designing robust parameters for injection-compression ... · light-guided plate; regression model....

International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 93

146601-4949-IJET-IJENS © February 2014 IJENS I J E N S

Designing Robust Parameters for

Injection-compression Molding Light-guided Plates

Based on Desirability Function and Regression Model Tsung-Yen Lin

Fu Chun Shin Machinery Manufacture Co., LTD Tainan, Taiwan

Ming-Shyan Huang*

Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology,

Kaohsiung, Taiwan

e-mail: [email protected]

*Corresponding author

Abstract-- This work describes a robust injection

compression molding parameter design method that uses linear

regression model and desirability function to reduce the effect of

environmental noise on injection molded parts quality. The

design objective was to achieve a uniform geometry and

dimensions of light-guided plate (LGP) after injection molding.

In this study, an experimental 2.5-inch LGP injection

compression molding was performed to test the feasibility of the

desirability function, regarding its construction of a composite

quality indicator that represents the quality-loss function of

multiple qualities. Firstly, the experimental design and ANOVA

methods were employed to select parameters that affect part

qualities and adjustment factors. Secondly, a two-level,

statistically-designed experiment using least squared error

method was performed to generate a regression model between

part quality and adjustment factors. The mathematical model

was then used to optimize process parameters. The experimental

findings show that the robust process parameters generated by

the proposed method yield a better uniform production quality

than the initial and thus improved and uniform production

quality, which validates its feasibility.

Index Term-- Desirability function; injection molding;

light-guided plate; regression model.

I. INTRODUCTION

A light-guided plate (LGP) is a key component of

backlight modules in liquid crystal displays that directs light

propagation to enhance luminance and uniformity. The

replication effect of the microstructures distributing on the

surface of LGPs determines the optical performance. For

v-grooves microstructures, the depth of the melt filling has a

strong correlation with the luminance of LGPs [1]. Although

injection molding (IM) is one of the most common processes

for manufacturing microfeatured parts, it has some inherent

problems [2-4]. The primary difficulty is that molten polymers

in a tiny cavity instanteously freeze once they touch the

relatively cooler cavity wall. Increasing the plastic

temperature, mold temperature, injection speed, and packing

pressure may enhance the luminance performance of an LGP

[5, 6] However, residual stress exists in LGPs, and the

uniformity of the microfeatures remains a problem with IM.

Injection compression molding (ICM) was developed to solve

these problems [7].

ICM introduces a compression action into the filling

process. With a reliance on pressure transmitted from the glue

sprue, pressure is also imposed by a compression action from

the mold wall. This process has many advantages, including

even packing, less molding pressure, less residual stress, less

molecular orientation, less uneven shrinkage, less density

variation, less warpage, and better dimensional accuracy than

found with the IM process. On the basis of these advantages,

ICM is typically used to fabricate parts requiring a high

accuracy and no residual stress, such as LPGs. For instance,

Wu and Su [8] who used ICM to reduce the shrinkage of

LGPs, found that the mold and barrel temperatures and

injection speed were the key parameters for enhancing the



accuracy of the optical components and eliminating shrinkage.

Shen et al. [9] applied ICM to mold 2-inch LGPs. Their

investigation demonstrated that the replication effects of

microstructures were improved with increasing plastic

temperature and were dependent on the proper compression

distance and speed.

Traditionally, parameter setting for injection compression

molding relied on statistical analyses and experimentation,

computer-aided simulations, or operator experience [10, 11].

However, if the setting for producing molded parts approaches

the specification limits, the process is easily affected by

environmental variation, which reduces the yield rate. In such

a case, the parameters are inadequate, and the process is not

robust. Other methods such as fuzzy theory and artificial

neural network (ANN) that have been proposed to address

such problems generally require substantial data [12-14]. For

instance, ANN is an empirical modeling technique that

mimics the nature of biological neural network systems and

possesses the ability to learn using learning algorithms such as

back propagation. An accurate representation of the process

can be obtained by training the network using just

experimental data, without precise understanding and

development of a rigorous mathematical model. Because of

the aforementioned benefits, various applications of ANN

have been reported for controlling the injection molding

process [15, 16].

The Taguchi method and response surface method have

been developed to target a single quality by designing

experiments to optimize process parameters [17-20]. However,

the Taguchi method of experimentally searching for optimal

process parameters is confined to the design ranges of factor

levels. The response surface method has no such limitation

despite its more complex experimental design.

