A METHOD FOR SIMULATING BILATERALLY NON-SYMMETRICAL
INJECTION MOULDING PROCESS
Field of the Invention
This invention concerns the use of improved numeric
techniques to enable computation of injection moulding cycle time and process
parameters and predict process output by way of using published computation
formulas as applicable to bi-laterally symmetrical heat transfer however enable
its application to bi-laterally non symmetrical heat transfer condition.
Background to the Invention
Injection moulding tools are used in industry to form
thermoplastic polymers into a variety of complex shapes. The process involves
the injection of a pre-prepared pliable thermoplastic into a tool whereupon it
acquires the shape of the mould CAVITY within the tool. The thermoplastic is
then cooled so that it sets while retaining the shape of the CAVITY. Other
common terms for the tool are mould or die.
In many industrial applications of injection moulding,
profitability is dependent on having the shortest cycle time between each
moulding process while ensuring the quality of the product produced by the tool
remains within permissible limits. It is vital that the product produced by the
tool reproduces the mould CAVITY accurately and that any residual stress in the
product is minimised so that there is less potential for warpage of the product
as it cools, and/or as it ages. Residual stress in the finished product can
cause warpage over the life of the product due to differential shrinkage. A
short cycle time means a more productive tool. However since the process
involves thermodynamics, the cycle time is significantly influenced by the
thermodynamic performance of the tool and quality is affected by uniformity of
tool temperature all over the tool. Accurate estimate of part thickness average
temperature is vital for prediction of mould shrinkage and thus size the
mould.
Based on traditional formulas published in literature
all cooling and temperature evolution happens in-between symmetrical walls
having identical cooling on both faces and geometric mid plane is the plane
having highest temperature.
However in practice this cooling is never identical due
to:
- Air gap developing on one side, by way of example CAVITY,
as material shrinks away from CAVITY face and shrinks onto CORE. This causes
additional impedance in cooling on the side with air gap.
- Cooling layout on two sides of mould may be different,
due to variety of reasons relating to tool manufacturing and restrictions
imposed by presence of lifters, ejector pins, side COREs etc.
- Various conductivity materials may have been used or
combined with in different sides of tool.
- Differing coolant temperatures and or flow rate may have
beeen used on different sides to have preferential cooling.
- In case of sequential two shot moulding the CORE from
first shot will carry the first shot moulding and present it to second CAVITY
(having additional gap). Second shot will then be moulded in this gap, and,
cooling of this second shot will experience substantial difference in cooling
rate on two sides as plastic from first shot generally will have lot less
thermal conductivity than that of the tool face on the other side and hinder
heat flow to CORE.
Many efforts have been made to date to address these
thermodynamic properties related issues.
Patent number WO97/37823 in name of Kao Corporation
(JP) discusses cycle time analysis when an In Mould Label is associated. When
an In Mould Label is associated, it has impact on heat transfer as the heat has
to traverse through the label on the side where label is and in turn impact
cycle time and cooling characteristic. The Kao's approach is to use finite
element method (FEM). This has a limitation in that you need to create accurate
3D model of tool, part and the label for such an analysis to take place. It
requires expert operators to create such models and also to run such
sophisticated FEM simulation tools. For each iteration of cooling variation, a
new model has to be created and thus the whole analysis process takes
substantial time and cost.
Patent number WO 2010/127772A2 in name of MAGMA
GIESSERITECHNOLOGIE GMBH discusses cycle time analysis and arrives at time to
eject the part after mould filling. This has approach to use finite element
method (FEM). This has a very big limitation in that this too requires very
detailed 3D model of tool with every detail you need to create accurate 3D
model of tool and part for such an analysis to take place. It requires expert
operators, very heavy duty computing power and it requires very long CPU time
to run such sophisticated FEM simulation tools. For each iteration of cooling
geometry, a new model has to be created and thus the whole analysis process
takes substantial time and cost. Thus it cannot be employed for process
development, simulation or scenario studies at early stage of process or even
earlier at project bidding stage.
Research publication 'The Design of Conformal Cooling
Channels in Injection Moulding Tooling, XiaorongXu, Emanual Sachs and Samuel
Allen, of Massachusetts Insititute of Technology, Cambridge, MA 02139,
published in Polymer Engineering and Science, July 2001, Vol41, No.7), has
provided a very effective methodology to estimate tool stabilisation
temperature and in turn cycle time and part average temperatures and midplane
temperatures. However this method has biggest limitation in that it assumes
bi-laterally symmetrical heat transfer and thus limits its use.
