Production of nylon 6 fr lever using an injection moulding tool and identification of optimum...

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME

270

PRODUCTION OF NYLON-6 FR LEVER USING AN INJECTION

MOULDING TOOL AND IDENTIFICATION OF OPTIMUM

PROCESS PARAMETER COMBINATION

S.Selvaraj1, Dr.P.Venkataramaiah

2

1

Research Scholar, Department of Mechanical Engineering,

Sri Venkateswara University College of Engineering and

Senior Lecturer, Department of Tool & Die Making, Muruagapp Polytechnic

College,Chennai

2

Associate Professor, Department of Mechanical Engineering,

Sri Venkateswara University College of Engineering, Tirupati, Andhra Pradesh, India-

517502.

ABSTRACT

This research work on Optimization of Injection Moulding has been done in three phases. In

the first phase, an Injection Moulding Tool is designed and fabricated for FR(Forward

Reverse) lever, which is to control the direction of rotation of spindles for conventional

machines. In the second phase, the influential parameters, called input parameters which

affect the quality of FR lever are identified. The response parameters, called output

parameters such as Shrinkage and Surface Roughness which are considered as quality

characteristics of this product have also been identified. FR levers are produced using the

fabricated injection moulding tool according to Taguchi L27 OA and response data are

recorded. In the third phase, recorded experimental data are analyzed and optimum process

parameters combination has been found by a combined method which is developed from the

integration of the Principal Component Analysis (PCA) and Utility based Taguchi method.

The obtained optimum parameters combination is conformed experimentally.

Keywords: Injection Moulding, Principal component analysis (PCA), Shrinkage, Surface

roughness, Utility based Taguchi method

1.0 INTRODUCTION

Now a days, plastic products have more demand since they are of low cost, good corrosion

resistant, light weight, flexible colours and have good life also. The costs of the plastic

products are made less by production using various types of moulds. Many engineers and

researchers have made research works on optimizing process parameters on Injecion

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)

ISSN 0976 – 6359 (Online)

Volume 3, Issue 3, September - December (2012), pp. 270-284

© IAEME: www.iaeme.com/ijmet.asp

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moulding for various thermoplastic materials and attempt to reduce shrinkage and warpage.

Some authors presented few case studies on improvement of Quality characteristic of surface

roughness, shrinkage and warpage by applying Taguchi technique, Artificial Neural

Network(ANN), Genetic Algorithm(GA), Fuzzy logics and combination methods. Deng et al.

applied Taguchi’s method and regression analysis to propose an approach for determining the

optimal process parameter settings in plastic injection molding under single quality

characteristic considerations [1]. Altan et al. minimized the shrinkage of rectangular- shaped

specimens by Taguchi experimental design and Neural network to predict the shrinkage of

the part [2]. Hasan Kurtaran et al. proposed an efficient minimization method of warpage on

thin shell plastic parts by integrating finite element (FE) analysis, statistical design of

experiment method, response surface methodology(RSM), and genetic algorithm [3]. Shen et

al. minimized the shrinkage of a plastic part by using the artificial neural network and genetic

algorithm [4]. Kurtaran et al. considered mold temperature, melt temperature, packing

pressure, packing time and cooling time as the key process parameters during PIM and got

the optimum values of process parameters in injection molding of a bus ceiling lamp base to

achieve minimum warpage by using neural network model and genetic algorithm [5].

Factors that affect the quality of a molded part can be classified into four categories:

part design, mold design, machine performance and processing conditions. The part and mold

design are assumed as established and fixed. During production, quality characteristics may

deviate due to variation in processing conditions caused by machine wear, environmental

change or operator fatigue. Determining optimal process parameter settings critically

influences productivity, quality, and cost of production in the plastic injection moulding

(PIM) industry. Previously, production engineers used either trial-and-error method or

Taguchi’s parameter design or ANN, Fuzzy method or combined method to determine

optimal process parameter settings for PIM[6-12]. However, these methods are unsuitable in

present PIM because the increasing complexity of product design and the requirement of

multi-response quality characteristics. A Principal Component Analysis(PCA) has been used

for optimation of process parameters in different industrial application.

