design of u-shape milled groove conformal coolin

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 1, pp. 73-84 FEBRUARY 2011 / 73

DOI: 10.1007/s12541-011-0009-8

1. Introduction

Injection molding is the most popular method for producing

plastic products because of its high productivity and the

manufacturability for making various complex shapes. The

injection molding process includes six stages: mold closing, mold

filling, packing, cooling, mold opening, and part ejection. Among

these stages, cooling stage is the most important phase because it

significantly affects the productivity and the quality of molded part.

Normally, 70%~80% of the molding cycle is taken up by cooling

stage. An appropriate cooling channels design can considerably

reduce the cooling time and increase the productivity of the

injection molding process. On the other hand, an efficient cooling

system which achieves a uniform temperature distribution can

minimize the undesired defects that influence the quality of molded

part such as hot spots, sink marks, differential shrinkage, thermal

residual stress, and warpage.1,2

Traditionally, mold cooling design is still mainly based on

practical knowledge and designers experience. This method is

simple and may be efficient in practice; however, this approach

becomes less feasible when the molded part becomes more complex

and a high cooling efficiency is required. In addition, conventional

straight cooling channels are machined by hole-drilling as close to

the cavitys surfaces of the mold as possible. The free-form surfaces

of the cavity surrounded by straight cooling lines and the molded

part will be cool unevenly because of the variation of the distances

between the cavitys wall and cooling lines. This not only results in

potential defects of molded part but also increases the cooling time.

Alternative cooling device such as baffles, bubblers and thermal

pins that are used to cool areas being far from main cooling

channels can improve the cooling quality. However, this method is

not always effective due to the high pressure drop in cooling

channels system, especially for medium-sized and large-sized parts

with free-form surfaces.

The importance of cooling process in injection molding has

drawn a great attention of plastic engineers and researchers. Some

researches have focused on analysis of the cooling system and on

how to optimize the cooling channels layout in terms of cooling

channel size and location by the mathematical calculation and

analytical method.3-5 These practical approaches were reported to

be more convenient and faster than finite difference and finite

element method. They demand less effort of plastic designers than

Design of U-shape Milled Groove Conformal Cooling Channels for Plastic Injection Mold

Xuan-Phuong Dang1 and Hong-Seok Park1,#

1 School of Mechanical and Automotive Engineering, University of Ulsan, San 29, Mugeo 2-dong, Namgu, Ulsan, Korea, 680-749# Corresponding Author / E-mail: [email protected], TEL: +82-52-259-2294, FAX: +82-52-259-1680

KEYWORDS: Design optimization, Injection molding, Conformal cooling channels, Milled groove cooling channels

Besides the solid free-form fabrication technology, milling operation is an alternative applicable method to make complex

cooling channels conform to the surface of the mold cavity. This paper presents the U-shape milled groove conformal

cooling channels and proposes the design optimization process in order to obtain an optimal cooling channels

configuration and target mold temperature. The relation between the cycle averaged thermal behavior of the mold cavity

and the two-dimensional configuration of cooling channels was first investigated thoroughly by an analytical method.

Design of experiment and 2D simulation were done to obtain the mold wall temperature and to check the feasibility of the

analytical method. The optimization process of the free-form conformal cooling channels is based on the combination of

both analytical method and 3D CAE simulation. The analytical step relies on explicit mathematic formulas, so it can

approach the neighboring optimal solution quickly. Subsequently, the three-dimensional heat transfer simulation is applied

to fine-tune the optimization results. A case study for a plastic car fender was investigated to verify the feasibility of the

proposed method. The results show that conformal cooling channel gives a uniform cooling, reducing the cooling time and

increasing the molded parts quality with less effort of plastic designers and high computational efficiency.

Manuscript received: January 5, 2010 / Accepted: October 24, 2010

KSPE and Springer 2011

74 / FEBRUARY 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 1

those of numerical and simulation software. However, these

methods can be applied to simple molded parts. Other approaches

used 2-D boundary element method and sensitive analysis in

conjunction with the gradient optimization algorithm or hybrid

optimizer to optimize cooling channels system.6,7 More recently,

applying 3-D CAE and 3-D FEM computer-aided simulation have

been widely used to investigate the thermal behavior of the cooling

system and the configuration of conformal cooling channels.8,9

These researches results showed that the conformal cooling

channels give a shorter cooling time and better temperature

distribution than those of conventional cooling channels. Park and

Pham10 introduced an optimization strategy and investigated some

types of conformal cooling layout for an automotive part by

applying analytic formulas. Subsequently, they used CAE flow

simulation for verifying the optimization results and showing the

cooling effect of conformal cooling channels.

