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
Grey relational analysis was first proposed by Dr. Deng in 1982 to fulfil crucial mathematical criteria for dealing
with poor, incomplete and uncertain system (Deng, 1989). Black, white and grey has special meaning in the grey
relational analysis. Black indicate the system have no information, white indicate the system have full of
information and grey represent the level of information between black and white. This technique solves the
problem of optimization of multiple-performance characteristics of modern machining method.
In GRA, for optimization of multiple performance characteristics following steps are followed (Rao, 2009):
• Conduct the experiments and tabulate the data.
• Normalization of the collected data. It is the process of transforming the original sequence to a
comparable sequence. Normalization is done in the range of zero and one, the process is known as grey
relational generating. Three types of data normalization are there in the GRA, lower the better (LB), the
higher the better (HB) and nominal the best (NB).
Lower is better (LB),
(i)
Higher is Better (HB),
Nominal is best (NB),
(ii)
(iii)
Where i = 1,2,………,n; k = 1,2,……, p; is normalized value of the kth element in the ith
sequence, is desired value of the kth quality characteristic, max is the largest value of
, and min is the smallest value of , n is the number of experiments and p is the number
of quality characteristics.
• Calculation of grey relational coefficient.
• Calculation of grey relational grade.
• Predict the single optimal setting for multi performance characteristics.
• Conduct confirmation experiments at optimum level of process parameters.
In GRA, optimization of multiple performance characteristics is converted into an optimization of single
performance characteristic called grey relational grade. Gray relational grade is the weighting sum of grey
relational coefficient.
3.1 Application of GRA
This methodology has been employed successfully for optimization of multiple responses. In last few years, grey
relational analysis with Taguchi method has been extensively used by various researchers for optimization of
multi-performance characteristics because it gives better results as compared to GRA.
3.1.1 Conventional Machining Processes
Ranganathan (2011) optimized the effect of cutting speed, feed rate, depth of cut and workpiece temperature by
using multi-response analysis. Using grey analysis, a grey relational grade is obtained and based on this value an
optimum level of cutting parameters has been identified. Liang Ku (2010) used taguchi Design methodology to
conduct the experiment and the multiple performance characteristics correlated with surface roughness and bush
length was investigated by grey relational analysis systematically and comprehensively. The experimental results
show that the thermal friction drilling revealed beneficial effects on Surface roughness and Bush Length for
drilling processes. Moreover, the optimal machining parameters for multiple performance characteristics
associated with Surface Roughness and Bush Length were attained. Tzeng (2009) investigated the optimization
of CNC turning operation parameters using grey relational analysis. Results show that depth of cut influence the
roughness average most. Haq (2008) presented a new approach for the optimization of drilling parameters on
drilling Al/SiC metal matrix composite with multiple responses based on orthogonal array with grey relational
analysis. A grey relational grade is obtained from the grey analysis. Based on the grey relational grade, optimum
levels of parameters have been identified and significant contribution of parameters is determined by Analysis of
variance.
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