A Realistic Approach to
Viewing Warp Results in Molding Simulation
Paul Van
Huffel, Altair Engineering, Inc., Troy, MI
Abstract
There’s a catch to understanding
the warp results given by molding simulation software; they are a comparison of
the deformed part to the mold cavity, and not the intended geometry.
This paper outlines a process to
generate a specialized “Warp” result, using ResultMath© in HyperView
11.0, that can be measured on the part.
Introduction
To date, various
attempts have been made, some very good ones, to properly account for the
shrink and warp induced by the materials, mold, and process of injection
molding of polymers. Historically, the
first method used was derived from the casting of metals and it involved the
application of an isotropic uniform shrink factor to the part as designed. This method is still used widely. The problem is that the application of a
uniform isotropic shrink factor on a material whose shrink properties are at
best anisotropic seems a bit misguided today.
A second
method utilizes molding of a part in a mold designed using the classical shrink-rate
method and then measuring the resulting parts under molding conditions designed
to robustly produce a quality part in all regards except for warpage. The parts are measured and a new mold is made
with “windage” applied to overcome the differential shrinking and resulting
warping of the parts. While this works
well for some geometries, others are less stable under the loading conditions
of the shrinking part. The instability
is rooted in the design, and causes a pitchfork bifurcation (buckling occurs). The term “bifurcation” is used here as it
denotes a mathematical instability in the stiffness of the part and thus a
non-linear divergence from the intended design (1). An example of this is the buckling seen in
deep-draw cross-hatched rib designs. In
cases where buckling is likely, getting the part to shrink “into” shape is not
a linear prospect, and in some cases any “windage” applied may only serve to
exacerbate the problem. For the purposes
of this paper, it is a prerequisite that buckling not be a significant
consideration in the warping of the part.
Another, more basic, problem with
this second method is the need to construct at least 2 molds. This is generally not an option for most mold
development processes.
A similar
method involves the use of finite element analysis to determine the amount of shrink
and warp in the part resulting from the process of injection molding. It involves analyzing the part as designed
and then applying the resulting warp deflections with a scaling factor between
-0.3 and -1.2 depending on the results of a comparison of a confirmation
analysis of the resulting cavity to the dimensions of the original mesh (the
one representing the part as designed).
This method serves two functions: 1) accounting for the overall shrink
and 2) accounting for some of the warp caused by the differential shrinking of
the polymer material. But something
still remains elusive in all these cases as they each require manually
measuring the data resulting from the analyses as well as the original model,
and then manually comparing the measurements.
What’s
missing is a viewable dataset and plot for the warp of the part as molded without
the shrink in it. The current problem
with the output from molding software today is that the warp results are a
comparison of the molded part to the mold cavity (see illustration A). The purpose of this paper is to outline a
process whereby the results of a molding simulation involving calculations of
the shrink and warp of the part can be viewed without the planned shrink
involved, thus only seeing the unintended deformations. This would reflect the deviations of the part
as molded to that of the part as designed, and forms the first major step in an
optimization process to establish a cavity that produces the part as designed
with a robust and cost-effective process as the cycle time can be minimized by
accounting for the additional unconstrained shrink and warp of the part from
being ejected as soon as the skin is able to withstand the force of ejection.
Again, the
main goal of this paper is to delineate a process to generate a plot that shows
the deformation of the part after the molding process as compared to the design
intent. ResultMath® is a
relatively new tool from Altair Engineering in the HyperWorks product suite
(11.0), and is part of HyperView. It
allows the user to perform mathematical operations on any analysis result and then
plot the solution as a new result. This
includes operations on scalar, vector, and tensor results.
Theory
Being as
the results of a warp analysis and that of scaling a model to account for
shrink are all vector operations, the lack of this capability in post
processing software has been a road block to developing this dataset and plot. With this being resolved in the
postprocessor, the equations below will reflect notations for vector and matrix
operations.
The simplest operation and the
focal point of this investigation is the final operation in the calculation of
the desired dataset. It is to subtract
the imposed shrink used to expand the part into a cavity from the result of the
molding simulation, specifically the shrink/warp analysis.