To obtain a uniform cooling, the cooling channels should

conform to the surface of the mold cavity. This type of cooling

system is called conformal cooling channels. The application of this

new kind of cooling channels is based on the development of solid

free-form fabrication (SFF) technology. Some of works studied the

advantages of the conformal cooling system and how to optimize

the conformal cooling channels in injection molding tools.11,12 The

results were reported that conformal cooling channels offer better

temperature uniformity within the mold cavity and better molded

parts quality compared to straight cooling channels. SFF or rapid

prototyping technology brings the opportunities to fabricate very

complex conformal cooling channels inside the mold core and mold

cavity,13 but this technique is still expensive, especially for large-

sized mold. On the other hand, the kinds of metal powders used in

rapid prototyping techniques, for example 3D printing, selective

laser sintering, electron beam melting, and laser engineered net

shaping, are limited. It means that the choice of mold material with

appropriate thermal and mechanical properties for making

conformal cooling channels by SFF is narrower than that of

conventional mold. These issues hinder the popular use of rapid

prototyping technique for making large injection mold.

Although a great of attention has been paid to improve the

performance of the cooling system, most of the published works are

only feasible for simple plastic parts. One of the evidence is that all

the examples used in various case studies are very simple.8 Some of

works3,6,7,12,14 relied on 1-D or 2-D heat transfer analysis meanwhile

the geometry of plastic parts are usually complex, and they need a

3-D analysis. Moreover, sensitive analysis, finite element or

boundary element coding for optimization of some specific cases

are still academic and lack of generalization, so they are

inconvenient to apply in reality. On the contrary, some of works8,9,15

applied 3-D CAE tools to solve the cooling problem for some more

complex parts. Yet, the method of reducing the cooling time and

optimizing the configuration of conformal cooling channels of these

studies were not adequate.

This paper is intended as a contribution to solve this on-going

problem by introducing U-shape milled groove conformal cooling

channels fabricated by CNC milling machine instead of rapid

prototyping method. This approach is suitable for medium-sized

and large-sized molded part with free-form surface. The relation

between the configuration of cooling channels and cycle averaged

thermal behavior of the mold cavity are investigated thoroughly.

The size, location, and layout of cooling channels for a quite

complex molded part are optimized by the combination of an

applicable analytical model based on the equivalent model,

computer-aided 3-D heat transfer analysis, and effective

optimization strategy. This approach would therefore offer a more

feasible and practical way to design an optimal conformal cooling

channel and to meet the requirement of reducing the cooling time

and increasing molded part quality with less effort of plastic

designers.

2. U-shape milled groove conformal cooling channels

Milled groove cooling channels in spiral form has been used for

flat parts with round and circular shape in order to obtain better

temperature control. This kind of cooling channels is more

expensive to make comparing to straight-drilled one, but produces

high-quality and distortion-free parts such as precision gears and

compact discs.16 Sun8 proposed a modified milled groove method

applied to medium free-form parts with two case studies of mouse

cover and iron cover. Intensive studies on this kind of cooling

channels have not been carried out adequately. In this paper, milled

groove cooling channels method is continued to investigate for

larger plastic part in automotive industry. Further more, the

influence of cooling channels configuration to the thermal behavior

of the mold cavity and the way of optimization are addressed in the

upcoming sections.

The conformal cooling channels are different from straight-

drilled conventional cooling channels. In conventional cooling

channels, the free-form surface of mold cavity is surrounded by

straight cooling lines machined by drilling method. It is clear that

the distance from the cooling lines and mold cavity surface varies

and results in uneven cooling effect. On the contrary, in the

conformal cooling channels, the cooling paths match the mold

cavity surface well by keeping a nearly constant distance between

cooling paths and mold cavity surface. It was reported that this kind

of cooling channels gives better even temperature distribution in the

molded part than that of the conventional one. Figure 1 shows an

example of a conformal cooling channel for a supposed free-form

Fig. 1 A conformal cooling channels surround a free-form part

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 1 FEBRUARY 2011 / 75

molded part.

Besides SFF method, milling by CNC milling machine is an

alternative method for making the conformal cooling channels,

even though it is not flexible than the SFF method. However, milled

groove cooling channels method can be applied to any material

which is used to make the mold. In addition, it is not necessary to

machine the cooling channel precisely, so the machining time can

be reduced by applying high-speed machining and high material

removal rate technology. Milled groove cooling channels pattern

can be designed freely to avoid interfering with other features in the

mold such as ejector pins or other components.