Literature review reveals that there is a lack of research on design and fabrication of

injection moulding tool and finding the optimal process parameters setting using PCA based

combined approach. Hence, this paper focused on design, fabrication of Injection mould and

production of Nylon-6 FR lever as well as the application of combined method which is

developed from the integration of the Principal Component Analysis (PCA) and Utility based

Taguchi method to determine the optimum parameter combination.

2.0 PHASE I: DESIGN AND FABRICATION OF AN INJECTION MOULDING

TOOL FOR FR LEVER

2.1 DESIGN OF AN INJECTION MOULDING TOOL FOR FR LEVER

2.1.1 Modeling of FR lever and Injection moulding tool First, F-R lever model is modeled using ProE according to standard specifications. Two plate

Injection moulding tool with taper parting surface is suitable for this kind of products and

hence it is selected in the present work. It is decided to fabricate fully Automatic Injection

moulding tool with ejectors assembly .Based upon the model of FR lever, the different parts

of the injection moulding tool is identified and a model of injection moulding tool is created

in ProE 5 wildfire. The different parts of injection moulding tool with materials and size is

listed in Table 1



272

2.1.2 Volume and Weight of FR Lever The volume and weight of FR lever are found from created model as follows

Volume of the component from model =23.750 cc

Density of the plastic material Used ( Nylon) =1.20g/cc (from standard data

book)

Weight of the component =volume * density = 23750*(1.20/10000) =28.5g

2.1.3 Shot Capacity of Mould Shot capacity of mould is the maximum amount of materials injected into the mould for one

shot.

Shot capacity of mould= [total weight of the component]+[total weight of feed system]

Weight of the feed system =10% of the component weight = (10/100)*28.5)=2.85g

shot capacity= [total weight of the component× no. of cavities] + weight of the feed system

= (28.5*1) +2.85 = 31.35g

2.1.4 Selection of Injection Moulding Machine

Based on shot capacity calculated above, the suitable injection moulding machine has

been selected. In the present study OPTIMA-75 of Electronica make is used for production of

FR lever.

Specification of OPTIMA-75 Clamping force : 75 tons

Injection pressure : 1486 bars

Shot weight : 123 grams

Pump drive : 7.5kw

Mould thickness : 125– 310 mm

Distance between the bars : 350 x 300mm

Max. Day light : 610 mm

Screw diameter : dia 35mm.

2.1.5 Selection of Plastic Material Nylon 6 has been selected for the F-R lever component because it have Very strong and rigid,

Good abrasion resistant, heat resistant and dimensional accuracy, resistant to oils greases and

cleaning fluids and high density.

Fig.1 3D MODEL OF FR LEVER- CCOMPONENT DIAGRAM



273

Fig 2 2D MODEL OF THE COMPONENT Fig.3. OPTIMA 75 INJECTION MOULDING

WITH DIMENSIONS IN ‘mm’ MACHINE

TABLE 1 BILL OF MATERIALS OF INJECTION MOULDING TOOL.

S.NO MOULD ELEMENT MATERIAL SIZE IN ‘mm’ QTY

1 CAVITY PLATE EN 24 150X100X50 1

2 CORE PLATE EN 24 150X100X50 1

3. CORE BACK PLATE MS 150X100X15 1

4. EJECTOR PLATE MS 150X55X15 1

5. EJECTOR BACK PLATE MS 150X55X15 1

6. SPACER BLOCKS MS 150X50X10 2

7. BOTTOM SUPPORT PLATE MS 150X100X15 1

8. TOP PLATE MS 200X150X25 1

9. BOTTOM PLATE MS 200X150X25 1

10. CORE INSERT EN 36 φ 24X25 1

11. CORE SUB INSERT EN 36 φ 12X31 1

13. CAVITY INSERT EN 36 φ 11X41 1

14. SPRUE BUSH EN 36 φ 23X52 1

15. EJECTOR PINS STD φ 6 4

16. ALLEN SCREW STD M6X25 4





274

2.2 FABRICATION OF INJECTION MOULDING TOOL FOR FR LEVER Based upon the design (shown in Table 1) of injection moulding tool, the following parts or

elements are fabricated as follows:

