Design and Molding Simulation of a Plastic Part

by

Jiajun Shen

An Engineering Project Submitted to the Graduate

Faculty of Rensselaer Polytechnic Institute

in Partial Fulfillment of the

Requirements for the degree of

MASTER OF ENGINEERING IN MECHANICAL ENGINEERING

Approved:

_________________________________________ Ernesto Gutierrez-Miravete, Engineering Project Adviser

Rensselaer Polytechnic Institute Hartford, Connecticut

Apr, 2010

1

CONTENTS LIST OF SYMBOLS ............................................................................................................... 2

LIST OF TABLES ................................................................................................................... 3

LIST OF FIGURES ................................................................................................................. 4

Abstract .................................................................................................................................... 5

1. Introduction ........................................................................................................................ 6

2. Problem Description ........................................................................................................ 10

3. Methodology and Analysis .............................................................................................. 11

3.1 Product Development Environment ....................................................................... 11

3.2 Mold Flow Theoretical Background ...................................................................... 12

3.2.1 Governing Equations .................................................................................. 12

3.2.2 Numerical Method ..................................................................................... 13

3.3 Finite Element Analysis and Details ...................................................................... 13

3.3.1 Pre-processor .............................................................................................. 13

3.3.2 Finite Element Optimization ...................................................................... 13

3.3.3 Single Cavity Mold Design ........................................................................ 16

3.3.4 Material Specification ................................................................................ 17

3.4 Design of Experiments (DOE) ............................................................................... 18

3.4.1 DOE Factors ............................................................................................... 18

3.4.2 Key Factors ................................................................................................ 19

3.5 Multi-cavity Mold Design ...................................................................................... 24

3.6 Additional Results and Discussion ........................................................................ 25

3.7 Another option to reduce warpage ......................................................................... 27

4. Conclusion ....................................................................................................................... 28

5. References ........................................................................................................................ 29

2

LIST OF SYMBOLS

=vector operator del, m-1 u=velocity vector, ms-1

=density, kgm-3 t=time, s

p=pressure, kPa

=momentum flux tensor, Nm-2. xx yx zx are components of the momentum flux tensor, where subscripts refer to direction of momentum transfer and direction of

velocity.

MS =body force due to gravity, N. MxS MyS MzS are components of the body force.

ES =a source of energy per unit volume per unit time, W

inletP =fluid inlet pressure, kPa

0P = fluid initial pressure at gate location, kPa

inletT = fluid inlet temperature, C

0T =fluid initial temperature at gate location, C

walln =normal vector, perpendicular to the surface

wallT =outer surface temperature, C

moldT =mold temperature, C

frontP =front fluid pressure, kPa

k =thermal conductivity, W m-1 K-1

3

LIST OF TABLES

Table 1 DOE factors ........................................................................................................ 18

Table 2 Parameters used in the analysis .......................................................................... 19

Table 3 Factorial design ................................................................................................... 19

Table 4 Single cavity analysis results .............................................................................. 20

4

LIST OF FIGURES

Figure 1 World consumption of plastics by weight ........................................................... 6

Figure 2Main components of the Schick intuition razor ................................................... 7

Figure 3 Razor shaving mechanism diagram ..................................................................... 8

Figure 4 Paddle movements to the right ......................................................................... 8

Figure 5 Paddle movements to the left ........................................................................... 9

Figure 6 Inner slider drawing .......................................................................................... 10

Figure 7 CAD/FEM data exchange ................................................................................. 11

Figure 8 Tetrahedral elements ......................................................................................... 14

Figure 9 Symmetrical mesh ............................................................................................. 14

Figure 10 Non-symmetrical mesh ................................................................................... 15

Figure 11 Mesh statistics ................................................................................................. 15

Figure 12 Aspect ratio ..................................................................................................... 15

Figure 13 Single cavity mold design ............................................................................... 16

Figure 14 a,b Mechanical properties of Ultraform N2320 .............................................. 17

Figure 15 DOE analysis result ......................................................................................... 20

Figure 16 Warpage under condition A ............................................................................ 21

Figure 17 Actual part under condition A ......................................................................... 21

Figure 18 Warpage under condition B ............................................................................. 22

Figure 19 Actual part under condition B ......................................................................... 22

Figure 20 Warpage under condition C ............................................................................. 23

Figure 21 Actual part under condition C ......................................................................... 23

Figure 22 Hot runner system ........................................................................................... 24

