub.k]). It includes all the geometrical-constructive component parts of the factual item multitude from F or V, by means of the [f.sub.ij] assigned functions and is described by the characteristic function ([f.sub.c]). Its composing is given by matrix relations (3). The geometrical-constructive configuration of any items ([I.sub.k]) is given by an ordering rule of the [f.sub.ij] assigned functions in the characteristic function ([f.sub.c]). The ordering rule is established by an engineering heuristic by using features of ordered sequence. This ordered sequence leads to the construction of a specific, filled, increment shaft, with external configuration, radial-axial bearing at both ends one--piece cog wheel in the center and right remate grooves. The real and peculiar item construction is shown in figure 1.

[FIGURE 1 OMITTED]

3. CONCLUSION

There will be created a data base for the synthesis of the geometric representation from the manufacturing task references, and by the applicative research there will be performed the simulation on the computer for real manufacturing items. The simulating program realized has as objective the application of flexible manufacturing systems for processing round shafts. Conclusion regarding time and working station number of FMS selection as well as machine number of each working station are resulting. These conclusions will be used in elaborating general flexible manufacturing systems strategies of round shafts processing.

Acknowledgement: This paper is a result of the research from the scientific project CNCSIS, code PCE_756 / 2008.

4. REFERENCES

Beno, B. (2003). Manufacturing: Design, Production, Automation and Integration, Marcel Dekker, ISBN: 08247-4273-7, New York, NY, USA

Fota, A. (2004). Machine systems design. Modelling and simulation, Transilvania University Publishing House, Brasov, Romania

Kusiak, A. (1993). Part families selection model for flexible manufacturing systems, proc. Annual IIE Conf., Louisville, KY, 1993, p. 575

Malta, A. & Semeraro, Q. (2005). Design of Advanced Manufacturing Systems, Springer Verlag, Berlin

Shivanand, M. K., Benal, M. M. & Koti, V. (2006). Flexible Manufacturing Systems, Editor: New Age International, ISBN 8122418708, 9788122418705

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Author: | Fota, Adriana; Buzatu, Constantin; Barabas, Sorin |
---|---|

Publication: | Annals of DAAAM & Proceedings |

Article Type: | Report |

Geographic Code: | 4EUAU |

Date: | Jan 1, 2009 |

Words: | 1564 |

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