2.2.1 Making of Cavity plate and Core plate

The cavity and core plate provides the complete profile of the FR lever and taper parting

surface is used because of complicated profile of the FR lever. CNC program has been

created from the profile drawing of FR lever and then the profile is made using VMC milling

machine. The runner is produced in the plate using EDM spark erosion machine, the ends are

chamfered to avoid sharp corners and the profile is polished by diamond polish.

2.2.2 Making other Elements of Injection Moulding Tool Core Back Plate, Ejector Plate, Ejector Back Plate, Spacer Block, Bottom Plate, and Bottom

Support Plate are prepared with help of shaping machine, grinding machine and the holes are

made and the counter bore for some plates are produced by position with DRO.

2.2.3 Making of Core Sub Insert, Cavity Insert, Core Insert And Sprue Bush

Core sub insert, cavity insert, core insert and sprue bush are produced by lathe and surface

grinding machine. Raw material is taken and the dimensions are checked, turning and facing

operation is done by using lathe machine to the required dimension. Grinding is done by

using surface grinding machine and

ends are chamfered.VMC milling machine is used producing special profile on core insert

and the profile is polished by diamond polish. Vertical machining center (VMC) is a

computer numerical control machine used to fabricate any type of complicated jobs. This

machine is used to produce core plate, cavity plate and top plate.After each component is

fabricated and assembled to get an injection moulding tool by checking the all alignment for

required mating parting as shown in Fig 6.

Fig 4 Core back plate and other elements of the mould



275

Fig 5 Vertical milling and VMC machine for Injection mould fabrication

Fig 6 Cavity plate, core plate, top plate and Assembly of Injection moulding tool

3.0 PHASE-II: PRODUCTION OF FR LEVER AND MEASUREMENT OF

RESPONSES

The fabricated injection mould tool is fitted in selected moulding machine and

experiments are conducted according to Taguchi L27 Orthogonal Array(OA) with 3 levels

and 10 input process parameters as shown in Table 2.

Dimension of each specimen component have been measured using 3D Coordinate

Measuring Machine with a machine resolution of 0.05 micron at Accurate Calibration

Service Laboratory which was certified by by National Accreditation Board for Testing and

Calibration Laboratories(NABL). Based on the dimensions of the specimen, the Volume of

each specimen has been calculated by creating a Model ProE 5.0 wildfire software.

Percentage of Shrinkage of the each specimen has been calculated using the formula

%of shrinkage= (�� )

��



276

The calculated value of percentage of shrinkage is recorded for each experiment as shown in

Table 3.

Surface roughness of each specimen is measured with portable stylus-type Talysurf

(Mitutoyo make) as shown in Fig 7 and recorded in Table.3.

Table 2 Process parameters and their levels in injection moulding machine of ER lever

S.N Input parameters

(Controllable parameters)

Symbol Level 1 Level 2 Level 3

1 Injection speed( mm/s , %) A 15 20 25

2 Injection pressure, (Bar) B 20 25 30

3 Holding pressure (Bar) C 15 20 25

4 Holding speed ( mm/s , %) D 15 20 25

5 Clamping pressure (Bar) E 30 40 50

6 Clamping speed ( mm/s , %) F 25 35 45

7 Injection time (Sec) G 1 1.5 2

8 Holding time (Sec) H 1.5 2 2.5

9 Cooling time (Sec) J 30 35 40

10 Nozzle temperature ( 0C) K 235 245 255

The other conditions are maintained as Refill speed is 80 mm/s, Refill pressure is 100 bar,

Shot weight is 50 gram and Pre heat temp is 850 C .

Fig 7 Measurement using CMM, Taylsurf and Injection moulding Tool with FR lever

Table 3 Average Surface Roughness Characteristics and % of shrinkage value

Exp.