Figure 23 Multi-cavity mold design ................................................................................ 24

Figure 24 Warpage results for a multi-cavity mold ......................................................... 25

Figure 25 Comparison of length results ........................................................................... 26

Figure 26 Comparison of warpage results ....................................................................... 26

Figure 27 Compensation design ...................................................................................... 27

Figure 28 Warpage result of opposite design ................................................................. 27

5

Abstract The Schick Intuition female all-in-one razor is the first refillable razor for women

designed to make shaving easier. It has gained a significant market share since it was

launched in 2003.The razor was designed with plastic components forming the overall

structure. This was achieved by utilizing Computer Aided Design (CAD) and analysis

models to ensure the success of the design.

In this project a component referred to as Inner Slider was chosen for a

comprehensive design review and mold flow analysis. The function of the inner slider is

to translate the movement of the soap in relation to the shaving cartridge. As the soap is

consumed during the shaving process the slider allows the cartridge to remain in contact

with the skin. As an additional requirement, the inner slider must have the ability to pass

a drop test when the entire assembly is dropped to the floor. This study will provide two

proposed design solutions for the inner slider. Each solution can be validated by using

two dimensions as a point of reference to measure deformation.

The design task is to construct the part while concurrently meeting the functional

requirements by using Pro/Engineer software. The mold flow analysis is used to predict

the deformation of the part, and then adjust the design accordingly and this is done using

the Mold-Flow system. A Design of Experiments (DOE) of the molding process

parameters is used to identify key molding parameters by analyzing a single cavity

injection system. An additional analysis of a multi-cavity system has been performed

and the results compared with those obtained for the single cavity system. Measurements

of an actual part were also collected.

6

1. Introduction Plastics are widely used in the modern world and it is hard to imagine our life

without them. The first human made plastic was invented by Alexander Parkes in 1855

[1] and since that time plastics have jumped to the No.1 material used, by weight, in the

past century (Figure 1) [2].

Figure 1 World consumption of plastics by weight

Plastics have advantages such as cost, lightweight structure, resilient, resistance to

corrosion, color fastness, transparency, ease of processing, etc. They are being used in a

wide variety of fields such as the medical industry, where they are used for detailed

modeling of organs. In the architectural design industry, plastic forms are used to create

scale replicas of proposed buildings.

The wide range and various types of plastic materials that are available today can be

designed and processed successfully while still meeting high quality, performance, and

profitability requirements. Today and in the future companies must continue to produce

high quality parts in order to remain competitive in the global marketplace. With the

help of computer technology plastic design and processing limitations have been

gradually reduced while the quality has improved significantly.

3D modeling is defined as the process of developing a mathematical representation

of any three dimensional surface of an object. Examples of 3D modeling software that

7

have been widely used for this task include systems such as Pro/Engineer, Uni-graphics,

and SolidWorks. Examples of analytical software include systems such as Ansys,

Comsol, Moldex3D, and Mold-Flow. The design and analytical computer programs,

when utilized together, can help to achieve a high degree of accuracy in manufacturing.

This ultimately leads to dramatically reduced development costs which results in a

shorter time period for delivering a product to the market.

The Schick Intuition female all-in-one razor is the first refillable razor for a woman

that was designed to provide a constant source of lubrication while shaving. This product

was developed in order to meet a need of consumers that was identified during the hair

removal process. It has claimed a significant portion of the market since it was launched

in 2003 (Figure 2).

Figure 2Main components of the Schick intuition razor

The Shaving Cartridge is assembled to the Inner Slider and these components are

then placed within the Outer Slider. The Soap is then fixed to the Outer Slider

completing the sub-assembly. Last, a Paddle component is attached to the exposed slot

on the Outer Slider and the entire assembly is placed within the Handle and secured.

Once this has been completed the Paddle is allowed to rotate on its axis (Figure 3).

When the Paddle rotates it drives the movements of the Inner Slider and Outer

Slider simultaneously. The Sliders now are allowed to transform the movement of the

Soap in a constant relationship to the Shaving Cartridge. If the Cartridge is pushed into

8

the Soap (Figure 4) during use the Soap will now touch the skin first. When the Soap is

consumed during the shave stroke cycle, the Cartridge Blades protrude slightly from the

Soap (Figure 5). As the Blades continue to be in contact with the skin they will be

pushed inward, resulting in the Paddle rotating, to drive the Outer Slider/Soap assembly

forward. This motion will now move the Soap which results in the blade tips and the

Soap to be on the same dimensional plane referred to as a mechanism neutral position

(Figure 3).

