INJECTION MOLDING COOLING TIME
REDUCTION AND THERMAL STRESS
ANALYSIS
Tom Kimerling
University of Massachusetts, Amherst
MIE 605
Finite Element Analysis
Spring 2002
ABSTRACT
A FEA transient thermal structural analysis was
performed to determine the effects of rapidly cooling the
mold surface. The results from the thermal analysis
correlate closely to theoretical values. One drawback of
rapidly cooling the mold surface is that large thermal
stresses are induced in the surrounding material. For this
reason a standard cooling channel geometry and microchannel cooling geometry were both analyzed to
determine robustness. The values from the analysis
predict a fatigue life of 1000 cycles for the standard
cooling channel geometry and 1615 cycles for the microchannel cooling geometry. Also an analysis was
performed on a system that uses a plate that contains
micro-channels. This plate is welded around the edge to
the mold. The analysis showed that a large deflection
would occur in the center of the plate and very large
stresses would be produced in the weld. This leads to the
conclusion that the micro-channels should be attached all
the way across the mold surface rather than just the edges.
BACKGROUND
Injection molding represents a large portion of the
entire plastics processing industry. Due to this fact a
large number of injection molding machine hours are
spent each year making products for the consumer
market. Any reduction in the number of machine hours
required to make a certain number of parts would result in
a substantial cost savings. A new technology developed
by the injection molding laboratory at the University of
Massachusetts has demonstrated the ability to
substantially reduce injection molding cycle time and
therefore machine time.
An injection molding cycle is composed of many
components. The critical components of this cycle are
shown in Figure 1.
Figure 1. Typical injection molding cycle clock
As seen in figure 1, part cooling time accounts for
approximately two thirds of the cycle. Cooling time is a
function of polymer material properties, part thickness
and molding temperatures. The relationship between
these variables is given in the following equation.
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In a standard molding process each of these variables
is fixed when the part geometry and material have been
selected. However, the injection molding laboratory at
the University of Massachusetts has developed a new
technology that allows independent control of mold wall
temperature (RTR). Figure 2 shows an experimental
temperature profile of the mold wall over time. The
temperature is raised above the melt temperature of the
polymer and lowered to ambient temperature in
approximately 5 seconds.
Figure 2. Temperature profile of mold wall over time
This technology allows the ambient temperature of
the mold to be much lower than what is currently used.
In effect, once the cavity has been filled a much larger
temperature differential exists between the polymer and
the mold, which results in an enhanced heat transfer rate
and therefore decreased cooling time. Cooling time
reduction results have been calculated for different
materials and are shown in Table 1.
Minimum
Minimum
cooling
cooling
Percent
Material Tw(C) time (s) Tw(C) time (s) Improvement
PC
PC/ABS
ABS
PMMA
HDPE
PBT
PS
Nylon
PP
104
79
57
60
33
41
55
85
45
46
63
26
89
26
24
36
37
32
10
10
10
10
10
10
10
10
10
24
32
17
55
22
20
25
27
27
48
48
37
38
18
16
30
29
14
Table 1. Cooling time improvement
Average material and molding temperature values
have been used for different types of thermoplastics in
table 1. A constant thickness of 3/16 inches has been
used for comparison purposes. The first minimum
cooling time column represents a standard molding
process while the second cooling time column represents
a mold at ambient temperature. The final column
represents the percent improvement, which results from
using the new technology. While most injection molders
try optimizing process settings to achieve a one or two
percent cycle time reduction, this new technology shows
the ability to reduce cycle time anywhere from 10 to 50
percent.
RAPID COOLING EFFECTS
Although there are many benefits to rapid cooling as
mentioned previously, there are also drawbacks in terms
of thermally induced stresses in the mold. For this reason
a transient thermal structural analysis has been performed
to determine if the new mold geometry will be able to
withstand the rapid cooling of the part. This analysis was
performed using ANSYS? FEA software.
A 2-D model was created of a slab with a large length
to width ratio. This model was used to simulate a section
of a thin walled part. For the thermal analysis only the
temperature at the center of the part was analyzed since
this point experiences the least amount of end effects. In
addition, due to the symmetry of the part and the mold,
only a quarter section of the model needed to be analyzed.