The warp, as calculated in the
analysis solver, is a negative value and thus this process actually involves
adding the applied shrink to the warp calculations from the solver. This can be expressed as follows:
EQ1: [W] = [R] + [Sapplied]
Where W represents the True Warp
versus the design intent, R represents the Result of the warp analysis, and Sapplied
is the Shrink applied to the nodes. The
operation is applied to a set of n vectors comprised of nodes and their vector
results.
NOTE: Bold print is used to define vector quantities and the
[ ] brackets are used to denote matrices in the operation over the set of
nodes.
The applied shrink can be derived
from either of two methods: 1) taken from HyperMorph as a saved shape or 2) by
back-calculating an isotropic or orthotropic shrink factor(s) previously
applied to the model. The first is a
direct read of data from the software.
The second is an operation that can be developed as:
EQ2: Dprt + ∆Dprt = Dcav
where Dprt is
some particular dimension of a part, ∆Dprt
is the increase in dimension based on the shrink rate of the polymer, and Dcav
is the same dimension in the cavity of the mold.
For the sake of clarity we will
assume a constant point being taken on the part and corresponding point taken
in the mold as the reference for all measurements. These dimensions are taken as vectors, and
the change in dimension will have components in the X, Y, and Z axes. The ∆Dprt term can be expressed alternately
as:
EQ3: ∆Dprt = Sfac ∙ Dprt
where Sfac
is the scale factor accounting for the shrink of the polymer. Sfac
can be taken to mean a scalar value, or as a vector with separate components in
the X, Y, and Z axes.
EQ3a: Sfac
∙ Dprt = <Sfac∙Dx, Sfac∙Dy, Sfac∙Dz>
EQ3b: Sfac ∙ Dprt
= <Sx∙Dx,
Sy∙Dy,
Sz∙Dz>
If interpreted as a vector, then
the 1 denotes a vector of
<1,1,1>. This means that Dcav
can be alternately expressed as:
EQ4: Dcav = Dprt (1 + Sfac )
But what is needed is an expression
of ∆Dprt in terms of Dcav. Depending on the coding preferences, it can
be expressed in one of two ways:
EQ5: ∆Dprt = (Sfac ∙
Dcav) ∕ (1 + Sfac)
Or…
EQ6: ∆Dprt = Dcav (1 − (1 ∕ (1+Sfac)))
But ∆Dprt is actually the same as
Sapplied from EQ1, so EQ1
can be rewritten as either:
EQ7: [W] = [R] +
[(Sfac ∙ Dcav) ∕
(1 + Sfac)]
Or…
EQ8: [W] = [R] + [Dcav (1− (1 ∕
(1+Sfac)))]
It should
be noted that the use of EQ7 or EQ8 bypasses the need to read results from 2
sources (warp result from molding software and a morph shape from the
preprocessor). This is a distinct
advantage when considering the prospect of adding in small adjustments to the
nodes, by way of morphing them in the preprocessor, based on the calculated
dataset. This is the next step toward
optimization of the cavity geometry.
If the
cavity is now assumed to be comprised of two components, shrink and windage,
then EQ2 can be rewritten as:
EQ9: Dprt + ∆Ds + ∆Dw = Dcav
Thus…
EQ10: ∆Dprt = ∆Ds + ∆Dw
EQ11: ∆Ds = Sfac
∙ Dprt
Where ∆Ds now denotes
the accounting of shrink (isotropic or orthotropic) and ∆Dw now accounts for windage adjustments made in
the preprocessor to specific nodes. When
reconfigured similarly to EQ6, the resulting equation is:
EQ12: ∆Dprt = Dcav
– ((Dcav – ∆Dw)∕(1+Sfac))
Once again
this can be inserted into EQ1 replacing Sapplied to get:
EQ13: [W]
= [R]–[Dcav–((Dcav–∆Dw)∕(1+Sfac))]
In an optimization context, ∆Ds would be the first term optimized and then ∆Dw would be optimized to fine-tune the cavity shape until
[W] = 0.
One other calculation is important
to this operation. It can be found in
almost any textbook on injection molding and that is the determination of the
shrink rate. In this case, the need will
arise to compute the shrink rate(s) from an initial analysis of the part finite
element model without any shrink applied.