Figure 3 Razor shaving mechanism diagram

Figure 4 Paddle movements to the right

9

Figure 5 Paddle movements to the left

In order to keep the cost of goods (COG) as low as possible, the molding cycle time

must be as efficient as practical in order to keep high productivity while still maintaining

acceptable quality levels.

10

2. Problem Description

Within the Intuition shaving cartridge, the angle of the blades plays a critical role

during the shaving process. This can be adversely affected even by slight deformation of

the inner slider component. The key task in the design and analysis is how to make the

inner slider as dimensionally accurate as possible.

The shape of the inner slider is determined by the design and is also influenced by

the injection molding process. Post molding deformation could change the shape of the

part completely. The objective of this project is how to optimize the design, while

accounting for the process deformation by analyzing the molding process.

To meet the required movement of the cartridge, while still considering the

manufacturing variance, the inner slider was designed using standard GT&D tolerance

criteria (Figure 6). A critical dimension of the component is the overall inner slider

length (340.15mm) and the flatness (0.15mm) of the top surface. The plastic material

that was chosen, in part, due to its mechanical and lubricious characteristics is a

Polyoxymethyene (POM) Ultraform N2320-003.

Figure 6 Inner slider drawing

This study focused on two conditions:

The location of the deformation within the part The minimal deformation that can be expected by utilizing various process

conditions during molding.

11

3. Methodology and Analysis

3.1 Product Development Environment

The part was designed using the Pro/Engineer software. This is a CAD application,

using feature-based parametrical construction tool modules that support all activities

related to modeling of the plastic part as well as the injection mold. It maintains all

parameters, which is also useful during the injection molding analysis, in order to

identify the parting plane and define cavity layouts.

The mold design is carried out by using both feature-based and parametric

approaches. When the type and structure of the mold are initially defined, the values

associated to the main parameters are given in order to specify the mold geometry. As

the CAD and FEM process are interactive, designers are required to prioritize important

elements within different parts. The data exchange between CAD and FEM is realized in

several steps (Figure 7) [3].

Figure 7 CAD/FEM data exchange

12

3.2 Mold Flow Theoretical Background

3.2.1 Governing Equations

The mold filling problem involves the solution of the governing equations for mass,

momentum and energy transport.

The equations governing the flow of incompressible fluid include [4]:

The conservation of mass (continuity)

0= u The momentum conservation equations in three dimensions

Mxzxyxxx Szyx

pDtDu +

++

+= )( x-moment

Myzyxyyy Szxy

pDtD +

++

+= )( y-moment (1)

Mzyzxzzz Syxz

pDtDw +

++

+= )( z-moment

And the energy conservation equation

Ezzyzxzzy

yyxyzxyxxx

SkgradTdiv

zw

yw

xw

z

yxzu

yu

xu

DtDE ++

+

++

+

++

++

= )(

)()()()(

)()()()()(

(2)

The boundary conditions are [5]:

at the injection gate,

0

0

TTPP

inlet

inlet

==

(3)

at the mold wall,

moldwall

wall

TTnP

==

0 (4)

and on the front flow region,

0=frontP (5)

13

3.2.2 Numerical Method

The mold filling process requires solving a non-steady state flow problem involving

a moving free surface, which means that the computation domain changes continuously

with time.

The numerical solution is based on a hybrid finite-element finite-difference method

of solving the pressure, flow and temperature fields, and a control-volume method to

track down the moving flow fronts. In order to solve the governing equations, the

domain is discretized using a collection of tetrahedral finite elements (Figure 8). A

tetrahedral element consists of four sub-volumes divided by four control surfaces. Each

control volume is composed of sub-volumes surrounding a node. The net flux of mass,

momentum, energy through the control surfaces is conserved rigorously within the

corresponding control volume.

Equations (1) and (2) include a generation term which is a function of the

temperature, they are all coupled and must be satisfied simultaneously. The key step of

the numerical method is the integration of the governing equations over a control volume

to yield a discretized equation at its nodes. The resulting system of linear algebraic

equations is solved using the Algebraic Multi Grid (AMG) method.

3.3 Finite Element Analysis and Details

3.3.1 Pre-processor

The pre-processor is used to confirm the integrity of the model in order to achieve

an accurate analysis. It is acceptable to remove small features such as corner blends,

radii from mid-plane and dual models in order to reduce computing time without

significantly affecting the results.