In practice, seeking the ideal process parameters and

focusing on multi-quality characteristics is difficult but

generally necessary. When studying multi-quality

characteristics, i.e., numerous correlated quality characteristics,

experimental data may be contradictory and data analysis may

be difficult. Principal component analysis (PCA) can convert

data for multi-quality characteristics into several independent

quality indicators. Some of these indicators can then be

selected to construct a composite quality indicator that

represents the mathematical function of the required

multi-quality characteristics. However, if any of the multiple

principal components have eigenvalues exceeding one being

selected, the feasible solution generated by PCA may not

satisfy each quality indicator. To resolve this problem, Liao

[21] proposed the weighted principal component (WPC)

method of estimating quality by the accountability proportion

of PCA. Another approach, suggested by Derringer and Suich,

is the desirability function (DF), which redefines composite

quality [22]. The desirability function approach is one of the

most widely used methods for solving the multi-quality

characteristics problem, first introduced by Harrington [23].

This technique involves estimating each of the characteristics

with response surface functions and then using a

transformation routine to simplify the problem into a single

measure of performance. A number of researchers have

suggested improvements to the desirability function approach

over the past four decades [24]. This work used the DF

method of generating composite quality indicators. A

regression-model based searching method was then used to set

the robust injection molding parameters proposed by Huang

and Lin [25]. This method first uses DOE and ANOVA

methods to select the main parameters affecting parts quality

as adjustment factors. A two-level statistically designed

experiment using least squared error method is then performed

to generate a regression model between parts quality and

adjustment factors. Based on this mathematical model, this

study employed the steepest decent method to optimize

process parameters. A 2.5-inch injection-compression molding

experiment were then performed to verify model performance.

II. DESIGN OF ROBUST PARAMETERS

Figure 1 shows the proposed robust parameter searching

method, which includes the following three phases: (1) setting

the composite quality indicator, (2) executing full factorial

experiments, and (3) searching for robust process parameters.

The three phases are discussed in detail below.

A. Phase 1 – Setting the Composite Quality Indicator



Data containing information about multi-quality

characteristics were first collected and normalized to generate

dimensionless values, each of which is between 0 and 1. If the

quality requirements differ, the corresponding normalization

may differ as well: (1) larger-the-better - the target value of

quality objectives is uncertain but was expected to be large, (2)

smaller-the-better - the target value of quality objectives was

uncertain and was expected to eventually be small, and (3)

target-the-best – the target values of quality objectives were

certain and were expected to be achieved.

Second, the DF was used in this phase to convert

observed data into a composite quality indicator, which

represents a mathematical model of multi-quality

characteristics. The desirability function method proposed by

Derringer and Suich [22] suggests that the composite quality

indicator can be defined as

n

i

n1

idDF1

/ (1)

where, ‘n’ denotes the number of quality characteristics; the

DF value becomes zero if one of the di is zero. It becomes one

only if all instances of di are one. The di represents the

desirability value of the ith

quality characteristic defined by

Derringer and Suich[22]

as follows:

USLii

USLiiLSLi

t

LSLiUSLi

LSLii

LSLii

i

xx

xxxxx

xx

xx

d

,

,,

,,

,

,

1

0

(2)

where ix represents the mean value of the ith

quality

characteristics; USLix , and LSLix , are the upper

specification limit and lower specification limit of the ith

quality characteristics, respectively. The value t is the

relaxation factor, and its value is set between 0 and 10.

Adjustment factors are selected according to the

contribution percentage of experimental factors to the

composite quality indicator , which is determined by

ANOVA method. The adjustment factors have two distinct

characteristics: (1) a change in adjustment factors caused by

environmental interference substantially affects parts quality.

If the adjustment factors are controlled, the required product

quality is assured. By varying adjustment factors, this research

discovered a process window that enables adjustment of

selected factors within the window so that molded parts meet

their quality specifications. (2) If the process parameters

within the process window obtain parts with insufficient

quality, the range is further adjusted until quality requirements

are met.

In this phase, the composite quality indicator is

generated using many quality indicators with different

adjustment factors. However, this work examines only the

three most important adjustment factors. The factors are used

again in phases 2 and 3 to optimize the process parameters.

