OCTOBER 19-20, 2012 - YMCA University of Science & Technology

Proceedings of the National Conference on
Trends and Advances in Mechanical Engineering,
YMCA University of Science & Technology, Faridabad, Haryana, Oct 19-20, 2012
The permanent of the matrix (i.e. equation 2) represented is a mathematical expression in symbolic form. It
ensures an estimate of the system as a whole. The above equation (2) contains 6! terms. Each term is useful for
system assessors as each term serves as a test of the effectiveness of the relevant group in permanent of the
matrix A, i.e. per(A). Equation (2) contains terms arranged in N+ 1 groups, where N is the number of
elements..In the permanent, per(A) various groupings have their own physical significance. The first term
(grouping) represents a set of seven independent subsystem characteristics as V 1 , V 2 , V 3 ,….V 6 . As there are no
self loops with in the system itself, second groupings are absent. Each term of the third grouping represents a set
of two elements attribute loops (i.e. a ij .a ji ) and is the resultant dependence of attribute i and j and the evaluation
measure of N-2 connected terms. Each term of the fourth grouping represents a set of three element attribute
loops (a ij .a jk .a ki or its pair a ik .a kj .a ji ) and the evaluation measure of N-3 unconnected elements or attributes with
in the system. The fifth grouping contains two subgroups. The terms of first subgrouping consists of four element
attribute loops (i.e. a ij .a jk. a kl. a li ) and the 3- subsystem evaluation index component (Dm.Dn.Dp). The terms of the
second grouping are the product of two element attributes loops (a ij .a ji) ( a kl. a lk) ) and the index evaluation
component (i.e. Dm.Dn.Dp). The terms of the sixth grouping are also arranged in two subgroupings. The terms
of the first subgroupings are of five element attribute loop (i.e. a ij .a jk .a kl .a lm .a mi ) or its pair (a im .a ml .a lk .a kj .a ji ). the
second subgrouping consists of a product of two attributes loops (i.e. a ij .a ji ) and a three attribute loop (i.e.
a kl .a lm .a mk ) or its pair (i.e. a km .a ml .a lk ) and the index evaluation component (i.e. D n D p ). The terms of seventh
groupings are also arranged in three subgrouping. The terms of first subgrouping of seventh subgrouping are of
six elemental attribute loop (i.e. a ij .a jk .a kl .a lm .a mn. .a ni ). the terms of second subgrouping of seventh grouping are
of four element attribute loop (i.e. a ij .a jk .a kl .a li ) and two element attribute loop (i.e. a mn .a nm) with one - subsystem
evaluation index component (Dp). The third subgrouping of the seventh grouping is a set of 3- two element
attribute loops (i.e. a ij .a ji , a kl .a lk , a mn .a nm ) and a one - subsystem evaluation index component (Dp). Thus the
permanent function characterizes a system for selected number of attributes as it contains all possible
components of attributes and their relative importance.(h). Arrange the type of systems in descending order of
the evaluation index. The system having the highest value of the calculated index is the best choice for the given
set of attributes over their prescribed operating ranges. (i). perform the sensitivity analysis for the attributes over
the domains of influence for a few cases.
3. Formulation of The EDM process problem and its Solution
In the present work, the Electric Discharge Machining process is modeled as a process Graph Model where in the
attributes have been considered which affect the material removal rate significantly under constrained
operational conditions of the process. It has been observed that even though there are a number of controlling
factors including ambient conditions as well as related to MCU (i.e. Machine Control Unit of Electric Discharge
Machine- conventional or CNC type), but when operation is performed on a work piece with some of the desired
outcomes like surface finish, tool wear with in the prescribed limits, then several controlling variables or the
attributes are almost constant and becomes the inherent but constant attributes for a given process conditions.
Desired outcomes of the Electric Discharge machining process:
Material removal rate , MRR, Absolute wear of Tool electrode, Ua,Productivity of the machined surface, Qp,.
Wear of the Tool electrode, γ ES, ,Roughness of the machined surface, Ra,. Power consumption, P. Working
Speed, Vp, Gap Size, S
Following input parameters are considered for analyzing any of the above mentioned desired output:
(a). Current intensity, I,. Pulse time, Ta,. Pulse Interval, Tb, Working depth, h,. Polarity of the Tool electrode P(-
), Polarity of the Tool-Piece P(+)As per the technical recommendations of the Electric discharge Machine tools,
while testing generally, following considerations are generally taken into account for further process analysis:
(i). The working depth is generally kept constant and is recommended as equal to 2 mm for testing purposes.
However, once the data analysis has been carried out through the theory of experiments, higher order working
depths may be considered.
(ii). The polarity of the Tool electrode P(-) and the polarity of the Tool Piece P(+) are kept as constant and the
entire experimental data is collected and analyzed for a constant vale of P(-) and P(+), however, these variables
are not of fixed type and their variation affect the Material removal rate and the surface finish parameters
significantly..At present, in this work, a particular case of EDM process has been analyzed. It is granted that
cylindrical copper electrode is to be used as a tool and tool steel as the machining material. It is assumed to have
constant dielectric pressure and average working voltage while taking the experimental readings which are to be
used further for regression analysis. After analyzing the experimental data, as available in the literature,
following attributes or the system variables, which affect the performance parameters of the Electric Discharge
machining Model, are listed as below in their increasing order using
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