3.3.2 Finite Element Optimization

The use of an optimized 3D mesh for this part is critical in order to achieve accurate

results. A 3D mesh represents the CAD model by filling the volume of the model with

four-node tetrahedral elements (Figure 8). 3D meshes work well for parts that are thick

or solid, since the tetrahedral elements give a true 3D representation of the model. Other

14

examples of meshes are Mid-plane and Dual Domain. These types however, are more

applicable for thin-walled, shell-like parts.

The 3D mesh analysis that is used in this project requires more computational time

to complete. However, this 3D tetrahedral mesh is more appropriate for our thick,

complicated shaped model.

Figure 8 Tetrahedral elements

Due to the part being symmetrical, the correct approach consists in creating a mesh

from one half of the part and then mirrors it (Figure 9). This guarantees that the resulting

complete part is symmetrical. By choosing to mesh the entire part one cannot guarantee

that features within the part are truly symmetrical (Figure 10).

Figure 9 Symmetrical mesh

15

Figure 10 Non-symmetrical mesh

When checking a completed mesh for errors, important mesh statistics must be

closely watched in order to achieve accurate results. The report below (Figure 11) shows

that the selected mesh is of good quality and that it is acceptable for further analysis.

Figure 11 Mesh statistics

The aspect ratio of an element is described as the ratio of the longest side in relation

to the height perpendicular to that side (a/b in Figure 12). While for tetrahedral elements

the max AP allowed by Mold-Flow is 50:1. The maximum used in this study is about 9.

Figure 12 Aspect ratio

16

3.3.3 Single Cavity Mold Design

The purpose of the single cavity analysis is to verify the key factors involve in

plastic part warpage and to provide parts for quality testing, color selection, and samples

for demonstration purposes. The mold should be designed in order to be simple enough

to be fabricated quickly at minimal cost. In this project a cold runner system was used in

order to further reduce these costs (Figure 13).

A cold runner system is an economical process used to produce plastic parts of

simple design. The intent is to reduce the complexity of the tool when compared to a full

hot runner system. It also has the advantage of requiring less skill to set up and operate

as well as providing reduced maintenance costs.

In regards to the type of gating that is required on plastic parts there are many types

that are acceptable. The location of the gate is determined by three main factors

The gate location should allow molten plastic material to fill the most outward areas simultaneously.

The gate should be located on a flat surface when possible. In other instances a specific feature may be added to the part design in order to incorporate a gate.

The location should be a result of the whole mold layout considering cooling system, ejection pin location, and steel thickness.

Figure 13 Single cavity mold design

17

3.3.4 Material Specification

Polyoxymethyene (POM) Ultraform N2320-003 [6] was used in this study. This

molten polymer is non-Newtonian fluid whose flow properties are complex functions of

temperature and shear rate (Figure 14 a, b).

Figure 14 a,b Mechanical properties of Ultraform N2320

18

3.4 Design of Experiments (DOE)

3.4.1 DOE Factors

There are three main contributors to the warpage of a plastic part. One is the

shrinkage of the material due to differential cooling. The second is differential shrinkage

which is due to shrinkage variations between the length and the width of a part. The third

one is orientation. Since this resin is isotropic, there is no orientation shrinkage.

Differential cooling shrinkage is the shrinkage contribution due solely to

temperature gradients within the part. While the part is in the mold, temperature

differences from one side of the mold to the other cause variations in shrinkage through

the thickness of the component.

Differential shrinkage is linear shrinkage given by isoSS = 11 which is used for the fill+pack analysis, where isoS is the isotropic shrinkage of the material, which is

2% from the material data sheet. The part is scaled to 02.1%21

11

1 == isoSto

compensate for the isotropic shrinkage.

Many parameters can be used to control the injection process such as cycle time,

injection pressure, coolant flow rate, mold surface temperature, ejection temperature, etc.

In this study the two key parameters that were chosen to do a Design of Experiments

(DOE) analysis were the cycle time and coolant flow rate (Table 1).

Cycle time is the overall sum of the different process steps of the injection molding

process. It consists mainly of the time required for the part to fill and 80% of the part

thickness to freeze.

cycletime(second) coolantflowrate(liter/min)10 1020 1530 20

Table 1 DOE factors

19

The values of all the other parameters used in the analysis are given in Table 2.