The steps in phase 1 can be summarized as: (1) normalize the

measurements - after performing the suggested Taguchi design

experiment, normalize the observations of each quality. (2)

Determine - by using DF for the above normalized

observations, the composite quality DF can be generated using

Eq. (1). (3) Select the three most significant adjustment factors

- adjustment factors are selected according to their

proportional contribution to the composite quality indicator as

revealed by ANOVA analysis. These adjustment factors were

then used as the experimental factors in the 2K full factorial

experiments in phase 2, where K is less than 3 considering

experimental cost.

B. Phase 2 – Executing Full Factorial Experiments

As mentioned above, environmental noise may degrade

the quality of injection molded parts. For quality

characteristics to meet quality specification limits, the process

window must be robust and allow varying adjustment factors.

By varying the adjustment factors caused by environmental

interference and by performing the 2K full factorial

experiments, a robust process window can be identified. The

experimental runs were designed to combine the extreme

points of a three-dimension process window. If a defect occurs



at extreme points in the process window, a better region can be

found by using the steepest decent method to relocate the

parameter settings.

The steps of phase 2 are: (1) design the 2K

full factorial

experiments - the experiments were designed according to the

number and the possible ranges of adjustment factors. The

initial central point for 2K

full factorial experiment was

obtained by referring to the optimal parameter setting of DOE

suggested in phase 1. (2) Obtain the new new by using PCA

for observation after normalization - the new quality indicators

new are obtained. (3) Check robustness - if all the new

for

running 2K

full factorial experiments meet the quality

specification levels, this means that the set-points of the

process parameters of this experimental group could be robust

for the new. However, if the robustness confirmation fails at

this point, the next step is to repeat phase 3 and search for

another set of process parameters by employing the regression

model-based robust parameter search method.

C. Phase 3 – Searching for Robust Process Parameters [25]

After establishing a regression model based on the

relationship between the process parameters and quality

observations, the steepest decent method was used to

determine the distance and direction to the target. For any

given quality observation, y and k number of process

parameters were assumed to significantly affect quality, such

as k21 ,x,,xx . The sample data of full factorial experiment

in the previous phase could be used to fit the regression model.

Therefore, the following matrix can be used to obtain the data

sample that fits the model:

εXβY

(3)

n

2

1

y

y

y

Y ;

nkn2n1

2k2221

11211

xxx1

xxx1

xxx1

k

X ;

k

1

0

β (4)

where Y represents the vector of observation, which may be

DFnew

or wnew

here; X represents the matrix of experimental

runs; xnk represents the kth

process parameter in the

experimental run ‘n’. β represents the vector of estimated

coefficients of the regression model, and ε represents the

random error vector.

The β vector can be estimated by the least squared error

method as follows:

YX'XX'β1

2

1

(5)

The composite equation of the relationship between the

process parameters and the product quality can then be

determined. Additionally, Y and matrix X in Eq. (8) must be

converted into Eq. (9) to get coefficient β in the regression

model.

The steps of phase 3 are as follows: Step 1: establish the

regression model – Eq. (7) represents the relationship between

process parameters and parts quality. The Y and X in Eq. (8)

can also be substituted into the following equations:

8

2

1

y

y

y

Y ;



11111111

11111111

11111111

11111111

11111111

11111111

11111111

11111111

X (6)

The X matrix contains the values 1 and -1, which represent the

upper and lower levels of each control factor, respectively.

The second, third, and fourth columns represent control factor

levels x1, x2, and x3, respectively. The fifth, sixth, and seventh

columns represent interaction effect levels x1 to x2, x1 to x3,

and x2 to x3, respectively. The eighth column indicates the

interaction effect among x1, x2, and x3. Entering vector Y and

matrix X into Eq. (9) obtains the coefficient vector of the

regression model, β. Step 2: estimate the responses for all

possible treatments in the varying ranges. The set-point of the

process parameters (or the predicted points of the robust

molding parameters) and the least resolution of machine

control are used as the basis for arranging all possible

treatments in the varying ranges. For example, if there are

three adjustment factors and if the upper and lower limits are

five times the least resolution of the injection molding

machine, the number of treatments is 5K. Step 3: determine

whether or not the inference process should be continued - this

step determines whether or not the inference of the robust

molding parameters should continue. By substituting all

treatments to construct coefficient vectors of the regression

model and to generate predicted values, stopping the inference

process has two conditions: either all predicted values meet

the quality specifications or only some predicted values do. In

the latter case, the set-point should be selected in the inference

process before proceeding to step 4. In the former case, phase

2 is performed to test robustness. Step 4: Infer the next robust

molding parameter - set the search direction by using steepest

decent method. The forward distance relies on the least

resolution of the machine control. Return to step 2.

