optimization of collar cleaning machine using … · 2018. 11. 26. · can use grey relational...

OPTIMIZATION OF COLLARCLEANING MACHINE USING

TAGUCHI METHOD

M. Paulraj1, R.Immanual2,R.Immanuai3, J. J. Adri Jovin4

K. Augustine Babu5,1Professor, Department of Computer Science and Engineering,2 Assistant Professor, Department of Mechanical Engineering,

3Associate Professor , Department of Mathematics,4Assistant Professor, Department of Information Technology

5Sri Ramakrishna Institute of Technology,

October 13, 2018

AbstractThe world we live today is a world where everything is

fast paced with the fittest surviving. Technology is rapidlygrowing but still washing the stains of a collar of a shirt isvery difficult and hence a machine for washing the stainsthat still persist even after a machine wash. This machinecan wash the stains even before the machine wash. To getthe optimized design of this machine the weight and cost ofthe design optimized built on Grey-Taguchi analysis. Basedon the optimized design the product was developed.

Key Words: Collar cleaning machine,Cost,Weight,TaguchiMethod,Grey Relational Grade;

1 INTRODUCTION

The laundering process has substantial environmental impact dueto the ingestion of energy, water and chemicals[01]. Washing clothes

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International Journal of Pure and Applied MathematicsVolume 120 No. 6 2018, 849-863ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

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are one of the most extensive housework in the world [02].In mostof the time, when we use the washing machines for our time con-venience, there is a chance of poor washing especially in shirt col-lars.To satisfy the customers regarding this problem some washingmachines have a separate top in which we can wash our clothesby hands than we can put in to the washing machine. Indulgentcustomers behaviour and retorts to product design and marketingare grave for manufacturers [03]. To satisfying both current andpotential customers needs to make a collar washing machine whichwould be attached to the normal washing machine.When design aproduct to commercialize it, two major things play the importantrole first one is cost and second one is weight[04]. For this projectboth cost and weight of the design should be minimum. So thatit is a multi objective problem. By using Taguchi method a singleobjective problem only be solved. For multi objective problem onecan use Grey relational grade Taguchi method.Sivaprgash et.al [05] attempts to find optimal condition the fric-tional coefficient and to reduce the wear rate by optimizing the biasvoltage, target current, pulse frequency, gas flow rate and work dis-tance using the Taguchi grey relational analysis. Silaskar SM et.al[04] attempted to optimize the overall weight of a ball valve forcost effectiveness by modification in the design of valve parts usingthe concept of value engineering. Rajkumar et. al [06] in theirwork find the weld bead for better the depth of penetration andthe lesser the bead width by optimizing the input current, voltageand feed. Chokkalingam et.al [07] studied the effect of micro alloy-ing elements like vanadium, niobium and titanium on the hardnessand tensile strength of the normalized cast steel using the Taguchimethod.This research is aimed at optimizing the design of a sustainableCollar cleaning machine which can have low cost and weight. Thisis achieved by Grey Taguchi method.

2 Multi objective Taguchi centered grey

relation optimization theory

Optimization of design parameters using a least number of experi-ments by espousing the Taguchi grey method provides high quality

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result [08,09] . In Taguchi method, the S/N ratio is utilized tocompute the deviation between the measured value and the antic-ipated value. For this S/N ratio calculation, a loss function canbe transmuted into S/N ratio. Usually, this loss function is alien-ated into three categories namely lower the better, higher the betterand nominal the best [10] . In this work, lower the better liked tofix the desired value. The loss functions for the lower the bettercharacteristic can be articulated as

Lij = 1/n∑

yij2 (1)

nij = −10log(Lij) (2)

where, Lij is the loss function of the i th performance character-istic in the j th experiment, y ijk is the experimental value of thei th performance characteristic in the j th experiment at the k thtrial, and n is the number of trials.Moreover, the Taguchi method isa single response characteristic optimization approach. Thereforemulti performance approach such as grey relative grade is consid-ered to solve this problem. The objective of the grey relation anal-ysis is used to find out the parameters that give better performance[11,12].In the grey relation analysis, the normalization process is essen-tial because the extreme deviations in S/N ratio are converted intodimensionless as zero and unity by Eq. ( 3 ). Secondly, this nor-malized S/N ratio is transformed into grey relation coefficient usingEq. ( 4 ) which represents the correlation between the required andactual S/N quantitative relation. Then by Eq. ( 5 ) the Grey rel-ative grade is calculated by averaging the grey relation constant.Thus the multiple performance response can be converted into asingle grey relative grade. The normalized S/N ratio ij for the ithperformance characteristic in the j th experiment can be expressedas

xij =nij −minnij

maxnij −minnij

(3)

where ij is the value after the grey relational generation, min ijis the smallest value ji of the j th response, and max ij is the largestvalue of ij for the j th response.The grey relational coefficient ζijfor the j th performance characteristic in the j th experiment can