It can be derived here from EQ4:
EQ14: Sfac = (Dcav ∕ Dprt) − 1
Description of Analysis Process
The process
of analysis starts with making a finite element model of the part
geometry. It then takes one of two
paths: 1) an assumed isotropic shrink rate is used to expand the part to the
dimensions of a mold cavity, or 2) the part is left “as-is” for the first
analysis and anisotropic qualities of the material and part design with respect
to the mold design will be included in calculating orthotropic shrink properties. For the purposes of this study, the second
path will be utilized.
Either way, a finite element mold
model is then constructed around the part model so that a cooling analysis can
be performed and included in the molding simulation process.
For the path chosen here, #2 above,
a “Morph Volume” is created in the preprocessor using the elements from the
cavity and utilizing an offset of 0%. This
represents a bounding box around the part that reveals a set of consistent
rectangular dimensions to be used to later obtain the orthotropic shrink
properties.
The models are then passed to the
molding simulation software. In this
case, the molding simulation software utilized is Moldflow. Here, the ideal process conditions are
determined (minimized pressure to fill with low sensitivity to fill time,
polymer temperature, and mold temperature) before running an analysis that
includes cooling, filling, packing, and part warp. It is also strongly advised that, for complex
geometries and geometries involving complex rib structures, a buckling analysis
should be performed to determine if there are areas that should not be adjusted
beyond accounting for iso- or orthotropic shrink rates.
At this point, if Path #1 were
chosen then the desired plot could be created and assessed by the analyst. However this study is an attempt to forge a
“best-practices” methodology and as such path #2 was chosen. Therefore, the next step would be to export
the deformed shape as an STL model with a scale factor of 1.0. An STL model is a tessellated surface mesh of
triangles that forms a boundary mesh.
This boundary mesh is then imported
into the original preprocessor database file.
A new “Morph Volume” is created around the newly imported boundary mesh
(using only those elements as its basis), again, with an offset of 0%. The dimensions of both the initial and the
new bounding boxes are taken and used along with EQ14 (Dcav = Initial Box & Dprt = New Box) to compute the orthotropic shrink rate
of the part model. The post processing
capabilities of most injection molding simulation software include capabilities
to query nodal results and will automatically calculate shrink rates between
the nodes queried. The bounding box
method is designed for oddly shaped parts that defy measurement by this method.
Once the shrink rates have been
determined along each axis, the cavity and mold models are expanded by those
factors to yield a mold cavity that should produce a part of the proper size
along each axis. This model is then
exported and passed to the molding software for subsequent analysis.
When the warp analysis is complete,
the results are exported to a file in H3D format as this is the format for the designated
post- processor.
The H3D
file is brought into the designated post processor and the Result Math template
is selected on the import panel. After
the data is imported, a “Derived Result” is created and in the pop-up editor either
EQ7 or EQ8 is used to calculate the true warp of the part versus the CAD
geometry. Measurements are then taken
along various axes of the part and then compared to the original part data to
determine the amount of true warp generated.
The result is then queried and results taken on opposite sides of the
part are summed to determine the amount of true warp predicted by the derived
result. These two “True Warp”
calculations are then compared to each other to see if they are, as they should
be, the same.
Application of Analysis Process
This study
utilizes a model known as the “Mouse Coffin” that was supplied by Jim McGuire
of BASF (Illustration B). A sprue and a mold
base were added to the model along with waterlines, and this data was passed to
a colleague at Cascade Engineering, Tim VanAst, for simulation.
The
material used for the simulation was Ticona Celcon M90 (unfilled POM) from the
database of the molding software. The process
conditions for the simulation were:
Melt Temp: 182.22℃
Fill Time: 2.00
sec
Packing Time: 20.0
sec
Packing Pressure: 80%
of Filling Pressure
Inj.+Pack+Cool time: 30.00
Seconds
Coolant Temp: 82.22℃
Coolant Flow Rate: 4.167
liters/sec
The
measurements of the Mouse Coffin (CAD) are 60.000 X 40.000 X 120.000
(mm). The orthotropic shrink factors were obtained using the post
processing utilities of the molding software as the part was generally
rectangular in shape. The model was then
scaled to reflect these shrink rates and to represent a mold cavity that would
ideally produce a part that represents the CAD data.