III. EVALUATION OF 2.5-INCH LGP INJECTION

COMPRESSION MOLDING

A. Experimental Setup

This study analyzed the injection compression of a

2.5-inch LGP, which is characterized by V-shaped

micro-structure. The objective of the experiment was to

replicate these micro-structures. Figure 2 shows that the

light-guided plates was 55 mm long, 41 mm wide, and 0.7 mm

thick. The V-shaped micro-structure had a depth of 15 μm, a

width of 52 μm, and an included angle of 120°. The LGP

stamper was clipped to the core of the mold and was filled by

a fan gate. The mold design was single cavity with two

cooling channels. The molding material was PMMA (Japan),

and the molding machine was a FANUC ROBOSHOT α-30iA.

Injection compression molding technology was used to

experimentally increase the replication ability of the

micro-structure. The eight experimental parameters included

filling speed, melt temperature, mold temperature,

compression distance, compression speed, holding pressure,

holding time and cooling time, and the Taguchi’s L18

orthogonal array was used for verification. Table 1 shows the

combinations of the eight parameters in the L18 orthogonal

array and measured observations. Three samples were

obtained in each experimental run. Figure 3 shows the points

of the molded micro-structure of LGP that were measured by a

3D profiler. The two observed objectives were based on the

average and range value of micro-structure height of the nine

measured points. The measured points were fixed in the same

micro-structure by making clips, and the average range and

maximum deviation in range were larger than 13.5 m and

smaller than 0.41 m, respectively, which was in accordance

with industrial specifications.

B. Taguchi Analysis

Table 2 shows the L18 experimental results of 2.5-inch

LGP injection compression molding, including the average

normalized values of average/range of nine-point heights and

the composite quality indicator DF. Of these eighteen

combinations of Taguchi orthogonal array, the best

combination was that in Exp. No. 3. Table 3 shows the



ANOVA results for these DF values. Since the results showed

that compression distance, compression speed, and cooling

time significantly affected the DF values, these three factors

were selected for adjustment.

Tables 4(a) and 4(b) show the results of the full factorial

experiment for the first two inferences of robust parameters. In

the two failed tests in the full factorial experiment, the set

points were compression distances of 5.0 mm and 3.9 mm,

compression speeds of 100% and 98%, and cooling times of

45 s and 44.5 s. The DF values in the tables did not meet all

robustness criteria in this phase. Thus, the search was repeated

until a set-point that met the robustness criteria was found (see

Table 4(c)).

C. Verification

The additional verification was performed to test the

robustness of the optimal process parameters found by the DF

method. The two set points, the initial central point of Table

4(a) and the robust central point of Table 4(c), were used to

inject fifty molds as measurement samples, i.e., the initial

setting of robust process parameters were compression

distance of 5 mm, compression speed of 100%, and cooling

time of 45 s. The robust process parameters were compression

distance of 4.8 mm, compression speed of 99.6%, and cooling

time of 45.4 s. results of robustness testing. Figures 4(a) and

4(b) show the normal distribution of quality characteristics in

terms of probability density function. The dashed and solid

lines indicate the initial setting of process parameters and the

robust setting of process parameters, respectively. In this case

study, the initial setting of process parameters obtained almost

unqualified LGP for the average 9-point micro-structure

height, and eighteen of fifty parts were unqualified within the

range (Table 5). In contrast, the performance of the proposed

method for optimizing process parameters generated 100%

qualified products. Thus, the average value and standard

deviation of part qualities were substantially improved by the

proposed method.

IV. CONLCUSION

This work proposed a robust parameter searching

method that not only identifies the set-point of robust

parameters of an injection molding process for multi-quality

characteristics, but also meets the requirements of

multi-quality characteristics of molded parts. A light-guided

plate experiment was performed to examine this method. The

proposed search method was based on a DF method that can

successfully construct a composite quality indicator, which

represents the mathematical model of multi-quality

characteristics and a regression model-based search method

that can reflect variables to adjust search distance and

direction.

The proposed method has five major advantages:

1) The operator is not required to use complex experimental

designs.