Mold temperature 90 C Melt temperature 200 C Coolant inlet temperature 25 C Material injection pressure 70-120MPa Injection speed medium-high Filling control automatic Velocity/pressure switch-over Automatic Tool open/close time 5s Pack/holding control 80% filling pressure VS time

Table 2 Parameters used in the analysis

3.4.2 Key Factors

There are nine combinations of the selected parameters. The maximum deflection is

the result used to find the relationship between the factors (Table 3). The maximum

deflection is not the dimension that we would like to be measured, but rather the most

easily identified (red colored areas in Figure 16) and we can take advantage of that in

order to identify the relationships between parameters by using the DOE.

Conditions Max deflection(mm)

A cycle time 10 seconds 0.4806 flow rate 10 liter/min

B cycle time 20 seconds 0.4734 flow rate 10 liter/min

C cycle time 30 seconds 0.4692 flow rate 10 liter/min

D cycle time 10 seconds 0.4694 flow rate 20 liter/min

E cycle time 20 seconds 0.4735 flow rate 15 liter/min

F cycle time 30 seconds 0.4692 flow rate 20 liter/min

G cycle time 20 seconds 0.4735 flow rate 20 liter/min

H cycle time 30 seconds 0.4694 flow rate 15 liter/min

I cycle time 10 seconds 0.4812 flow rate 15 liter/min

Table 3 Factorial design

20

From the factorial DOE analysis (Figure 15), the cycle time was identified as the

most significant contribution to the maximum deflection, whereas the flow rate is not as

important. Therefore the next step was to use a flow rate of 10 liters per minute in order

to get as much productivity as possible and in order to reduce the cycle time as much as

possible.

Figure 15 DOE analysis result

Since the deformation is not very sensitive to the flow rate, a flow rate of 10 liters

per minute was used as a fixed parameter for further analysis. Since the deformation is

very sensitive to the cycle time, the dimension 340.15 can meet design requirements

with a cycle time in the range of 10s~30s (Table 4), (Figure 16-21).

Conditions MaxDeflection Dim1(340.15) Dim2(

21

Figure 16 shows the computed warpage obtained by the Mold-Flow software using

a single cavity with a cycle time of 10s, coolant flow rate of 10 liter/min and a cold

runner system; all the other parameters are given in Table 2.

Figure 16 Warpage under condition A

Figure 17 shows the actual warpage obtained in a single cavity mold under the same

conditions as in the previous figure. Although the locations of largest warpage are well

predicted by the software, the actual magnitude in the real part is larger.

Figure 17 Actual part under condition A

22

Figure 18 shows the computed warpage obtained by the Mold-Flow software using

a single cavity with a cycle time of 20s, coolant flow rate of 10 liter/min and a cold

runner system; all the other parameters are given in Table 2. Figure 19 shows the actual

warpage. As seen in the previous case, the overall behavior is well predicted by the code.

Figure 18 Warpage under condition B

Figure 19 Actual part under condition B

23

Figure 20 is the computed warpage obtained by the Mold-Flow software, while

Figure 21 shows the actual warpage using a single cavity with cycle time 30s, coolant

flow rate 10 liter/min, colder runner system, all other parameters are given in Table 2.

The trend observed before still shows here, however, the warpage is slightly smaller as

the cycle time increases.

Figure 20 Warpage under condition C

Figure 21 Actual part under condition C

24

3.5 Multi-cavity Mold Design

The ideal injection molding system delivers molded parts of uniform density and

free from runners, flash, and gate stubs. To achieve this, a hot runner system, in contrast

to a cold runner system, is usually employed (Figure 22). The material in the hot runners

is maintained in a molten state and is not ejected with the molded part. Hot runner

systems are also referred to as hot-manifold systems, or runnerless molding.

Figure 22 Hot runner system

In a production environment the material is delivered within the mold by utilizing

an externally heated runner system that consists of a cartridge-heated manifold with

interior flow passages. The manifold is designed with various insulating features to

separate it from the rest of the mold, thus reducing heat transfer loss. In order to simulate

an actual production mold scenario, the parameters of a mold flow analysis must match

the mold design (Figure 23).

Figure 23 Multi-cavity mold designs

25

Figure 24 is the computed warpage obtained using the Mold-Flow software for 4

cavities with a cycle time 10s, coolant flow rate 10 liter/min, hot runner system; all other

parameters are given in Table 2. The maximum deflection calculated in this case is

0.4967mm. This is a little larger than the computed single cavity deflection of

0.4806mm (Table 4) due to the cold runner system losing heat resulting in a lower fluid

temperature within the cavity when compared to a hot runner system.