The milled groove cooling channels are modeled by extruding

the cooling layouts including lines and curves with a thickness d in

XY plane up to the offset surface of the cavity impression. There

are two ways to make U-shape milled groove cooling channels. The

first method is applied when milled groove is deeper than the

permitted length of ball end milling tool. In this case, the big pocket

is machined first then the U-shape pockets are milled with a

constant depth into the offset surface of the mold core and mold

cavity as shown in Fig. 2. An inserted block is also machined and

assembled to the main mold cavity part to make complete U-shape

mill groove cooling channels for a haft mold. Sealing by O-rings is

required to prevent coolant leakage. The second method should be

used when the deepest milled groove is shorter than the length of

the milling tool. In this method, the pocket milling operation is

performed for the cooling channel groove in the cavity part as

shown by a cross-section in Fig. 3. A similar pattern core insert on

which their bottom surfaces must be offset from the mold

impression to keep the constant cross-section of cooling paths is

also milled. A complete U-shape cooing is obtained when the mold

cavity part and core inserts part are assembled and fixed by socket

screws. The cross-section of a U-shape cooling channels is depicted

in Fig. 3. In heat transfer analysis and finite element method,

cooling channels are treated as beam elements; hence equivalent

diameter de based on equivalent cross-sectional area is defined as

follows:

2

14

2 2 4

e

d dW H

d

+

= (1)

The shape factor defined by the ratio of perimeter of the U-

shape cross-section and the perimeter of the circle is calculated as

follow:

2( )c

H dS

d

+= (2)

Milled groove cooling channel burdens the mold manufacturing

cost compared to straight-drilled channels due to extra expenditure

of mold material and milling operation. In plastic injection molding,

trade-offs are sometimes required. It can be seen that the volume of

material removal of two previously mentioned milled groove

methods are the same and equal to the bounding box volume of the

whole core inserts in Fig. 2. However, the second method can

reduce the volume of removal if the parallel and zigzag types of

insert are formed by bending a sheet of soft metal material with an

appropriate thickness corresponding to milled groove. Subsequently,

these inserts are fixed on a plate with similar grooves patterns, and

then the whole insert block is milled to obtain the final shape. It is

noticed that there can be three types of milled groove conformal

cooling channels layout: parallel type, zigzag type and spiral type.

This paper mainly focus on the parallel and zigzag type because it is

easier to form the parallel inserts using sheet metal as previously

mentioned for reducing the extra machining cost of U-shape

conformal cooling channels. In this case, the control of mold

temperature can be done by adjusting the position of cooling

channels closer to or farther from the surface of molded part in Z

direction. This method is more convenient for automatic

optimization as the number of variables is reduced.

3. Physical and mathematical modeling

In the physical sense, cooling process in injection molding is a

complex heat transfer problem. To simplify the mathematical model,

some of the assumptions are applied.4,6 The objective of mold

cooling analysis is to find the temperature distribution in the

molded part and mold cavity surface during cooling stage. When

the molding process reaches steady-state after several cycles, the

average temperature of mold is constant even though the true

temperature fluctuates periodically during the molding process

because of the cyclic interaction between the hot plastic and the

cold mold. For the convenience and efficiency in computation,

Fig. 2 Milled groove method for deep cooling groove

Fig. 3 Cross-section of U-shape milled groove cooling channels


cycle-averaged temperature approach is used for mold region and

transition analysis is applied to the molded part.4,6,17

The general heat conduction involving transition heat transfer

problem is governed by the partial differential equation. The cycle-

averaged temperature distribution can be represented by the steady-

state Laplace heat conduction equation. When the heat balance is

established, the heat flux supplied to the mold and the heat flux

removed from the mold must be in equilibrium. Figure 4 shows the

sketch of configuration of cooling system and heat flows in an

injection mold. The heat balance is expressed by equation:

0m c e

Q Q Q+ + = (3)

where ,m

Q c

Q and e

Q are the heat flux from the melt, the heat

flux exchange with coolant and environment, respectively.

The heat from the molten polymer is taken away by the coolant

moving through the cooling channels and by the environment

around the molds exterior surfaces. The heat exchange with the

coolant is taken place by force convection, and the heat exchange

with environment is transported by convection and radiation at side

faces of the mold and heat conduction into machine platens. In

application, the mold exterior faces can be treated as adiabatic

because the heat lost through these faces is less than 5%.6,18

Therefore, the heat exchange can be considered as solely the heat

exchange between the hot polymer and the coolant. The equation of

energy balance is simplified by neglecting the heat lost to the

surrounded environment.

0m c

Q Q+ = (4)

Heat flux from the molten plastic into the coolant can be

calculated as5

310 [ ( ) ]2m p M E m

sQ c T T i x

= + (5)

Heat flux from the mold exchanges with coolant in the time tc

amounts to6:

( )1

1

3

3

1 110

10c c W C

st e

Q t T Td k S

=

(6)

In fact, the total time that the heat flux transfers to coolant

should be cycle time including filling time tf, cooling time tc and

mold opening time to. By comparing the analysis results obtained

by the analytical method using the formula (6) and the analysis

result obtained by commercial flow simulation software, the

formula (6) under-estimates the heat flux value. On the contrary, if

tc in (6) is replaced by the sum of tf , tc and to, the formula (6) over-

estimates the heat flux from the mold exchanges with coolant. The

reason is that the mold temperature at the beginning of filling stage

and mold opening is lower than other stages within a molding cycle.