2) The regression model for describing the mathematical

relationship between part quality and process parameters is

simple and the inference of robust process parameters is

efficient.

3) The ratio of products disqualified due to unstable

machines and non-uniform materials is decreased, and the

effectiveness of the molding process is improved.

4) The treatment applied in the full-factorial experiments can

be confirmed to ensure that the molding process is robust.

5) The search for robust parameters is not restricted to the

designed levels of controlled factors.

In summary, the experimental results indicate that the

proposed method effectively solves the problem of

multi-quality characteristics, significantly improves the

stability of the molding process, and increases yield.

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[26]



Fig. 1. Flowchart of the robust parameter searching method for multi-quality characteristics.

Yes

Get the optimal setting and

normalize the observations from

Taguchi D.O.E.

Get and choose adjustment

factors by ANOVA analysis

Construct the 23 full factorial

experiments

Get new

Satisfy

robustness?

No

Buildup regression model

Estimate the response for all

possible treatments in their

varying range

Inferring next robust process

parameters

Stop the inference

process?

No

Phase 1

Phase 2

Phase 3

Finish Yes



(a)

(b)

Fig. 2. 2.5-inch LGP molding: (a) geometry of the injection compression mold; (b) micro-structure of the LGP stamper for injection compression molding

(Materials: Beryllium copper alloy).

55 mm

41 mm

8 mm

Fan gate

Round sprue

Cooling

channels

0.0

15 m

m

120°

0.052 mm

0.7 mm



Unit: mm

Fig. 3. Measuring positions of 2.5-inch LGP microstructures.

Averaged LGP’s 9-point micro-structure height (m) (a)

0

10

20

30

40

50

60

12.60 12.80 13.00 13.20 13.40 13.60 13.80

0

10

20

30

40

50

60

12.60 12.80 13.00 13.20 13.40 13.60 13.80

Lower Specification Limit: 13.50 m

NG Good Robust setting

Initial setting

Mean StDev N

13.62 0.008 50

12.71 0.010 50

Fre

quen

cy



Range of LGP’s 9-point micro-structure height (m)

(b)

Fig. 4. Heights of 2.5-inch LGP 9-point micro-structures: (a) average, (b) range.

0

5

10

15

20

0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48

Robust setting

Initial setting

Mean StDev N

0.38 0.024 50

0.40 0.024 50

Upper Specification Limit: 0.41 m

Good NG

Fre

quen

cy



TABLE I

The L18 (21×37) experiment for 2.5-inch LGP injection compression molding

Control factors Observations (gray digits).

Exp.

No. Filling

speed

(mm/s)

Melt

temp.

(oC)

Mold

temp.

(oC)

Compress.

distance

(mm)

Compress.

speed

(%)

Holding

pressure

(kgf/cm2)

Holding

time

(s)

Cooling

time

(s)

Avg.

9-point

heights1

(μm)

Avg.

9-point

heights2

(μm)

Avg.

9-point

heights3

(μm)

Range

9-point

heights1

(μm)

Range

9-point

heights2

(μm)

Range

9-point

heights3

(μm)