Run

A B C D E F G H J K Surface Roughness Shrinkage

(%) Ra (µ) Ry (µ) Rq (µ)

1 1 1 1 1 1 1 1 1 1 1 2.515 16.8225 3.26875 2.290960976

2 1 1 1 1 2 2 2 2 2 2 2.6425 16.62875 3.565 5.878247823

3 1 1 1 1 3 3 3 3 3 3 2.85875 16.79125 3.645 2.131741189

4 1 2 2 2 1 1 1 2 2 2 2.64 16.71125 3.47125 5.232735172

5 1 2 2 2 2 2 2 3 3 3 3.585 22.84375 4.70625 5.265334059

6 1 2 2 2 3 3 3 1 1 1 3.87375 22.91 5.0775 4.029811766

7 1 3 3 3 1 1 1 3 3 3 3.11125 22.31875 4.39875 5.746519484

8 1 3 3 3 2 2 2 1 1 1 3.35625 18.83 4.18625 6.77336339

9 1 3 3 3 3 3 3 2 2 2 3.17375 20.78625 4.13625 3.15421767

10 2 1 2 3 1 2 3 1 2 3 2.8775 16.89125 3.68875 7.372633732

11 2 1 2 3 2 3 1 2 3 1 3.94 25.10125 5.225 5.867920125



277

4.0 PHASES-III: IDENTIFICATION OF OPTIMUM PARAMETERS USING A

COMBINED APPROACH

The recorded responses data are analysed and optimum analysis of experimental data using

combined approach of Principle Components Analysis and utility based taguchi method.

The experimental data(Table 3) are analyzed using Combined Approach to identify the

optimum process parameters setting as follows

Step 1: Normalization of the responses (quality characteristics) When the range of the series is too large or the optimal value of a quality characteristic is too

enormous, it will cause the influence of some factors to be ignored. The original experimental

data must be normalized to eliminate such effect. There are three different types of data

normalization according to the requirement LB (Lower-the-Better),HB (Higher-the-Better)

and NB (Nominal-the-Best). The normalization is taken by the following equations.

(a) LB (Lower-the-Better)

)(k X

)(k i Xmin = )(k * X

----(1)

(b) HB (Higher-the-Better)

)(k i Xmax

)(k i X )(k * X =

----(2)

(c) NB (Nominal-the-Best)

)}(k 0b X ),(k i max{X

)}(k 0b X ),(k i min{X )(k * X =

----(3)

Here,

i = 1, 2, ........, m;

k = 1, 2, ........., n

X * (k ) is the normalized data of the k th element in the i th sequence.

X 0 (k ) is the desired value of the k th quality characteristic. After data normalization ,the

Value of X*(K) will be between 0-1.The series X*i i=1,2,3…m ,can be viewed as a

comparative sequence used in the present case. For present study LB is applicable because

there is a need to minimize the responses (surface roughness, shrinkage)