The under-estimation or over-estimation is considerable when the

filing time and mold opening time is not a small portion compared

to the cooling time, especially for the large part with small

thickness. For this reason, the formula (6) is adjusted approximately

based on the investigation of the mold wall temperature of

rectangular flat parts by using both practical analytical model and

numerical simulation.

( )1

3

3

1 1 1 110

2 3 10c f c o W C

st e

Q t t t T Td k S

= + + +

(7)

The influence of the cooling channels position on heat

conduction can be taken into account by applying shape factor19 Se

2

2 sinh(2 / )lne

Sx y x

d

=

(8)

Heat transfer coefficient of water is calculated by20:

0.831.395

e

Rd

= (9)

where the Reynolds number

e

dR u

= (10)

The cooling time of a molded part in the form of plate is calculated

as16,20:

2

2

4lnM W

c

E W

s T Tt

a T T

=

(11)

where

m

p

ka

c= (12)

From the formula (11), it can be seen that the cooling time only

depends on the thermal properties of a plastic, part thickness, and

process conditions. It does not directly depend on cooling channels

configuration. However, cooling channels configuration influences

the mold wall temperature ,W

T so it indirectly influences the

cooling time.

By combining equations from (4) to (12), one can derive the

following equation:

0.8

2 sinh(2 )[ ( ) ]1 12 ln

2 0.03139

p M E m

W C st e

ysxc T T i x

x

T T k d R

+

+

2

2

4 1 1ln

2 3

M W

f o

E W

s T Tt t

a T T

= + +

(13)

Fig. 4 Physical modeling of heat flow and the sketch of cooling

system


Mathematically, with preset TM, TE, ,W

T predefined tf and to,

and others thermal properties of material, equation (13) presents the

relation between cooling time tc and the variables related to cooling

channels configuration including pitch x, depth y and diameter d. In

reality, the mold wall temperature W

T is established by the cooling

channels configuration and predefined parameters TM, TE, tf , to, and

thermal properties of material in equation (13). The value of ,W

T in

turn, results in the cooling time calculated by the formula (11). This

issue will be analyzed more details in the next sections.

4. Optimization of conformal cooling channels

The purpose of design optimization of cooling channels is how

to obtain the target mold temperature, how to reduce the cooling

time and minimize the non-uniformity of the part surface

temperature distribution. Before proceeding with optimization

method, it is necessary to understand thoroughly the reaction of the

thermal behavior of the mold to cooling channels configuration

physically and mathematically.

4.1 The relation between thermal behaviors of the mold and

cooling channels configuration

There are some factors that affect the cooling system

performance such as the layout of channels, coolant parameters, and

mold material into which cooling channels are cut. This paper

mainly focuses on the physical layout of cooling channels because

of its importance. Once the cooling channels were cut, they could

not be reconfigured or adjusted as other factors. For mold cooling

design, the important things are how to achieve a desired target

mold temperature, and how to minimize the cycle time, and

uniformly cool the part. To investigate the relation of thermal

behaviors of the mold and cooling channels configuration

thoroughly and check the feasibility of the analytical model, both

analytical method and design of experiment (DOE) method in

conjunction with CAE simulation were used.

4.1.1 Analytical method

It is known that minimum cooling time depends on mold wall

temperature ;W

T lower mold temperature can significantly reduce

the cooling time21 according to formula (11). ,W

T in turn, depends

on the configurations of cooling channels.22 Therefore, the problem

is optimizing the cooling channels layout and their configurations to

satisfy a pre-determined .W

T To have a general look at this problem,

the relation between thermal behaviors of the mold and cooling

channels configuration is investigated first.

Considering equation (13), this equation has three unknowns

including x, y, and d, so countless roots exist. It means that there are

many combinations of x, y, and d to satisfy the preset .W

T In other

words, different configurations of cooling channels result in

different average mold surface temperature. However, a good

combinations of x, y, and d is the one that makes a uniform

temperature distribution in the mold cavity surfaces.

In mold design practice, the pitch x, the depth y, and diameter d

of cooling channels are chosen as:

1

1

2

1

8mm 14mm

and 2 5

1 5

dx d

y d

=

=

(14)

The figure 5 illustrates the effect of cooling channels

configuration on W

T for a given molded part thickness. Thermal

properties of materials and specific processing conditions are shown

in Table 1. This graph is drawn by using the system of equations

(13) and (14). The graph shows that when the pitch x and depth y

increase, the mold temperature W

T increases. In other words, when

the cooling channels locate near the mold cavity surface and/or the

pitch of cooling channels are small, the mold temperature decreases

and the cooling time also decreases because the time required for

solidifying the product decreases.23 The effect of the depth y on the

mold temperature is greater than those of the pitch x because the

slope of the temperature surfaces in Fig. 5 in y/d axis is greater than

those of x/d axis.