Figure 24 Warpage results for a multi-cavity mold

3.6 Additional Results and Discussion

Additional tests were done with fixed flow rate 10 liter/min and with different cycle

times from 10s to 30s at interval of 2s. Both computed warpage by Mold-Flow software

and measurements of actual molding parts were collected and compared (Figure 25, 26).

26

Figure 25 shows measured overall inner slider lengths as well as computed values

for both single-cavity (SC) and multi-cavity (MC) mold. There is a slight increase in

length with cycle time. However, the differences among all these lengths decrease as the

cycle time increases. Also the rate of the decrease is larger for the measured data than for

the predictions.

Figure 25 Comparison of length results

Figure 26 shows flatness data collected from both single-cavity (SC) and multi-

cavity (MC) mold. Computed flatness values are also shown for comparison. The

agreement between measurements and predictions is better for longer cycle time. The

warpage decreases with cycle time. This is more likely due to the longer time spent by

the part inside the mold at long cycle times.

Figure 26 Comparison of warpage results

27

The theoretical analysis produces results that are comparable to measured data,

although a slightly larger. Also, the parts obtained using the hot runner system deviate

more than those from the cold runner system.

Some additional observations include:

The analysis does not simulate the ejection. A different ejection pin layout could change the deflection which can change the residual stress.

When the part reaches the ejection temperature, theoretically, this should be the same as the mold temperature (~90C). Because the tool temperature varies, and the

inside of the part is like a sandwich, it still retains a considerable amount of heat.

Therefore, it continues to warp even after it is ejected from the tool.

3.7 Another option to reduce warpage

Another way to minimize the warpage is to compensate in the design of the part. If

one designs the deformed area (top surface) with a compensation factor of 0.15mm

(Figure 27). The warpage results show that the top surface is straight which means the

final deflection is zero (0.15mm compensation minus 0.15mm warpage) (Figure 28).

Figure 27 Compensation design

Figure 28 Warpage result of opposite design

28

4. Conclusion The result of this study using 3D design tools in conjunction with Mold-Flow warp

analysis produced an accurate representation of plastic part deflection.

In summary, the results of this paper have shown the following

Cycle time is the most critical factor affecting warpage. The longer cycle time, the less warpage.

There are three contributors of warpage, the shrinkage due to differential cooling shrinkage, differential shrinkage and orientation shrinkage. In most cases, the

differential cooling shrinkage and differential shrinkage cannot be avoided.

A high quality mesh is critical to ensure accurate results. A simple DOE is helpful to identify key factors affecting warpage and to

minimize the amount of future work. Experimental evidence collected from

single cavity mold can be used to improve and verify the accuracy of the finite

element solution.

Compensating the identified areas of potentially high deformation by using opposite design can also reduce warpage.

Alternately, the study suggested another way of minimizing the deformation by

using a method of compensation in the design. However, if the part is complex, this will

require a substantial amount of time due to features being interactive with one another.

At present, this method has not been tested or verified within our company.

It has been shown in this study that the Mold-Flow analysis can have a significant

positive impact in the design and manufacturing processes. The using of Mold-Flow

could help shorten development time.

29

5. References [1] Edward Chauncey Worden. Nitrocellulose industry. New York, Van Nostrand, 1911.

[2] Dominick V. Rosato, Donald V. Rosato, Marlene G. Rosato; Plastic Design Handbook; Kluwer Academic Publishers, Norwell, MA, 2001, p13. [3] L.M. Galantucci; Evaluation of Filling Conditions of Injection Molding by Integrating Numerical Simulations and Experimental Tests; Materials Processing Technology, July 11 2002. [4] Robert S. Brodkey, Harry C. Hershey; Transport Phenomena; Brodkey Publishing; Columbus, Ohio, 2001

[5] Seong Taek Lim, Woo II Lee; An Analysis of the Three-dimensional Resin-transfer Mold Filling Process; Composites Science and Technology; South Korea; Apr 13 1999.

[6] Auto desk Mold-Flow Insight material data warehouse.

[7] E. Alfredo Campo; The Complete Part Design Handbook for Injection Molding of Thermoplastics; Hanser; Cincinnati, Ohio, 2006.