1 50 240 70 3 80 700 3 35 12.72 12.71 12.71 0.42 0.36 0.41

2 50 240 80 4 90 800 4 40 13.18 13.19 13.19 0.54 0.50 0.46

3 50 240 90 5 100 900 5 45 13.55 13.59 13.54 0.49 0.36 0.35

4 50 250 70 3 90 800 5 45 13.09 13.10 13.12 0.48 0.42 0.44

5 50 250 80 4 100 900 3 35 13.50 13.45 13.45 0.55 0.41 0.38

6 50 250 90 5 80 700 4 40 13.61 13.62 13.62 0.46 0.45 0.45

7 50 260 70 4 80 900 4 45 13.26 13.26 13.26 0.43 0.31 0.34

8 50 260 80 5 90 700 5 35 13.48 13.45 13.50 0.48 0.43 0.55

9 50 260 90 3 100 800 3 40 13.45 13.50 13.51 0.49 0.43 0.32

10 55 240 70 5 100 800 4 35 13.20 13.16 13.18 0.34 0.38 0.39

11 55 240 80 3 80 900 5 40 13.19 13.20 13.18 0.47 0.50 0.43

12 55 240 90 4 90 700 3 45 13.45 13.46 13.45 0.44 0.58 0.37

13 55 250 70 4 100 700 5 40 13.34 13.36 13.34 0.46 0.45 0.42

14 55 250 80 5 80 800 3 45 13.52 13.47 13.53 0.49 0.35 0.46

15 55 250 90 3 90 900 4 35 13.58 13.61 13.62 0.50 0.49 0.49

16 55 260 70 5 90 900 3 40 13.47 13.46 13.45 0.47 0.41 0.49

17 55 260 80 3 100 700 4 45 13.47 13.48 13.45 0.42 0.44 0.40

18 55 260 90 4 80 800 5 35 13.61 13.68 13.66 0.56 0.49 0.53 1, 2, 3

mean sample 1, 2, and 3 at the same run, respectively.

TABLE II

The composite quality indicators DF generated by DF method in the L18 experiment of 2.5-inch LGP injection compression molding

Exp. No. Average normalized averaged

nine-point heights

Average normalized range of

nine-point heights DF

1 0.004 0.68 0.05

2 0.487 0.30 0.38

3 0.876 0.67 0.76*

4 0.403 0.49 0.45

5 0.779 0.49 0.62

6 0.928 0.47 0.66

7 0.563 0.81 0.68

8 0.789 0.35 0.52

9 0.795 0.62 0.70

10 0.482 0.78 0.61

11 0.488 0.42 0.45

12 0.762 0.43 0.57

13 0.652 0.51 0.57

14 0.818 0.54 0.67

15 0.915 0.32 0.54

16 0.770 0.46 0.59

17 0.774 0.59 0.68

18 0.969 0.20 0.44



TABLE III

The ANOVA analysis of the composite quality indicator DF in 2.5-inch LGP injection compression molding

SV DOF SS MS F PSS CP (%)

Filling speed 1 0.01

Melt temp. 2 0.06 0.03 2.49 0.04 7.86 Mold temp. 2 0.04 0.02 1.83 0.02 4.40 Compression distance 2 0.08 0.04 3.19 0.05 11.57 Compression speed 2 0.10 0.05 4.25 0.08 17.17 Holding pressure 2 0.03

Holding time 2 0.01

Cooling time 2 0.09 0.04 3.67 0.06 14.10 Error 2 0.01

Pooled error (7) (0.08) (0.01) 0.20 44.90 Total 17 0.45 0.16 100.00

SV, source of variation; DOF, degrees of freedom; SS, sum of squares; MS, mean square; PSS, pure of sum squares; CP,

contribution percentage; F1,7,0.01=12.25, F2,7,0.01=9.55.

TABLE IV

Full-factorial experiment and principal component analysis in 2.5-inch LGP injection compression molding

(a) The first inference of robust parameters by the proposed method.

Initial central point Average

normalized

averaged

nine-point heights

Average

normalized

range of

nine-point

heights

DF

Exp.

No.

Compression

distance

5 mm

Compression speed

100%

Cooling time

45 s 0.90 0.68 0.78

1 +0.5 +1% +0.5 0.91 0.70 0.80

2 -0.5 +1% +0.5 0.67 0.28 0.44

3 +0.5 -1% +0.5 0.88 0.21 0.43

4 -0.5 -1% +0.5 0.85 0.20 0.41

5 +0.5 +1% -0.5 0.97 0.88 0.92

6 -0.5 +1% -0.5 0.94 0.67 0.79

7 +0.5 -1% -0.5 0.97 0.67 0.80

8 -0.5 -1% -0.5 0.70 0.37 0.51

Normalized lower specification limit ≧0.81 ≧0.63 ≧0.71



(b) The second inference of robust parameters by the proposed method


normalized

averaged

nine-point heights

Average

normalized

range of

nine-point

heights

DF

Exp.

No.

Compression

distance

3.9 mm

Compression speed

98%

Cooling time

44.5 s 0.82 0.64 0.73

1 +0.5 +1% +0.5 0.49 0.30 0.38

2 -0.5 +1% +0.5 0.93 0.47 0.66

3 +0.5 -1% +0.5 0.80 0.59 0.69

4 -0.5 -1% +0.5 0.92 0.60 0.75

5 +0.5 +1% -0.5 0.78 0.43 0.58

6 -0.5 +1% -0.5 0.92 0.56 0.72

7 +0.5 -1% -0.5 0.80 0.62 0.70

8 -0.5 -1% -0.5 0.87 0.65 0.76


(c) The third inference of robust parameters by the proposed method


normalized

averaged

nine-point heights

Average

normalized

range of

nine-point

heights

DF

Exp.