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be expressed as

ζij =miniminj|x0i − xij|+ ζmaximaxj|x0i − xij|

|x0i − xij|+ ζmaximaxj|x0i − xij|(4)

The grey relational grade j can be obtained

γj =1

m

n∑

k=1

wiζij (5)

where γj is the grey relational grade for the j th experiment, withe weighting factor for the ith performance characteristic, and mis the number of performance characteristics.

3 Methodology

3.1 Materials

The materials used for this study were Steel, Acrylic, Aluminium.These materials are widely available and their machinability waseasy. So that we have to choose these materials to optimize theirlength,width,height based on design for minimum weight and min-imum cost.

3.2 Parameters and levels

Several trials were conducted and finally the levels of the parameterswere determined. The selection of parameters dependent upon theweight and cost of the materials. The parameters and their rangesare given in Table 1 . L 9 orthogonal array was used for conductingthe experiments.

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Table 1 Parameters and their Levels

3.3 Cost and weight

The cost of the product based on the input parameters along withthe design was getting from the industries. The weight of the prod-uct was getting from the density of the input materials multipliedwith the volume of the product based on the input parameters alongwith the design. The design of the product as showed in figure 1.

Figure 1 Product design

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4 Results and Analysis

4.1 Mean response

The average value for each factor at different levels is referred asthe mean response. The average values of S/N data and cost dataare given in Table 2 and Table 3 respectively. The S/N ratio andthe mean response for the factors are shown in the Fig.2 and Fig.3respectively. From these observations to reduce the cost we haveto fix the design parameters as A2,B1,C1,D1.The average valuesof S/N data and weight data are given in Table 4 and Table 5respectively. The S/N ratio and the mean response for the factorsare shown in the Fig.4 and Fig.5 respectively. In this experiment,the level which gives the minimum cost and weight is the optimumlevel for that factor. These observations to reduce the weight fixthe design parameters as A2,B1,C1,D1.

Table 2. Average values of S/N data (COST)

Table 3. Average values of mean data (COST)

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Fig. 2. Average values of S/N ratios for each parameter atdifferent levels(Cost)

Fig. 3. Average values of hardness for each parameter at differentlevels

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Table 4. Average values of S/N data (Weight)

Table 5. Average values of mean data (Weight)

Fig. 4. Average values of S/N ratios for each parameter atdifferent levels (Weight)

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Fig. 5. Average values of Weight for each parameter at differentlevels

4.2 Grey relation analysis

The Taguchi-grey approach has been used to find out the optimalprocess parameters for multiple performance responses [13,14] . Ta-ble 6 shows the normalized, grey coefficient and grey grade of costand weight.The normalized value for S/N ratio of cost and weightwas calculated by Eq.( 3 ). The distinguishing coefficient was con-sidered as 0.5 for calculating the grey relation coefficient. Thengrey relation coefficient and grey grade were determined by usingthe Eq.( 4 ) and ( 5 ). It has been observed from the Table 6. It isinferred from these observations to reduce the cost and also reducethe weight the design parameters should be fixed as A2,B1,C1,D1.

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Table 6

The average values of S/N data and Cost data are given in Table7 and Table 8 respectively. The S/N ratio and mean response forthe factors are shown in the Fig.6 and Fig.7 respectively.

Table 7. Average values of S/N data (GREY RELATIONALGRADE)

Table 8. Average values of mean data (GREY RELATIONALGRADE)

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Fig. 6. Average values of S/N ratios for each parameter atdifferent levels (GREY RELATIONAL GRADE)

Fig. 7. Average values of GREY RELATIONAL GRADE for eachparameter at different levels

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5 CONCLUSION

The Taguchi based grey relation analysis results are summarized asfollows:

• Taguchi based grey relation analysis was employed for opti-mizing the cost and weight of the product called Collar Clean-ing Machine.

• In Taguchi method the optimal parameter for each character-istic performance was same.

• The Taguchi grey relation analysis method found out that theoptimal design parameter levels were A2,B1,C1,D1.

• Based on optimized design parameters the product developedas shown in figure 8.

Fig. 8. Product-Collar Cleaning machine

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optimization of collar cleaning machine using … · 2018. 11. 26. · can use grey relational...

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