It can be seen that analytical method based on explicit function

(13) only gives the average mold temperature. In cooling design, as

previously mentioned, not only the target average mold temperature

but also so the uniformity of temperature of mold cavity surfaces

should be obtained. To investigate the influence of cooling

Table 1 Example values of parameters that are used in calculating

cooling channels configuration

Parameters Value

Molded part thickness s (mm) 3.0

Melt temperature TM (C) 230.0

Demolding temperature TE (C) 97.0

Specific heat of the melt cp (KJ/(kgK)) 1.79

Melt density (g/cm3) 0.929

Thermal conductivity of the melt km (W/m.K) 0.189

Thermal conductivity of the steel kst (W/m.K) 45.0

Kinetic viscosity of water (m2/s) 1.210-6

Velocity of cooling water u (m/s) 1.0

Temperature of cooling water TC (C) 20

Fig. 5 Effect of cooling channels configuration on TW for a specific

processing conditions


channels configuration to mold temperature variation and

temperature distribution, simulation and design of experiment were

used as a supplementary method.

4.1.2 Simulation and design of experiment method

The analytic equations (13) is derived from the two-

dimensional heat transfer problem of mold cooling for a plastic

plate, so a FEM model for identifying mold temperature distribution

on the cavity surface was built for a flat molded part. The mold

cross-section is considered, and two-dimensional heat transfer

computation is considered as a suitable model because it is

unnecessary to perform the simulation for the whole mold. Figure 6

depicts the FEM model for calculating the mold surface

temperature distribution.

Instead of spending a lot of time to investigate all the value of d

in its range, d = 10 mm was chosen to analyze the affect of cooling

channels location to the temperature distribution of the mold wall.

This choice retains the generality since the pitch x and depth y are

multiples of diameter d. When d is fixed, there are only two factors

left including x and y. Full factorial design of experiment for two

factors and four levels was selected so that there were sixteen

experiments. The necessary input data is shown in Table 1. Figure 7

depicts the DOE results of the mold temperature variations with

respect to different locations of cooling channels. It can be seen that

if the pitch x is large and the depth y is small, the mold wall

temperature variation increases. As a result, the mold temperature

distribution and molded part temperature distribution are uneven.

Response surface methodology (RSM) was used to find

approximated mathematical equations that express the response of

mold temperature to the cooling channels configuration. The mold

temperature is represented by the quadratic equation.

Tw = 0.268x2 + 0.257y2 + 0.157xy +3.430x + 4.131y + 13.6 (15)

The R-squared coefficient that indicates the goodness of fit of

this model is 0.983. The fidelity of RSM model was verified by

comparing this model with the analytical model obtained from

equation (13). The shape of analytic and RSM surfaces were drawn

on the same graph for the comparison purpose as shown in Fig. 8.

The maximum error between analytic surface and RSM surface is

about 7.4%; however, most of the points in design space have the

error below 3.6%. Therefore, the analytic model can be applicable

for estimating the behavior of mold temperature towards cooling

channels configuration.

DOE method and FEM simulation also gave the results of

temperature variation in mold surface. For a specific input data

given in Table 1, the variation of mold temperature is represented

by the quadratic response surface equation:

TW =0.149x2 + 0.448y2 - 0.540xy + 1.162x 1.604y +0.505 (16)

Figure 9 shows the shape of mold temperature variation of the

equation (16). Fortunately, this surface has an extremum point in

the middle region of design space. For example, if the designer

wants the mold temperature variation to be lower than 0.5C, the

feasible region to select the pitch and the depth of cooling channels

Fig. 6 FEM model to identify mold temperature distribution

(1)

(9)

(5)

(13)

(14)

(10)

(2)

(6)

(3)

(11)

(15)

(7)

(12)

(16)

(8)

(4)

Fig. 7 Mold surface temperature variations for different cooling

channel depth y and pitch x

Fig. 8 Comparison between analytic surface and RSM surface

Fig. 9 Shape of response surface of mold temperature variation


will be the one in Fig. 10. It is clear that the feasible region for the

solution of equation (13) is narrowed down when the uniformity of

mold temperature is considered strictly. The more the temperature

uniformity is required, the less the feasible region is. The optimal

cooling channels configuration should be in the feasible region.

There exists a line in the feasible region that there is smallest

temperature variation (see Fig. 10). This line shows the good

combinations between y and x and it can be estimated by an

approximate linear equation:

0.7 1.6y x d= + (17)

Although approximate equations (15), (16) and (17) are

estimated based on a particular polymer and mold material, the

thermal behavior of the mold towards cooling channels

configuration for other polymer material and molding condition

also has a similar response as shown in Fig. 5 and Fig. 10.

Consequently, equation (17) can be used as a guideline to support

the selection of x and y. In some cases, to satisfy other constraints,

the linear equation (17) that represents a line should be widened

into its left and right side to make a ribbon area (see Fig. 10)

described by inequality equations:

0.7 (1.6 )

0.7 (1.6 )

y x d

y x d

+

+ + (18)

Even though the feasible region is getting smaller when stricter

constraints are considered, there are still many combinations of

cooling channels location and diameter as above mentioned. The

raising question is that what are the best values of pitch x, depth y,

and diameter d for a particular mold cooling design. This issue is

discussed in the optimization method section.