No.

Compression

distance

4.8 mm

Compression speed

99.6%

Cooling time

45.4 s 0.93 0.70 0.81

1 +0.5 +1% +0.5 0.88 0.64 0.75

2 -0.5 +1% +0.5 0.88 0.78 0.83

3 +0.5 -1% +0.5 0.89 0.65 0.76

4 -0.5 -1% +0.5 0.96 0.83 0.89

5 +0.5 +1% -0.5 0.88 0.67 0.77

6 -0.5 +1% -0.5 0.98 0.77 0.86

7 +0.5 -1% -0.5 0.98 0.70 0.83

8 -0.5 -1% -0.5 1.03 0.88 0.95




TABLE V Robustness quality of 2.5-inch LGP injection compression molding obtained using the proposed method

The initial setting The robust setting

Exp.

No.

Average

nine-point

heights

(μm)

Range of

nine-point

heights

(μm)

Exp.

No

Average

nine-point

heights

(μm)

Range of

nine-point

heights

(μm)

Exp.

No.

Average

nine-point

heights

(μm)

Range of

nine-point

heights

(μm)

Exp.

No

Average

nine-point

heights

(μm)

Range of

nine-point

heights

(μm)

1 (12.71) 0.36 26 (12.71) (0.44) 1 13.62 0.39 26 13.63 0.41 2 (12.72) 0.35 27 (12.70) 0.40 2 13.62 0.39 27 13.62 0.39 3 (12.72) 0.40 28 (12.70) 0.38 3 13.61 0.34 28 13.64 0.39 4 (12.70) 0.40 29 (12.72) (0.43) 4 13.61 0.38 29 13.63 0.35 5 (12.70) 0.40 30 (12.70) 0.39 5 13.61 0.36 30 13.60 0.33 6 (12.70) (0.44) 31 (12.73) 0.39 6 13.63 0.38 31 13.62 0.38 7 (12.69) (0.43) 32 (12.70) (0.43) 7 13.62 0.42 32 13.64 0.36 8 (12.72) (0.43) 33 (12.69) 0.36 8 13.63 0.39 33 13.63 0.40 9 (12.71) 0.40 34 (12.71) 0.38 9 13.62 0.37 34 13.62 0.38

10 (12.71) 0.34 35 (12.73) 0.40 10 13.63 0.41 35 13.62 0.36 11 (12.72) (0.42) 36 (12.71) 0.36 11 13.63 0.39 36 13.62 0.38 12 (12.70) 0.37 37 (12.70) (0.42) 12 13.62 0.39 37 13.60 0.35 13 (12.72) 0.39 38 (12.73) 0.38 13 13.61 0.39 38 13.62 0.37 14 (12.73) (0.41) 39 (12.71) (0.42) 14 13.62 0.36 39 13.62 0.33 15 (12.72) 0.37 40 (12.70) (0.41) 15 13.63 0.39 40 13.63 0.40 16 (12.71) 0.39 41 (12.72) 0.39 16 13.62 0.34 41 13.63 0.37 17 (12.72) 0.40 42 (12.72) 0.36 17 13.62 0.41 42 13.62 0.37 18 (12.72) 0.40 43 (12.73) 0.39 18 13.62 0.33 43 13.61 0.33 19 (12.70) 0.39 44 (12.71) (0.42) 19 13.62 0.39 44 13.61 0.37 20 (12.70) (0.41) 45 (12.71) 0.38 20 13.62 0.39 45 13.63 0.37 21 (12.71) (0.42) 46 (12.71) (0.41) 21 13.63 0.40 46 13.62 0.38 22 (12.72) 0.38 47 (12.70) 0.38 22 13.62 0.39 47 13.63 0.38 23 (12.71) (0.41) 48 (12.71) (0.43) 23 13.62 0.37 48 13.62 0.35 24 (12.72) 0.38 49 (12.71) (0.42) 24 13.63 0.39 49 13.62 0.33 25 (12.71) 0.37 50 (12.72) 0.40 25 13.62 0.35 50 13.62 0.41

designing robust parameters for injection-compression ... · light-guided plate; regression model....

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