12 2 1 2 3 3 1 2 3 1 2 2.9525 19.255 3.9475 7.058997561

13 2 2 3 1 1 2 3 2 3 1 3.22 17.41875 4.02 4.438114356

14 2 2 3 1 2 3 1 3 1 2 3.0275 18.035 3.89625 9.0251992

15 2 2 3 1 3 1 2 1 2 3 3.2625 18.9925 4.2 8.166390242

16 2 3 1 2 1 2 3 3 1 2 2.6575 16.67375 3.53125 4.02846559

17 2 3 1 2 2 3 1 1 2 3 3.14875 20.37875 4.08375 7.519388001

18 2 3 1 2 3 1 2 2 3 1 3.24625 15.7025 3.84 10.93867623

19 3 1 3 2 1 3 2 1 3 2 2.18375 13.3575 2.93375 7.680699715

20 3 1 3 2 2 1 3 2 1 3 2.85375 17.3525 3.85375 7.405005069

21 3 1 3 2 3 2 1 3 2 1 2.84 18.19375 3.6775 6.721344377

22 3 2 1 3 1 3 2 2 1 3 2.17125 13.8325 3.0275 5.754424446

23 3 2 1 3 2 1 3 3 2 1 2.8125 15.6575 3.625 2.464883534

24 3 2 1 3 3 2 1 1 3 2 2.49 16.29375 3.2275 6.36134543

25 3 3 2 1 1 3 2 3 2 1 2.4275 14.6275 3.19875 5.012226112

26 3 3 2 1 2 1 3 1 3 2 2.26625 13.6825 3.08375 6.149924974

27 3 3 2 1 3 2 1 2 1 3 2.49625 16.82875 3.3125 5.441488134



278

Step 2: Checking for correlation between two quality characteristics Let,

Qi = {X 0 (i), X1 (i), X 2 (i), ............, X m (i)}

where, i = 1, 2, ......., n

It is the normalized series of the ith quality characteristic. The correlation coefficient between

two quality characteristics is calculated by the following equation:

-----(4)

j = 1, 2, 3......, n. here, k = 1, 2, 3, ........, n.,

j ≠ k

Here, ρjk is the correlation coefficient between quality characteristic j and quality

characteristic k ; Cov (Q j , Qk ) is the covariance of quality characteristic j and quality

characteristic k ; σ and σ are the standard deviation of quality characteristic j and k

quality characteristic k , respectively.

The correlation is checked by testing the following hypothesis.

0 = : 0 H jkρ (There is no correlation)

0 : H1 jk ≠ρ (There is correlation) -----(5)

Step 3: Calculation of the principal component score (a) Calculate the Eigen value λk and the corresponding eigenvector

βk (k = 1, 2, ......, n) from the correlation matrix formed by all quality characteristics.

(b) Calculate the principal component scores of the normalized reference sequence

and comparative sequences using the equation shown below:

---(6)

Here, Yi (k ) is the principal component score of the k th

element in the ith

series.

X * ( j) is the normalized value of the j th

element in the i th

sequence, and βkj is the j th

element of eigenvector βk

Step 4: Estimation of quality loss ∆0,i (k ) ∆0,i (k ) is the absolute value of difference between X 0 (k ) and X i (k ) difference

between desired value and ith experimental value for kth response. If responses are

correlated then instead of using X 0 (k ) and X i (k ) , Y0 (k ) and Yi (k ) should be used.

∆0,i (k )=

Step 5: Adaptation of utility theory: Calculation of overall utility index According to the utility theory, if X i is the measure of effectiveness of an attribute (or quality

characteristics) i and there are n attributes evaluating the outcome space, then the joint utility

function can be expressed as:

Here Ui ( X i ) is the utility of the ith

attribute.

n. ,2,........ 1, =k m; 2,......., 0,1, = i ,(j)X= )(k Y1J

ii ∑=

∗n

kjβ

X i0 i

0 i

X (k) X (k)

Y (k) Y (k)

∗ ∗ −

−

j

j k

Q

Cov(Q , Q )

KQ

ρσ σ

=×

)) X ( .........U)......... X ( ).U X ( (U f = ) X ........,,......... X , X ( U nn22 11n 21

no significant correlation between quality characteristics

-----(7)

significant correlation between quality characteristics



279

The overall utility function is the sum of individual utilities if the attributes are

independent, and is given as follows:

(8)) X ( U = ) X .......,.......... , X ,X ( U ii

1i

n2 1 −−∑=

n

The attributes may be assigned weights depending upon the relative importance or

priorities of the characteristics. The overall utility function after assigning weights to the

attributes can be expressed as:

) X ( .UiW = ) X ........,,......... X ,X ( U i i

n

1i

n21 ∑=

Here, Wi is the weight assigned to the attribute i . The sum of the weights for all the

attributes must be equal to 1.

A preference scale for each quality characteristic is constructed for determining its utility

value. Two arbitrary numerical values (preference number) 0 and 9 are assigned to the just

acceptable and the best value of quality characteristic respectively. The preference number

Pi can be expressed on a logarithmic scale as follows:

×=

'log

i

i

X

XAPi

-----(9)

Here, X i is the value of any quality characteristic or attribute i,Xi ' is just acceptable value of

quality characteristic or attribute i and A is a constant. The value A can be found by the

condition that if Xi = X * (where X * is the optimal or best value), then Pi = 9 .