4.2 Optimization method for designing conformal cooling

channel

4.2.1 Objective function

The aim of mold cooling design optimization is obtaining

uniform temperature distribution of the part surface, achieving

target mold temperature, and minimizing the cooling time. Even

though the required cooling time is calculated by formula (11),

improper cooling channels design will result in longer actual

cooling time due to the uneven cooling and high temperature at

some location in the part surface. Satisfying uniform cooling, a

strong point of conformal cooling, somewhat satisfies the

requirement of reducing cooling time. Optimization conformal

cooling channels focuses on how to make the mold cool uniformly

and to meet the target average mold temperature.

Cooling process of a curved surface is different from those of a

flat part due to 3D effect in heat transfer. With the same cooling

channel deployment, the cooling effect of the inner and outer

surface on the molded part is different. The difference of

temperature distribution in both sides will cause residual stress and

bend the product after cooling. For above reasons, the design goals

include:

- Obtaining the target average mold temperature W

T represented in

equation (13)

- Minimizing the difference of average temperature between the

inner faces and outer faces of molded part:

1 1

1 1( ) ( ) 0N M

i i o j

i j

T TN M= =

= (19)

where N and M, Ti and To are the number of elements, the

temperature at corresponding elements in the inner and outer

surfaces, respectively. The temperature at any element is obtained

by querying the simulation results of 3D CAE analysis.

4.2.2 Constraints

Proper constraints have to be enforced upon all design variables

in form of equality or inequality constraints in order to keep the

design optimization realistic from the design and manufacturing

point of view. Constraints on cooling channels design includes the

lower and upper limit of the pitch distance x of channels, the

distance from the cavity surface to the channels y, and cooling

channel diameter d. Diameter of cooling channels should be

properly selected to ensure heat removal and to allow sufficient

flow rate and turbulent flow. In reality, the cooling channel diameter

depends on average part thickness s, and it can be determined by

empirical formulation as follows5:

2 8 10

4 10 12

6 10 14

s mm mm d mm

s mm mm d mm

s mm mm d mm

(20)

Furthermore, according to the manufacturers view point, the

diameter of milled groove cooling channels also depends on how

deep the milled grooves are because the standard length of milling

tools depends on the tool diameter.

The range of validity for the pitch x and depth y of cooling

channels vary within the range described in formula (14). The

distance of pitch x and depth y are also confined by the requirement

of avoiding the interference of cooling channels with other

components such as ejector pins or sliders.

Fig. 10 An example of feasible region to select the parameters of

cooling lines


4.2.3 Systematic procedure for optimization

With the advancement of both computers hardware and CAE

software, three-dimensional computation of heat transfer and flow

simulation in injection molding is widely used in mold design

engineering. Instead of performing the simulation for each cross-

section, the entire mold with all cooling channels is simulated. The

advantage of 3D simulation over analytical computation is the more

accurate simulation of cooling conditions, especially for complex

part.16 In fact, the thermal properties of polymers are time-

dependent, and this characteristic significantly influences the

analysis results.24,25 Three-dimensional CAE simulation software

tackles this problem very well, so the precise result can be obtained

in comparison with applying the analytical method with constant

thermal properties. Moreover, the ability of coupling with filling

and packing computation, warpage and residual stress analysis as

well as convenient graphical visualization are also the strong points

of 3D CAE simulation. However, the computation cost of 3D

analysis for each run is still very high while the optimization

process always requires a loop of analysis, modifying input, and

reanalysis for searching the optimum design point. In addition,

when the number of design variable increases, the number of

iterations and computation cost also increase correspondingly. To

improve the accuracy of analysis and reduce the computation time,

combination approach in which analytical method and CAE

simulation-based method is proposed in this paper.

The cooperation between analytic approach and CAE

simulation-based approach can be carried out by two steps. In the

first step, analytical method is used to determine the initial

configuration of cooling channels including pitch x, depth y, and

diameter d. Even though this step is called initial design, its result

tends to come up to the optimal design since the analytical method

has been reported to be applicable for simple molded part.5 This

statement was also confirmed in Section 4.1.2 by DOE method. In

the second step, the number of design variables is reduced to only

one (the distance from the cavity surface to the channels y). The

target mold temperature and the uniformity of temperature between

the top and bottom faces of molded part can be reached after a few

iterations by adjusting the variables y using linear interpolation

method (Regula Falsi method). Consequently, the number of

simulations is reduced and the computational efficiency increases.

The systematic procedure for optimizing conformal cooling

channels design is shown in Fig. 11.

