Page 190 - Modular design for machine tools

150 Modular Design Guide and Machine Tools Description

resulting in a considerable number of variants as shown together
in Fig. 4-16, although the structural stiffness is not so high. In contrast,
pattern C, i.e., double closed type, shows completely opposite behavior.
In fact, there have been a considerable number of research works to
exemplify the higher potential of the structural description. Such
research work range from the similarity evaluation of the structural con-
figuration for investigating the possibility of modular design to the vari-
ant and free designs of the machine tool.

4.2.1 Similarity evaluation of structural
configuration—availability constraints
of modular design
The structural pattern can provide us with valuable leading informa-
tion as follows.

1. Fundamental shape of each structural module
2. Leading function of each structural module
3. Adjacency relationships between both modules
4. Starting and terminal vertices within FOF
5. Total number of structural modules
6. Pattern of FOF

On the basis of these information, the structural similarities of both
machine tools can be calculated, using both the rates of commonness and
pattern similarity, as typically proposed by Ito and Shinno [16].
More specifically, the rate of commonness can be defined as the rela-
tive value of the identical to whole numbers of the structural modules
between both structural patterns. Then it can be calculated by using the
information for the fundamental shape of each structural module, lead-
ing function of each structural module, and total number of structural
modules in the structural pattern.
By assuming a set to be a machine tool as a whole, the rate of com-
monness can be represented with a graph such as shown in Fig. 4-17.
Then, by defining |X | and |Y |as the kinds of structural modules in
s
s
sets X and Y , respectively, and after eliminating the duplicate struc-
s
s
tural modules in both sets, structural modules in both sets are in one-
to-one correspondence, as shown in Fig. 4-17. Given that one structural
module, mathematically called the vertex, in the set |X | cannot be
s
connected with more than one structural module in the set |Y |, the rate
s
of commonness S can be written as
r
(|R(X ) |R(Y )|)/(|X | |Y |) 2|R(X )|/(|X | |Y |)
S r s s s s s s s
)|/(|X | |Y |) (0 S 1) (4-2)
2|R(Y s s s