Therefore,

iX

XA

∗=

log

9

----(10)

The overall utility can be expressed as follows:

∑−

=n

i

iiPWU1 ---(11)

Subject to the condition:

∑=

=n

i

Wi1

1

Among various quality characteristics types, viz. Lower-the-Better, Higher-the-Better, and

Nominal-the-Best suggested by Taguchi, the utility function would be Higher-the- Better

type. Therefore, if the quality function is maximized, the quality characteristics considered

for its evaluation will automatically be optimized (maximized or minimized as the case may

be).In the proposed approach based on quality loss (of principal components) utility values

are calculated. Utility values of individual principal components are accumulated to

calculate overall utility index. Overall utility index servers as the single objective function

for optimization.

Step 6: Optimization of overall utility index using Taguchi method

Finally overall utility index is optimized (maximized) using Taguchi method. For

calculating S/N ratio, HB criterion is selected.



280

5.0 RESULTS AND DISCUSSION

Experimental data with L27 OA are noted and listed in Table 3. For all surface roughness

parameters and % of shrinkage, LB criterion has been selected. Normalized experimental

data are shown in Table 4. The correlation coefficients between individual responses have

been computed using Equation 4. Table 5 represents Pearson’s correlation coefficients. It has

been observed that all the responses are correlated (coefficient of correlation having non-zero

value). Table 5 presents Eigen values, eigenvectors, accountability proportion (AP) and

cumulative accountability proportion (CAP) computed for the four major quality

indicators (ψ ) . It has been found that the four principal components, ψ1 ,ψ 2 ,ψ 3, ψ 4 can

take care of 71.48%, 0.3%, 2.93% and 25.29% variability in data respectively.

Table 4 Normalized values of Surface roughness and % of shrinkage Exp.

No Ra Ry Rz

% of

shrinkage

1 0.638325 0.670186 0.625598 0.209437

2 0.670685 0.662467 0.682297 0.537382

3 0.725571 0.668941 0.697608 0.194881

4 0.670051 0.665754 0.664354 0.47837

5 0.909898 0.910064 0.900718 0.48135

6 0.983185 0.912704 0.97177 0.3684

7 0.789657 0.889149 0.841866 0.52534

8 0.85184 0.750162 0.801196 0.619212

9 0.80552 0.828096 0.791627 0.288355

10 0.73033 0.672925 0.705981 0.673997

11 1 1 1 0.536438

12 0.749365 0.767093 0.755502 0.645325

13 0.817259 0.69394 0.769378 0.405727

14 0.768401 0.71849 0.745694 0.825072

15 0.828046 0.756636 0.803828 0.746561

16 0.674492 0.66426 0.675837 0.368277

17 0.799175 0.811862 0.781579 0.687413

18 0.823921 0.625566 0.734928 1

19 0.554251 0.532145 0.561483 0.70216

20 0.724302 0.6913 0.73756 0.676956

21 0.720812 0.724815 0.703828 0.614457

22 0.551079 0.551068 0.579426 0.526062

23 0.713832 0.623774 0.69378 0.225337

24 0.63198 0.649121 0.617703 0.581546

25 0.616117 0.58274 0.612201 0.458211

26 0.57519 0.545092 0.590191 0.562218

27 0.633566 0.670435 0.633971 0.497454



281

Table 5 Eigen values, Eigen vectors and Accountability proportion

Table 6: Major Principal Components and Quality loss estimates for principal

components

Eigen values

2.8594 0.0119 0.1172 1.0115

V =Eigen vectors

-0.5757 -0.5371 -0.6127 0.0685

-0.5677 -0.2800 -0.0903 -0.0903

-0.5884 0.7957 -0.1433 0.0118

-0.0049 0.0021 0.1138 0.9935

Accountability Proportion (AP)