This reduced the processor time needed to analyze the
model.
Material properties were next assigned to the part and
mold geometries. PMMA was chosen for the
thermoplastic due to its large range for cycle time
improvement and its use in common products such as an
LCD light guide panel. The mold material was assigned
as 420 stainless steel. This is the metal currently used by
the injection molding laboratory for the construction of
mold inserts for the RTR process. The material
properties for each of these materials were found using
the matweb website (1).
Initial and boundary conditions were assigned to the
model based on an actual molding process. This included
both free edge convection from the mold exterior to the
air as well as forced edge convection from the mold to the
cooling channels. Initial conditions included setting the
part temperature to the melt temperature of PMMA as
well as the mold temperature to the cooling channel
temperature.
In order to perform a coupled structural analysis,
displacement constraints were needed. These included
fully constraining the exterior surface of the mold as well
as constraining the symmetric surfaces from moving
across the associated plane of symmetry.
An appropriate element needed to be used for the
transient thermal structural analysis. For this purpose,
Plane13 was selected. This element is a 2-D four noded
quadrilateral element that has temperature and
displacement degrees of freedom as well as limited
coupling between fields. The only drawback of this
element is that it also has magnetic properties. In this
analysis, however, the magnetic properties were set to
zero, which negated their effect.
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Since a coupled element was chosen for the analysis
it was possible to perform a direct coupled analysis. For
a transient analysis this is an advantage, because the
sequential method requires inputting the last time step
temperature solution from the transient thermal analysis.
With a large number of time steps this becomes an
arduous process. Using the center temperature nodal
values for both regular cooling and micro-channel cooling
the following plot was created.
Figure 4. Maximum stress in standard cooling
channel geometry
Figure 3. Part centerline temperature
The theoretical cooling curves represent the solution
obtained using the minimum cooling time equation
(theoretical 1) as well as an adjusted equation which more
accurately represents a standard molding process
(theoretical 2). To find the cooling time, an ejection
temperature is set and the corresponding time values are
read off the chart. In the case of a PMMA LCD light
guide panel this value is approximately 85 ?C. The
following table gives the cooling time results for the FEA
models as well as the theoretical formulas.
The maximum stress occurs during the initial time
step. This is due to the temperature gradient having the
greatest value at the start of the transient analysis. The
location of maximum stress occurs in the region of
minimum cross-section between the two channels. This
is the expected location because the mold surface
displacing upwards due to the temperature gradient thus
causing the material between the cooling channels to
elongate. The maximum equivalent stress on the legend
(306 ksi) occurs at the corner where the part and mold
intersect (not shown in figure). This point is considered
to be an artificially induced stress concentration and is
therefore disregarded in the analysis.
Using the
maximum value between the cooling channels of 238 ksi
a high cycle fatigue analysis was performed (figure 5).
Minimum Cooling Time (sec)
Ejection
Temperature
(C)
85
Standard
7.4
Micro- Theoretical Theoretical
Channel
1
2
6.3
5.9
9.1
Table 2. Cooling time comparison
Table 2 and Figure 3 show that the micro-channel
results more closely conform to the theoretical minimum
cooling time while the standard cooling channel results
are closer to the adjusted theoretical value.
The thermal results from the preceding analysis were
coupled with a structural analysis.
This coupling
produced equivalent stress results for each of the
geometries. Figure 4 shows the maximum stress in the
standard cooling channel configuration.
Figure 5. Fatigue analysis of standard cooling
geometry
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The high cycle fatigue formula is only applicable in
the range of 103 to 106 cycles. Since the calculated
fatigue life is at the lower limit of the formula the results
may have a certain amount of error. Also, the formula
assumes the loading is fully reversed. The calculation is
therefore conservative since the mold heating and cooling
only produces tensile stress in the critical region between
the cooling channels.
An equivalent transient structural analysis was also
performed on the micro-channel cooling geometry.
