Analytical synthesis model of the manufacturing task for design of flexible systems for the round shafts processing.
Fota, Adriana ; Buzatu, Constantin ; Barabas, Sorin 等
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,
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