Ap1 Ap2 Ap3 Ap4

0.7148 0.003 0.0293 0.2529

Cumulative Accountability Proportion (CAP)

cap1 cap2 cap3 cap4

0.7148 0.7178 0.7471 1

Exp. No

Major Principal Components

Quality loss estimates

P1 P2 P3 P4 QL1 QL2 QL3 QL4

Ideal

sequence -1.7368 -0.0193 0.1267 0.9834 - - - -

1 -1.1171 -0.0323 0.0584 0.1986 0.6197 -0.013 -0.0683 -0.7848

2 -1.1663 -0.0017 0.0618 0.528 0.5704 0.0176 -0.0649 -0.4554

3 -1.2089 -0.0215 -0.008 0.1911 0.5278 -0.0022 -0.1347 -0.7923

4 -1.157 -0.0167 0.0606 0.4688 0.5798 0.0026 -0.0661 -0.5146

5 -1.5729 -0.0258 0.068 0.4689 0.1639 -0.0065 -0.0587 -0.5145

6 -1.6578 -0.0096 0.0021 0.3623 0.079 0.0097 -0.1247 -0.6211

7 -1.4574 -0.0021 0.139 0.5056 0.2794 0.0172 0.0123 -0.4778

8 -1.3908 -0.0288 0.0106 0.6152 0.346 -0.0095 -0.1162 -0.3682

9 -1.4011 -0.034 0.0626 0.2762 0.3357 -0.0147 -0.0641 -0.7073

10 -1.2212 -0.0175 0.0455 0.6672 0.5156 0.0018 -0.0812 -0.3163

11 -1.7345 -0.0203 0.074 0.5229 0.0023 -0.001 -0.0528 -0.4605

12 -1.3146 -0.0148 0.0959 0.6321 0.4221 0.0045 -0.0308 -0.3514

13 -1.3192 -0.0202 -0.0312 0.4054 0.4176 -0.0009 -0.1579 -0.578

14 -1.2931 -0.0188 0.0687 0.8162 0.4437 0.0005 -0.058 -0.1672

15 -1.3829 -0.0154 0.0442 0.7395 0.3538 0.0039 -0.0825 -0.2439

16 -1.1649 -0.0097 0.0426 0.36 0.5719 0.0096 -0.0842 -0.6234

17 -1.3843 -0.0332 0.1008 0.6736 0.3525 -0.0139 -0.0259 -0.3099

18 -1.2669 -0.0308 -0.0153 1.0021 0.4699 -0.0115 -0.142 0.0186

19 -0.9551 0.0016 0.069 0.6941 0.7817 0.0209 -0.0577 -0.2893

20 -1.2468 0.0057 0.0591 0.6684 0.49 0.025 -0.0676 -0.315

21 -1.2436 -0.0288 0.0847 0.6026 0.4931 -0.0095 -0.042 -0.3808

22 -0.9737 0.0119 0.0629 0.5174 0.7631 0.0312 -0.0638 -0.466

23 -1.1744 -0.0055 -0.0315 0.2246 0.5624 0.0138 -0.1582 -0.7588

24 -1.0987 -0.0285 0.0896 0.5697 0.6381 -0.0092 -0.0371 -0.4137

25 -1.048 -0.006 0.035 0.452 0.6888 0.0133 -0.0917 -0.5314

26 -0.9907 0.0092 0.0461 0.5557 0.7461 0.0285 -0.0806 -0.4278

27 -1.1209 -0.0225 0.0931 0.4845 0.6159 -0.0032 -0.0336 -0.4989



282

Table 7 Utility values related Individual principal components and Overall utility

index and S/N values

Major principal components is obtained using Equation 6. These have been furnished in

Table 6. Quality loss estimates (difference between ideal and actual gain) for aforesaid

major principal components have been calculated (Equation7) and also presented in Table 6.

Based on quality loss, utility values corresponding to the four principal components have

been computed using Equations 9, 10.