Figure 6 shows the equivalent stress for the microchannel cooling geometry. As can be seen in this figure
the maximum stress occurs between the micro-channels.
This result is expected for the same reasons as the
standard cooling channel geometry.
Figure 7. Fatigue analysis of micro-channel cooling
geometry
An unexpected result of the micro-channel stress
analysis is that the maximum stress is lower than that of
the standard cooling channel geometry. A possible
reason for this is the load is distributed over a greater area
thus causing a lower stress. However, the channels are in
close proximity to the mold surface and therefore
experience a larger thermal gradient, which balance this
affect.
A final structural analysis was performed on a
geometry that simulates a separate thin layer of microchannels on the mold surface that are welded to the mold
around the edge. This is similar to what can be easily
constructed for a physical test of the micro-channel
cooling geometry. Of interest in this analysis is the
maximum deflection of the welded micro-channel plate as
well as the maximum stresses that occur in the weld. The
maximum stress for this geometry is shown in figure 8.
Figure 6. Maximum stress in micro-channel cooling
geometry
As in the standard cooling channel geometry, a stress
concentration exists in the corner where the part intersects
the mold (not shown in figure). For the fatigue analysis
the average equivalent stress value between the microchannels was used (224 ksi). The fatigue calculation is
shown in figure 7.
Figure 8. Maximum equivalent stress in welded
micro-channel plate
According to the analysis, the maximum equivalent
stresses are large enough to cause failure during the first
cooling cycle. While the location of the stress is correct,
the value may be influenced by an artificial stress
concentration due to the exact right angle formed at the
intersection of the surfaces.
To analyze the defle ction of the micro-channel plate a
theoretical calculation was first performed to determine
an approximate value for the displacement.
This
calculation is shown in figure 9.
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CONCLUSION
Figure 9. Theoretical deflection of beam with
temperature gradient
The formula in figure 9 assumes a beam with free
ends. Smaller deflection results are expected for the
model since the ends are fixed. A graph of the deflection
of the center node on the surface of the welded piece is
shown in figure 10.
Figure 10. Mold surface displacement
The displacement results match well with the
prediction. The curve indicates the maximum deflection
value from the FEA analysis will be slightly less than the
theoretical value. The values also become negative after
13 seconds, which is due to the welded micro-channel
piece displacing through the mold surface. This could not
physically occur, but the model did not contain any
contact parameters between the two surfaces.
A FEA transient thermal structural analysis was
performed to determine the effects of rapidly cooling the
mold surface. The results from the thermal analysis
correlate closely to theoretical values. An important
observation from the thermal analysis is that the cooling
time of the micro-channel geometry will approach the
theoretical minimum cooling time, as the channels are
placed closer to the mold surface. This is due to the
ability of the micro-channels to maintain a near perfect
surface temperature, which is assumed by the cooling
time formula.
One drawback of rapidly cooling the mold surface is
that large thermal stresses are induced in the surrounding
material. For this reason a standard cooling channel
geometry and micro-channel cooling geometry were both
analyzed to determine robustness.
This was
accomplished by coupling the results from the transient
thermal analysis to obtain a transient structural analysis.
The maximum equivalent stress values were then used in
a high cycle fatigue formula to determine the number of
cycles to failure of the mold. As expected a large stress
occurs on the initial time step between the cooling
channels. This was due to the thermal gradient being the
largest during the initial time step and the minimum
cross-section being located between the cooling channels.
The values from the analysis predict a fatigue life of 1000
cycles for the standard cooling channel geometry and
1615 cycles for the micro-channel cooling geometry.
An analysis was also performed on a micro-channel
cooling geometry that represents a system that can
currently be easily produced. This system uses a plate
that contains the micro-channels which has been welded
around the edge. The major concern for this geometry is
the deflection of the center of the plate due to thermal
loading and the associated stresses in the weld. The
analysis showed that a large deflection would occur in the
center of the plate and very large stresses would be
produced in the weld. This leads to the conclusion that
the micro-channels should be attached all the way across
the mold surface rather than just the edges.
REFERENCES
1. www.matweb.com
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