Production of nylon 6 fr lever using an injection moulding tool and identification of optimum process parameter combination

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 3, Issue 3, Sep- Dec (2012) © IAEME
AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online) IJMET
Volume 3, Issue 3, September - December (2012), pp. 270-284
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2012): 3.8071 (Calculated by GISI) ©IAEME
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PRODUCTION OF NYLON-6 FR LEVER USING AN INJECTION
MOULDING TOOL AND IDENTIFICATION OF OPTIMUM
PROCESS PARAMETER COMBINATION
S.Selvaraj1, Dr.P.Venkataramaiah2
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

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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

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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

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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 φ6 4
16. ALLEN SCREW STD M6X25 4

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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

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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
(୴୭୪୳୫ୣ ୭୤ ୲୦ୣ ୫୭୳୪ୢି୴୭୪୳୫ୣ ୭୤ ୲୦ୣ ୱ୮ୣୡ୧୫ୣ୬)
%of shrinkage=
୴୭୪୳୫ୣ ୭୤ ୲୦ୣ ୫୭୳୪ୢ

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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 Symbol Level 1 Level 2 Level 3
(Controllable parameters)
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
0
10 Nozzle temperature ( C) 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. A B C D E F G H J K Surface Roughness Shrinkage
Run 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

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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

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)
min X i (k )
X * (k ) =
X (k ) ----(1)
(b) HB (Higher-the-Better)
X i (k )
X * (k ) =
max X i (k ) ----(2)
(c) NB (Nominal-the-Best)
min{X i (k ), X 0b (k )}
X * (k ) =
max{X i (k ), X 0b (k )} ----(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)

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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:
Cov(Q j , Q k )
ρ= -----(4)
σ Q j × σ QK

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.
H0: ρ jk = 0 (There is no correlation)
H1: ρ jk ≠ 0 (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:
n
Yi (k ) = ∑Xi∗ (j)βkj, i = 0,1,2,.......,m; k =1, 2,........ n.
, ---(6)
J =1

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 β kj is the j th
element of eigenvector β k
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.
 X 0 ∗ X i (k ) − X i ∗ (k)
 no significant correlation between quality characteristics
∆0,i (k )=
 -----(7)
 Y 0 (k ) − Y i (k)
 significant correlation between quality characteristics

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:
U ( X1 , X 2 ,.........
........,X n ) = f (U1 ( X1 ).U2 ( X 2 ).........
.........Un ( X n ))
Here Ui ( X i ) is the utility of the ith attribute.

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The overall utility function is the sum of individual utilities if the attributes are
independent, and is given as follows:
n
U ( X1, X 2 , ................., X n ) = ∑ Ui ( X i ) − − (8)
i=1
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:
n
U ( X1, X 2 ,................., X n ) = ∑ Wi .Ui ( X i )
i =1
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:
 Xi 
Pi = A × log ' 
 Xi  -----(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,
9
A=
X∗
log
Xi ----(10)
The overall utility can be expressed as follows:
n
U = ∑WiPi
i −1 ---(11)
Subject to the condition:
n

∑Wi = 1
i =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.

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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. % of
Ra Ry Rz
No 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

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Table 5 Eigen values, Eigen vectors and Accountability proportion

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
Table 6: Major Principal Components and Quality loss estimates for principal
components
Major Principal Components Quality loss estimates
Exp. No
P1 P2 P3 P4 QL1 QL2 QL3 QL4
Ideal
-1.7368 -0.0193 0.1267 0.9834 - - - -
sequence
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

281


Table 7 Utility values related Individual principal components and Overall utility
index and S/N values

Exp. Overall
U1 U2 U3 U4 S/N
No. utility
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

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).

282


1 t 1 
SN ( Higher − the − better) = −10 log ∑ 2  ---(12)
 t i =1 yi 
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, it 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.

283


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