In all the cases minimum observed value of the quality loss (from Table 6) has been

considered as its optimal value or most expected value; whereas maximum observed value

for the quality loss has been treated as the just acceptable value. Individual utility measures

corresponding to four major principal components have been furnished in Table 7. The

overall utility index has been computed using Equation 11 and tabulated in Table 7 with their

corresponding (Signal-to-Noise) S/N ratio. In this computation it has been assumed that all

quality indices are equally important (same priority weight age, 25%). Figure 8 reflects S/N

ratio plot for overall utility index; S/N ratio being computed using equation (12).

Exp.

No. U1 U2 U3 U4

Overall

utility S/N

1 0.3568 1.9108 4.1761 0 1.6109 4.1414

2 0.4839 1.2448 4.4327 1.3088 1.8676 5.4254

3 0.6031 5.7564 0.7997 -0.023 1.784 5.0281

4 0.459 5.3827 4.3393 1.015 2.799 8.9401

5 2.3994 3.4099 4.927 1.0155 2.938 9.3609

6 3.521 2.5484 1.1854 0.5627 1.9544 5.8202

7 1.5801 1.2982 12.7112 1.1933 4.1957 12.4561

8 1.2519 2.5983 1.5359 1.8198 1.8015 5.1126

9 1.2984 1.6366 4.4892 0.2502 1.9186 5.6597

10 0.6393 6.2312 3.3151 2.1857 3.0928 9.8071

11 8.9583 7.54 5.4619 1.2819 5.8105 15.2843

12 0.9464 4.1981 8.1303 1.9326 3.8018 11.5999

13 0.963 7.6904 0.008 0.7356 2.3492 7.4186

14 0.87 9.021 4.9887 3.7183 4.6495 13.3481

15 1.2175 4.5444 3.2381 2.8106 2.9526 9.4042

16 0.4801 2.5729 3.1392 0.5537 1.6865 4.5395

17 1.2233 1.7583 9.0018 2.2347 3.5545 11.0156

18 0.7817 2.1721 0.5362 8.9959 3.1215 9.8872

19 -0.0001 0.8768 5.0174 2.3997 2.0735 6.3339

20 0.7174 0.4815 4.2288 2.1951 1.9057 5.6011

21 0.7076 2.5956 6.5992 1.7392 2.9104 9.2791

22 0.0369 0.0022 4.5161 1.2535 1.4522 3.2404

23 0.5059 1.7838 -0.0008 0.0809 0.5924 -4.5473

24 0.3118 2.6676 7.2061 1.5396 2.9313 9.3411

25 0.1944 1.8558 2.7113 0.9376 1.4248 3.0749

26 0.0715 0.1945 3.354 1.4594 1.2699 2.0751

27 0.3661 4.9475 7.7004 1.0894 3.5259 10.9453



283

−=−− ∑

=

t

i iytbettertheHigherSN

12

11log10)( ---(12)

Here t is the number of measurements, and yi the measured ith

characteristic value i.e. ith

quality indicator. Optimal parameter setting has been evaluated from Figure. The optimal

setting should confirm highest utility index (HB criterion).

Fig 8 S/N ratios for predicated optimal setting

The predicted optimal setting is A2 B1 C2 D2 E3 F2 G1 H2 J3 K3

6.0 CONCLUSIONS

Combined approach of PCA and Utility based Taguchi method is successfully applied in the

present study and the following conclusions are drawn from the results of the experiments

and analysis of the experimental data in connection with correlated multi- response

optimization in injection moulding of FR lever.

• Based on the analysis and results, i t is concluded that PCA is most

powerful tool to eliminate response correlation by converting the correlated

responses into uncorrelated quality indices, called principal components which have

been treated as response variables for optimization.

• Based on the PCA method, it has been found that first principal component ψ1 and

fourth principal component ψ 4 can take care of 71.48% and 25.29% variability in

data respectively, which shows that Surface roughness Ra and % of shrinkage are the

most influence quality characteristics.

• Utility based Taguchi method has been found fruitful for evaluating the optimum

parameter setting for these kind of multi-objective optimization problems.

• The proposed algorithm greatly simplifies the optimization of injection moulding

parameters with multiple performance characteristics. Thus, the solutions from this

method can be a useful reference for injection mould makers and related industry.



284

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