Presentation of Data & Results
Based on
the results of the first analysis, the orthotropic shrink factors applied to
the CAD to generate the mold cavity used in the second run were (0.0156,
0.0123, 0.0152). As such, the calculation made within the post processor for
the custom result plot was:
VectorFromScalar( V2.C1+(0.0156*LC0F1.V1.C1)/1.0156 ,
V2.C2+(0.0123*LC0F1.V1.C2)/1.0123 , V2.C3+(0.0152*LC0F1.V1.C3) / 1.0152)
where V2.Cn represent the warp result from the molding
analysis software in degree of freedom (DOF) 1, 2, or 3, and LC0F1.V1.Cn
represent the position of the cavity node (dimension - Dcav) in DOF 1, 2, or 3.
EQ8 was originally attempted, but the math parser refused to accept all
forms of “1 – …” so EQ7 was used.
The queried results are tabulated
and shown on illustration C. The results
are in meters by default. For the
purposes of discussion here, I will convert these to millimeters.
The measurement across the center
of the part after molding is 57.863 mm. This
is a deviation of 2.137 mm from the part dimension of 60.000 mm across the span
(from node 55905 – node 60363). The
queried warp is 1.071 mm at node 55905, and 1.067 mm at node 60363 for a total
deviation of 2.138 across the span.
A second span was also measured
across nodes 55562 and 60420. This span
measured 60.147 mm which deviates by 0.147 mm from the 60.000 mm CAD
dimension. The query shows a deviation
of -0.063 mm at node 55562 and 0.084 mm at node 60420. This makes a deviation of 0.147 mm across the
span based on the derived result.
Along the
longer dimension of the part, the measurement from the warp data is 120.561 mm,
which is a 0.561 mm deviation from the part as designed (120.000 mm). The queried results of the same nodes along
this axis show 0.2895 mm and -0.2718 mm for a deviation of 0.5613 mm.
Lastly,
along the vertical axis (Y in this case) the vertical height measures 39.961
mm, which is a deviation of 0.039 mm from the part dimension of 40.000 mm. Querying the data gives 0.4044 mm at node
50434 and 0.4434 at node 55567. This
makes for a total deviation of 0.039 mm (0.4044 – 0.4434 = –0.039 mm).
Interpretation of the Data
The results
of the plot created matched perfectly the theory outlined. One specific issue arose with the attempted
use of EQ8 as the use of, “1 – …” was not handled by the post processing
software. There are a few small
numerical rounding errors leading to minor variations of 0.001 mm in a few
places, but this seems negligible for the vast majority of injection molded
parts.
The method applied here varied some
from the outlined process as the shrink rates were acquired from the mold
software’s post processor directly. This
should not significantly affect the results as the part has a generally
rectangular shape.
Conclusion(s)
Because the
plot of true warp is calculated as a vector result and the math operation in
the post processing software manages this as a vector to produce a new vector
result, the method applied is valid. The
data in the results section shows that the new plot almost exactly matches the
measurements taken of the warped part based on the raw warp result.
It is
concluded that the plot here represents a true measurement of the warp of a
molded part versus the part as designed.
This is a plot with value to the molder as it is a prediction of the
quality of the parts as they will eventually be manufactured. The translation to reality will involve
making sure that the properties of the material used in the analysis are
properly characterized and that the process conditions developed in the
analysis are reasonably followed in the manufacture of the part. This plot is also extensible to calculating
further adjustment to the mold, windage, by multiplying the vector components
by -1.
Next year,
hopefully, the subject of my paper will be extending this plot into the
optimization of the mold cavity geometry so that an optimal cavity is made
where the result is precisely the part as designed with the most efficient and
reasonably robust process possible.
Nomenclature
Bifurcation – “When the solutions of a nonlinear system change
their qualitative character as a parameter changes.” (2)
POM – lit. Polyoxymethylene.
A Polymer resin commonly known as Acetal.
Acknowledgments
Special
Thanks to James McGuire and BASF for their contribution of the “Mouse Coffin”
model to this study.
Special
Thanks also goes to Tim VanAst and Cascade Engineering Inc. for providing
analysis results from Moldflow.
References
1. Drazin, P.G., Nonlinear Systems, Cambridge University
Press, 1997 pg.17
2. Drazin, P.G., Nonlinear Systems, Cambridge University
Press, 1997 pg.2
Illustrations
(A) The
Problem – Cavity vs. Molded Part
(B) Mouse
Coffin Cavity Model with Mold
(C) True
Warp Query Results (meters)
(D) Measurements
1 & 2
(E) Measurement
#2 Close-up.