An aim of the present invention is to provide an
injection moulding simulation tool with improved prediction of cooling or
heating performance that is easy and cost effective to deploy that overcomes at
least some of these aforementioned difficulties and particularly does not rely
on complex Finite Element Method.
Summary of the Invention
A method for simulating the injection moulding process
consisting of but not limited to cycle time to ejection of the moulded article
from tool and corresponding tool stabilisation temperature and the part
thickness average temperature and the part midplane temperatures by application
of published numeric formulas and methods that assume bilaterally symmetrical
thermal balance between CORE and CAVITY of an injection moulding tool applied
to numeric tasks in analyzing injection moulding process in tools wherein the
CORE and CAVITY may not be having bilaterally symmetrical thermal conditions,
the said method comprising the following steps however not limited to:
Step1 dividing the part thickness in two fractions
wherein by assuming a suitable starting figure of split proportion, arriving at
the first thickness by
multiplying component thickness with split
proportion and doubling it and determining a complimentary thickness,
the
second thickness
, by subtracting first thickness from doubled component
thickness.
Step2 All properties related to CORE of tool under
analysis is specified, for example cooling geometry consisting of cooling
channel cross section height, width, fillet radius, distance to tool surface
and distance between the two adjacent cooling channels, cooling channel
friction factor. In addition the tool material properties consisting of
density, thermal conductivity and specific heat of tool material
are
associated to the first thickness
and the same related to CAVITY of tool
under analysis
are associated to the second thickness
. From here on
everything related to CORE side of tool under analysis will be linked and used
in one side analysis, for example the first thickness and everything related to
CAVITY side of tool under analysis will be linked and used in one side
analysis, the second thickness
Step3 Now we specify coolant properties consisting of
but not limited to Density, Specific heat, flow rate and temperature of coolant
flowing through
CORE is associated to the first thickness
and coolant
properties consisting of but not limited to Density, Specific heat, flow rate
and temperature of coolant flowing through
CAVITY is associated to the
second thickness
.
Step4 Cycletime components made up of Tool closing,
Material injection, Machine Opening and Dwell
are associated equally to the
first thickness and the second thickness
.
Step5 Polymer thermal and mechanical properties and
melt temperature at time of injection
are associated equally to both the
first thickness and the second thickness.
Step6 Part ejection criterion is defined in the form
of midplane temperature at ejection or part thickness average temperature at
ejection.
Step7 There are many formulas available to simulate
cycle time when tool stabilisation temperature is known. However the tool
stabilisation is in turn dependent on cycle time. Hence MIT has published an
algorithm (fig8, prior art) that enables computing tool stabilisation and cycle
time reliably taking into computation their interdependence. Now suitable
traditional numeric formulas to estimate cooling time and corresponding tool
stabilization temperatures are applied to
both the first thicknesses
and
the second thicknesses
in bilaterally symmetrical analysis for a chosen
split proportion of original thickness and defined ejection criterion. In case
of error of tool stabilisation temperature the cycle time result is incremented
in small increments till real solution is achieved.
Step8 Since we want to analyse both split proportions
as pseudo analysis of main part under simulation, we must use same cycle time
for the analysis to be meaningful. Higher of the cooling time for first
thickness and the second thickness is associated to
both the first
thicknesses
and
the second thicknesses
, and the revised tool
stabilisation temperature and corresponding midplane temperature is
determined.
Step9 Difference of midplane temperatures so
determined from such analysis of two complimentary thicknesses is
determined.
Step10 The split proportion is incrementally changed,
accordingly revised figures of the first thickness and the second thickness are
obtained and above process is repeated till such time that the midplane
temperature difference is a very small number.
Step11 Tool stabilisation temperature, the part
average temperature is computed for the first thickness and the second
thickness and a symmetrical graph is generated for part temperature profile for
the first thickness and the second thickness having axis of symmetry being line
showing midplane temperature and end of temperature profile showing temperature
on part surface.
Step12 Now we synthesize graph of temperature profile
of part under simulation. To this end we generate simulated part temperature
profile by combining one half the graph between midplane temperature and part
surface temperature from the first thickness part temperature profile on one
side and one half the graph between midplane temperature and part surface
temperature from the second thickness part temperature profile from other side
and connecting them such that the midplane temperatures, here we ignore small
difference between the midplane temperature and replace them for example with
average values of the two, and are superimposed and part surface temperature
from the first thickness graph and that from the second thickness graph make
two opposite ends of combined graph, this graph represents base solution.