4.2.4 Implementation

Returning to how to determine the cooling channels

configuration, the possible roots of equation (13) is the intersection

of the surface W

T =f (x,y) and the plane W

T = const when a given

cooling channel diameter d and a target mold temperature W

T are

predefined (see Fig. 12). Applying the constraint condition that the

Fig. 11 Strategy for optimizing conformal cooling channels

Fig. 12 Shape of solution curve of equation (13) for a given d and

WT

Fig. 13 Example of the possible solutions of equation (13) when

considering mold temperature variation


variation of mold wall temperature does not exceed a given

allowance as illustrated in Fig. 9 and Fig. 10, the possible solution

curve must be in the feasible region as shown in Fig. 13. It can be

seen that the solution space is narrowed down. For instance, the

initial design space of the pitch x and depth y of cooling channels

are 2d to 5d and 1d to 5d down to approximately 2d to 4.2d and

2.9d to 3.7d respectively for above example.

If W

T increases, for example, W

T =45C, the possible solution

curve moves upward and the range of feasible x and y also changes

as shown in Fig. 13. It can be seen that the range of choice of pitch

x is wider than those of depth y. If the target mold temperature W

T

increases, the upper limit of pitch x and depth y can also increases

and vice versa. For milled groove cooling channels, the upper range

of pitch x should be selected in order to reduce the number of

cooling paths or reduce the machined cost of the cooling system.

When proper values of d and x are selected as experienced before,

the equation (13) becomes an equation with one variable y. If the

solution y violates the constraint of y, x must be re-selected and this

equation is solved again. An alternative method is that it is no need

to specify a certain value of x; the solver will search the solution of

equation (13) with two variables x and y to satisfy all constraints

and optimality conditions (18) and (20).

Besides solving explicit equation for finding the good initial

cooling channels configuration, CAD modeling and CAE

simulation and analysis are the important tools to support design

process, fine-tune and verify the result. The systematic procedure of

applying computer-aided design and CAE simulation for cooling

channels design optimization can be presented as follows (see Fig.

14). First of all, based on the results obtained from the analytical

analysis step, approximate cooling channels are modeled by

projecting cooling channels layout from a plane to the offset

surfaces of the molded part. Subsequently, the coordinate of cooling

channels are generated and stored in a text file. Next, the conformal

cooling channels are imported to CAE environment and meshed

automatically by an Application Programming Interface (API) via

Visual Basic Scripting (VBS) language. After that, cooling

simulation is performed to obtain the exact results of average mold

temperature and temperature distribution of the molded part. Finally,

the temperature of all elements or considered elements are queried

and stored in a text file to support data for optimization process.

The third step to the last step are looped until the optimal conditions

are satisfied. This process is controlled automatically by an

optimizer programmed by Matlab and VBS language.

5. Case study

In order to prove the applicability and the feasibility of the

milled groove conformal cooling channels, various practical cases

had been carried out. In this section, a typical case study is

presented. The molded part is a plastic car fender with the bounding

box dimensions and thickness are 348235115 mm and 2.5 mm

respectively as shown in Fig. 15. The polymer material is Noryl

GTX979 which can suffer a high temperature up to 180C in online

painting process. Material properties of polymer, mold, and coolant

are shown in Table 2.

The molding parameters are recommended by material

manufacturer as shown in Table 3. Filling time was obtained by

performing filling simulation using Moldflow software. The cooling

time was calculated analytically by using the formula (11). Mold

opening time was estimated by the ratio of mold opening distance

and mold opening velocity. According to formula (20) and the

required length of milling tool to machine the cooling groove, the

cooling diameter was selected as 12 mm. The range of pitch x was

selected from 4d to 5d due to a high level of ejection temperature

and requirement of reducing the number of cooling paths. By

applying the solver tools, the results of analytical method are shown

in Table 4.

Table 2 Material properties

Material Water (25C) Steel (P20) Plastic

Density (kg/m3) 996 7800 930

Specific heat (J/kg.K) 4177 460 4660

Thermal conductivity (W/m.K) 0.615 29 0.25

Viscosity (mm2/s) 0.801 - -

Fig. 15 A plastic car fender with free-form shape

Fig. 14 Application of computer-aided design and CAE simulation in cooling design and analysis


The results from analytical method were used to deploy the

conformal cooling channels as an initial design. Subsequently,

Moldflow software was used to perform the cooling analysis. The

simulation results for the first run showed that the average mold

cavity surface temperature is 98.6C. This figure nearly approaches

the target mold temperature (W

T = 100C). To approach the target

mold temperature, the pitch x of cooling channels was fixed and the

depth y of both core side and cavity side were adjusted. Linear

interpolation method was used as a strategy to reduce the number of

iteration of simulation.