In an alternative embodiment of the invention the
moulding tool consists of more than one material, for example may contain H13
and high conductivity BeCu layers. Here we can use any applicable formulas to
compute equivalent thermal conductivity, equivalent density and equivalent
specific heat. Now this allows us to use any standard formulas in analysis as
if it were a single homogenous material and used as input to material property
in CORE or the CAVITY as the case may be.
The second layer in tool as discussed above may be Air
and thickness of the air layer is equivalent to or proportionate to that of
thickness shrinkage in polymer at end of cooling cycle and is computed based on
melt temperature and thickness averaged eject temperature.
The second layer referred above may be moulding from
first shot as is the case with sequential two shot moulding process or
overmoulding process. That is also analyzed same way as an insulation layer on
tool face, typically on core side of tool. In this case also we compute
equivalent or effective tool properties combining with thermal properties of
plastic layer and that of the tool steel.
The part average temperature for the first thickness
and that for the second thickness according to previous discussion are used to
predict bending of the moulding by applying suitable structural formulas.
Typically the bimetal strip relies on differential shrinkage due to coefficient
of thermal expansion between two strips which are bonded together. The same
technique can be deployed here, slightly differently, to apply differential
shrinkage caused by the two sides having different thickness averaged
temperature.
Coolant temperature differential according to previous
evaluation between the CORE side and the CAVITY side coolant is varied such
that the part thickness averaged temperature differential between the CORE side
and the CAVITY side of geometric midplane through part thickness is reduced
representing optimized solution. It should be understood that a small
differential in two sides having similar values of part thickness average
temperature will shrink uniformly when part returns to room temperature and
thus will exhibit less warpage and part will hold shape more accurate to
designed geometry.
Once the temperature differential reaches within
specified permissible toleranceas above, it may happen that the part average
temperature is found to be below tolerance for specified ejection criterion, in
other words has cooled more than our desired target value. This can lead to
less shrinkage when part cools to room temperature after ejection from the
tool. Hence we have to raise part eject average temperature maintaining the
differential in limit already achieved above and hence both sides namely the
CORE and the CAVITY, coolant temperatures are raised equally to such level that
the part average temperature reaches within tolerance of the eject average
temperature specification (not shown).
Method for simulating the injection moulding
processaccording to invention described above is a computer program and
preferably runs in automatic mode for most part of computation including but
not limited to application of do loops and or goal seek methodology.
Furthermoremethod for simulating the injection
moulding processis a computer program and provides for graphic user interface
(GUI) enabling user interaction for defining input parameters as well as
executing preset commands.
Furthermore methodfor simulating the injection
moulding processis a computer program and provides output including but not
limited to temperature profile through part thickness graph, tool temperature
information, part temperature information and cycle time,includes information
of skin thickness having temperature below specified temperature that is
computed automatically by computing intersection between the part temperature
profile and that of the specified skin temperature.
Output as referred to above is produced in the form of
PDF document made up of preselected cell range of the program, for example only
but not limited to select range/ ranges of an Microsoft excel or like file.
Furthermore the output includesthermal response to
heating of tool for a specified time with specific fluid having specific
temperature and pressure.
Brief Description of the Drawings
In order that the invention may be more fully
understood there will now be described, by way of example only, preferred
embodiments and other elements of the invention with reference to the
accompanying drawings where:
Figure 1 Temperature profile of a part from a tool
having bilaterally symmetrical thermal design.
Figure 2 Temperature profile of a part from a tool
having bilaterally NON-symmetrical thermal design.
Figure 3 Temperature profile of a part having a second
shot moulded on top of first shot in sequential two shot moulding.
Figure 4 Temperature profile of a part from a tool
having bilaterally symmetrical thermal design having thermal design on both
sides same as that of a CAVITY of a tool having bilaterally NON-symmetrical
thermal design.
Figure 5 Temperature profile of a part from a tool
having bilaterally symmetrical thermal design having thermal design on both
sides same as that of a CORE of a tool having bilaterally NON-symmetrical
thermal design.
Figure 6 Temperature profile of a part from a tool
having bilaterally NON-symmetrical thermal design made up by combining parts of
graph from figure 4 and figure 5.
Figure 8 Prior Art-Schematic of numeric calculation of
cycle time, part average temperature and part midplane temperature.
Figure 9 Schematic of numeric calculation of cycle
time, part average temperature and part midplane temperature of a component
moulded out of a tool having bilaterally NON-symmetrical thermal design.
Figure 10 An output graph showing heating response in
one side of tol, by way of example CAVITY.
Figure 11 We are shown temperature profile through
part same as in figure 2 after optimization for reduced warpage.
Description of the Preferred Embodiment and Other
Examples of the Invention
Referring to Figure 1,
we are shown temperature
profile through a part bounded between tool face at CORE (1) and tool face at
CAVITY (2). As can be seen the temperature profile is symmetrical about plane
having highest temperature (3) also coincides with geometric midplane and
average temperatures bounded by plane having highest temperature and CORE tool
face (4) and that between plane having highest temperature and CAVITY face(5)
are same. This is expected temperature profile of a tool having bilaterally
symmetrical thermal heat transfer, typical when it is assumed that there is no
thermal resistance on interface of polymer and tool face and cooling geometry
made up of cooling channel size, distance to tool face and placement is
identical on both sides of tool - CAVITY and the CORE and temperature and flow
arte of coolant is assumed identical.
Turning to
Figure 2,
we are shown temperature
profile through a part bounded between tool face at CORE (1) and tool face at
CAVITY (2). As can be seen the temperature profile is NON-symmetrical about
plane having highest temperature (3) also the plane does not coincides with
geometric midplane (6) and average temperatures bounded by plane having highest
temperature and CORE tool face (4) and that between plane having highest
temperature and CAVITY face(5) are not the same. This is expected temperature
profile of a tool having bilaterally NON-symmetrical thermal heat transfer,
typical when it is assumed that there is thermal resistance on interface of
polymer and tool face, typical when air gap develops on shrinking of polymer
and or cooling geometry made up of cooling channel size, distance to tool face
and placement is not identical on both sides of tool - CAVITY and the CORE
having different cooling line geometry and or temperature and flow rate of
coolant may be assumed non-identical.
Figure3
We are shown temperature profile through
a part made up of two materials sequencially moulded,
Figure 4
We are shown temperature profile of a
part by way of example having thickness of 1.65 mm. and having symmetrical
cooling geometry on both sides having 15 mm. distance between top of cooling
channel and tool surface and 35 mm. centre distance between cooling channels
having 7 mm. cooling channel width.
Figure 5
We are shown temperature profile of a
part by way of example having thickness of 2.35 mm. and having symmetrical
cooling geometry on both sides having 6 mm. distance between top of cooling
channel and tool surface and 10 mm. centre distance between cooling channels
having 7 mm. cooling channel width. It is important to note here that the graph
represented here is that of a moulding process having same cooling time and all
machine parameters and the polymer parameters identical to that used for the
part described by way of figure 4 and also has same midplane temperature as for
the part described by way of figure 4.
In Figure 6
, We are shown temperature profile
of a part by way of example having thickness of 2.00 mm. and having
NON-symmetrical cooling geometry on CAVITY sides having 6 mm. distance between
top of cooling channel and tool surface and 10 mm. centre distance between
cooling channels having 7 mm. cooling channel width and on CORE side having 15
mm. distance between top of cooling channel and tool surface and 35 mm. centre
distance between cooling channels having 7 mm. cooling channel width. This part
thickness is essentially half of combined thickness of part described with help
of figure 4 and 5 and tool geometries described by way of example are
essentially that from figure 4 and fig 5 applied to CAVITY and CORE
respectively. It should be noted that the temperature profile is essentially
made up of two parts, one on left of plane having highest temperature is made
up of left side half of that described in Figure 4 and one on right of plane
having highest temperature is made up of right side half of that described in
Figure 4. It is important to note here that this synthesizing of graph is
possible because the two mouldings as described by way of graph 4 and 5 have
identical polymer input, have identical cycle time breakdown and have identical
midplane temperature. It should be noted that there will exist only one unique
thickness of the part in figure 4 and that of figure 5 such that meets above
described condition namely for identical cycle time breakdown and have
identical midplane temperature such that when the two thicknesses are combined
are double of that used in figure 6.
Figure 7
We are shown graphical representation
of scheme of synthesizing the part temperature profile described in the figure
6.