The final results were obtained rapidly after performing three

more simulations. The average mold temperature is 100.4C. The

maximum temperature at the middle layer of the part is 221.2C at

the end of cooling time, so it can allow ejecting the molded part

safely without distortion. The temperature on the part distributes

quite uniform even though the free-form shape of the part is

complex (see Fig. 16). The simulation result shows that the time to

freeze the part to ejection temperature is 6.1 second. This result

agrees well with the cooling time calculated by formula (11) (6.3

second). This means that the cooling design results satisfy the

optimality conditions. The optimum values of the distances from

the cooling channels to the part surface are 46.0 mm and 46.9 mm

for the core side and cavity side of the mold, respectively.

We compared the cooling effect of an un-optimized design and

the optimized design and found that the range between maximum

and minimum temperature in the case of optimized conformal

cooling channel is always smaller than that of the un-optimized one

(see Fig. 17 as an example). In addition, the comparison of the

warpage between the best straight cooling channel and the

conformal one was also carried out. The simulation result shows

that conformal cooling channel reduces 15.7% warpage for this case

study (see Fig. 18). The effect of conformal cooling channel varies

according to the complexness of the molded part. In general,

conformal cooling channels always offer a better uniform cooling

Table 3 Molding parameters

Parameters Value Unit

Melt temperature TM 305 C

Ejection temperature TE 247 C

Average mold temperature W

T 100 C

Filling time tf (obtained by simulation) 1.9 s

Cooling time tc 6.3 s

Mold opening time to 3 s

Velocity of cooling water u 1.0 m/s

Temperature of cooling water TC 25 C

Table 4 The results of optimization obtained from analytical

method

Parameters Value Unit

Cooling channel diameter d 12 mm

Cooling channels pitch x 57.7 mm

Cooling channels depth y 45.2 mm

Velocity of cooling water u 1.0 m/s

Reynolds number Re 11952

Total flow rate of coolant 40.7 l/min

Heat transfer coefficient 4667 W/m2.K

Fig. 16 Average temperature distribution of the part

(a) An un-optimized design (b) Optimized design

Fig. 17 Comparison of temperature profile between un-optimized

and optimized conformal cooling channels

Fig. 18 Comparison of warpage between conventional straight

cooling channel and conformal cooling channel

Fig. 19 The design of milled groove cooling channels for core plate

of the plastic car fender mold


and a lower warpage than straight cooling channels. These are the

advantages of conformal cooling channels.

The structure of the milled groove cooling channels for the core

side of the mold is illustrated in Fig. 19. This construction allows

reducing manufacturing cost as mentioned in Section 2. The

parameters of real U-shape cross-section were calculated by the

formula (1). These data will be used for the milling process when

making the mold.

6. Conclusion

Conformal cooling channels offer the benefit of uniform

cooling that, in turn, reduce the cooling time and increase the

quality of molded part, especially for products with large size and

free-from shape. Besides solid free-form fabrication technique,

milled grove cooling channels is an alternative method which can

be used to make conformal cooling channels. The strong points of

milled groove cooling method are the easiness of machining by

CNC milling machine and easily applicable for all kinds of popular

mold material. Using milled groove cooling channels, designers

have more freedom to deploy the cooling channels layout and the

ability of avoiding the interference with other components in the

mold.

Cooling design optimization of injection molding for a

complex free-form molded part requires a complicated analysis

steps, optimization strategy, and appropriate computer aided tools.

This study presents a systematic method for optimizing the milled

groove cooling channels in order to obtain the target mold

temperature and reduce the cooling time and the non-uniformity of

temperature distribution of the molded part. To increase the

computational effectiveness, both analytical method and

simulation-based method were used successively. The relation

between the thermal behavior of the mold and the cooling channels

layout parameters has been investigated meticulously. The

feasibility of analysis method was proven by comparing the results

of this method with DOE approximation. It can be concluded that

the analytical method is applicable for optimizing of conformal

cooling channels with a moderate preciseness.

When the fidelity of the optimization result is considered, the

support of CAE tools, API programming language, and the

combination optimization techniques are important to increase the

preciseness of the analysis results and to reduce the simulation cost.

The proposed method has been tested in various practical cases in

which the plastic car fender is one of the typical case studies. The

results obtained from the case studies point out that the proposed

method of conformal cooling channels optimization can be used

successfully with less time-consuming and less effort of designers

to improve the part quality and the productivity of plastic

production.

Although milled groove cooling channels increase the cooling

effect of the cooling system in the injection mold, its manufacturing

cost hinders the popular use of this kind of cooling channels.

Nevertheless, the initial extra investment in mold making is

acceptable in mass production and industrial application if the

productivity and part quality improves considerably. The future

work is required for calculating the exact value of break-even point.

Physical experiments are required for verifying the simulation

results. Investigating the manufacturing cost, finding the way to

reduce the manufacturing cost of milled groove cooling channels

and adding the cost factor in optimization will be the objects of

further researches.

ACKNOWLEDGEMENT

This work was supported by Research Fund of the University of

Ulsan (2009). The authors would like to thank the reviewers for

their valuable comments and suggestions.

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