Turning to Figure 8
We are shown an example of
prior art published by the MIT(XiaorongXu, Emanual Sachs and Samuel Allen),
showing a process flow to compute tool stabilisation temperature and
corresponding cycle time and part average temperature and midplane
temperatures, applicable to bilaterally symmetrical thermal design of tool.
In Figure 9
, process flow to compute tool
stabilisation temperature and corresponding cycle time and part average
temperature and midplane temperatures, applicable to bilaterally
NON-symmetrical thermal design of tool. As will be clear following the flow
diagram we start by inputting all material, tool and coolant data. We assume a
split proportion to divide the actual part thickness under analysis in two
parts such that the sum of two parts is same as that actual part thickness they
were separated from. Now one part is used after doubling it with bilaterally
symmetrical thermal design same as that of CORE and another part is used after
doubling it with bilaterally symmetrical thermal design same as that of CAVITY.
For example if air gap is to develop on CAVITY face in final design, it is used
in bilaterally symmetrical mode in the design with CAVITY as if air gap exists
on both faces of tool. The purpose of doubling it is such that when integrating
graph of temperature profile from figure 4 and figure 5, two halves will be
used and since two together were already doubled, we arrive at final thickness
as required for final design in graph in figure 6. Now we solve these two
systems of CORE and CAVITY for cooling time to reach required ejection
temperature as specified by user. In case of error a small time increment is
added to achieve a real value of cooling time that will produce eject
temperature that is no more than specified by user. Now the midplane
temperatures are calculated and difference computed. If the difference is more
than specified maximum value which is typically a small number, the split
values is changed and whole process repeated till the two midplane temperatures
are same within small permissible tolerance as mentioned above. Now the final
product moulding temperature profile can be predicted in a non-thermally
symmetrical tool by combining above two graphs in half, one from left side and
one from right side and will form respective side of final analysis as they
were arrived at from CAVITY or CORE as shown in graph 4,5,6 and 7.
It is understood the whole process described above
will be programmed into a software algorithm such that it operates
automatically and finds ideal value of split and generates final tool analysis
without any more manual operation by the user and the code for such an
implementation is not the purpose of this invention and as such not disclosed.
It will be obvious that such an implementation or variation in algorithm by any
code will be obvious to anyone competent in art of writing software code and as
such that will be covered by essence of the invention.
Now turning to Figure 10
This invention also is
applicable for predicting thermal response for a tool having bilaterally non
symmetrical thermal design of RHCM (Rapid Heat Cycle Moulding) providing the
benefits of a high quality surface and quick cycle times. Heating response of
tool on each side of tool is computed (Figure 10) by using published formulas
available in literature however this algorithm enables doing so when the tool
has non-symmetrical thermal design, as is the case in just about every
tool.
Finally in figure 11
It should be noted that any
temperature differential between two halves of plane will lead to higher
shrinkage in one plane relative to another and that will lead to bending of the
whole part known as warpage-more specifically out of plane warpage and it will
be beneficial to have this difference as small as practically and commercially
feasible. As shown in figure 9, flow chart, last operation step is that of
minimizing warpage. In figure 11 we are shown temperature profile of the same
part as in figure 2 where it can be noted that the differential between the
temperatures shown at point 4 and 5 has been reduced substantially, by way of
example only from 11 degrees C to 3 degrees C, through the process of
optimization described above, by changing coolant temperature by way of example
only from 30 degC, , on both sides of tool to 53 and 33 deg. C respectively for
CAVITY and CORE. It may be noted that once the temperature differential reaches
within specified permissible tolerance, the part average temperature if found
to be below tolerance for specified ejection criterion, both side coolant
temperatures are raised equally to such level that the part average temperature
reaches within tolerance of the eject average temperature specification (not
shown).
Whilst the above description includes the preferred
embodiments of the invention, it is to be understood that many variations,
alterations, modifications, combinations and/or additions may be introduced
into the computational process flow previously described without departing from
the essential features or the spirit or ambit of the invention.
It will be also understood that where we refer to
injection moulding are used in this specification variations such as die
casting, glass moulding, rubber curing are included and form part of the
invention.
It will be also understood that where the word
'comprise', and variations such as 'comprises' and 'comprising', are used in
this specification, unless the context requires otherwise such use is intended
to imply the inclusion of a stated feature or features but is not to be taken
as excluding the presence of other feature or features.
The reference to any prior art in this specification
is not, and should not be taken as, an acknowledgment or any form of suggestion
that such prior art forms part of the common general knowledge.