USE OF PROCESS SIMULATION
TO ASSESS TOLERANCE FEASIBILITY
David R. Busick
Leyshon Miller Industries
Kurt A. Beiter
The Ohio State University
Kos Ishii
Stanford University
Introduction
Background
One of the most significant design issues causing problems for designers
is tolerancing of injection molded parts. Many designers do not understand
how to design or tolerance plastic parts and end up over tolerancing many
dimensions. Functionality and assembly concerns generate a set of Critical
to Function Dimensions (CFD's) and corresponding tolerances (CFT's). Designers
may quantify these CFT's with no consideration of the manufacturing process.
Often this drives up manufacturing costs if not making production completely
impossible. Designers need to understand the pattern of manufacturing variations
in injection molded parts and how design affects these variations. Designers
of thermoplastic parts need a methodology that helps them to assign optimal
tolerances without severely constraining the process engineers.
Our Approach
Tolerance issues in injection molded parts remain to a large extent unexplored
territory. Several manufacturing handbooks site dimensional capabilities
of the process as a function of material (Bralla, 1986; Rosato, 1986), but
few have related the machine capabilities to design guidelines. We feel
that designers need guidelines for appropriate tolerancing of thermoplastic
parts which consider the characteristics of the manufacturing variations
associated with injection molding.
This paper presents research on using process simulation programs for evaluating
the feasibility of a tolerancing scheme on injection molded parts. Our approach
is to utilize process simulation programs that are to an extent capable
of predicting dimensional errors in injection molding. There are several
commercial packages available: Moldflow, C-MOLD, and Ideas Master Series
are a few of the more popular packages. Our method addresses the effective
utilization of these packages for tolerancing and generation of design guidelines
for injection molded parts.
The resulting methodology would help the designer in assigning tolerances
as follows: Given the part geometry and the processing window, simulation
predicts the change in dimension within this window. The prediction enables
the designer to asses the feasibility of the assigned tolerances. Thus this
methodology can guide the designers to develop the best overall tolerancing
scheme on critical dimensions.
Technical Preliminary
Molding Process and Dimensional Accuracy
Shrinkage in plastic material is due to its Pressure-Volume-Temperature
(PVT) characteristics. In addition to imparting a volumetric change, the
shrinkage also induces residual stresses in the plastic part because of
anisotropic material properties, geometric constraints, and variations in
the time-temperature history. The residual stresses will generally cause
"out-of-plane" distortion in the part. The degree of distortion
depends primarily on the distribution and magnitude of the stresses. Flow-induced
residual stresses will also cause distortion. Since injection molding is
a net-shape process, attempting to control one dimension affects other dimensions.
In addition, the coupling between control dimensions is more prominent in
injection molding because polymers have such pronounced PVT behavior.
Before deciding how to use simulation in assigning tolerances, an examination
of tolerances is necessary. Deviations in injection molding incorporate
a component due to average shrinkage, for which mold modification can compensate,
and a component due to noise in the process, which can only be alleviated
by improvements in process control. The remainder of this sub-section defines
several relations necessary to discuss tolerances in injection molded parts.
Figure 1 shows a hypothetical injection-molded part. Each part has n
target dimensions xj. The vector of target dimensions
for the entire part is:
Target dimensions =X= [x1, x2,
x3,..., xn] (1)
j=1 to n dimensions
The entire part will have a set of actual dimensions aj
(not shown), where j is the index for the n target dimensions,
and i is the index for the m parts molded. The actual dimensions
for m parts form a matrix A:
Actual dimensions = A = [aij](2)
i =1 to m parts
j =1 to n dimensions
Each target dimension xj has a corresponding deviation
range 
, due to noise in the process. The
deviation range corresponds to the difference between maximum and minimum
actual dimension over the m parts, or, for fixed j:
(3)
i =1 to m parts
j =1 to n dimensions
Each target dimension has a corresponding tolerance tj
(not shown in Figure 1), either prescribed or assumed. We define tolerance
here as a range; i.e., if a tolerance is prescribed as +/-0.010, then tj
= 0.020. The tolerance vector for the entire part is:
Tolerance vector =T= [t1, t2,
t3,..., tn] (4)
Each target dimension also has a corresponding mold dimension mj.
The vector of mold dimensions is:
Mold dimensions =M= [m1, m2,
m3,..., mn] (5)
To evaluate tolerance feasibility, designers must determine both the overall
part distortion and the deviations due to process noise. This paper focuses
on the prediction of the 's, assuming engineers
have used simulation and mold modifications to correct for the average shrinkage.
In this case, we make the assumption that designers have configured M
such that M yields X, ignoring for the moment the 's due to process noise.
Injection molding involves many independent and dependent process variables.
We define a process vector as:
Process vector =P= [p1, p2,
p3,..., pq] (6)
where there are q process parameters p. The process parameters
pk include such variables as injection pressure,
melt temperature, mold temperature, and packing pressure. For example, one
such process set is P= [1.50sec, 540deg, 180deg, 4000psi]. Since
any process parameter pk is continuous over a particular
range, in principle an infinite number of process parameter sets P
exist.
The variation in pk from shot to shot is 
pk. Each pk induces a change
in the actual dimensions of each part. For example, a change in the mold
temperature will cause a change in the time-temperature history of the part
and thus a change in the residual stress in the part. Likewise, all process
parameters have some effect on dimensional error. We define dimensional
error 
as the difference between target
and actual part dimensions:
(7)
i =1 to m parts
j =1 to n dimensions
Each process set P yields a corresponding error for a given dimension
xj. In principle, each pk
has an optimum setting and, neglecting higher-order effects, optimizing
each pk will yield a minimum , or an optimum
P. However, typical injection molded parts have multiple critical
to function dimensions. Therefore, a technique for determining the overall
optimum P must exist as an integral part of a tolerancing scheme.
Prediction of the Injection Molding Process
Designers have several methods to determine whether an injection molded
part will meet specified tolerances. These methods include shrinkage tables,
area shrinkage estimations, expert opinions, and trial and error. Shrinkage
tables predict shrink for a specific shape and material (Rosato, 1991).
The shapes are relatively simple and do not take into account any effects
of geometric features such as walls, ribs, bosses, or holes. While these
tables provide a rough estimate, they do not adequately address more complex
parts typical of today's designs. Area shrinkage estimations characterize
the overall shrinkage of a part but do not help in warpage prediction. Both
shrinkage tables and area shrinkage estimations only address the average
shrinkage component of a dimension neglecting change due to the process.
For more complex geometries, the responsibility for predictions often falls
upon experts such as experienced molders. Often, engineers must resort to
pilot production runs to determine tolerance feasibility, a time-consuming
and expensive process in today's competitive market. More recently, designers
have turned to injection molding process simulation to address this need.
The flow analysis portion of injection molding process simulation is gaining
wide acceptance. Many companies use flow analysis to point out potential
problems in part filling, determine gate locations, balance runners, predict
weld-line locations, predict cycle times, and determine machine capacity
requirements. Some companies also use the cooling analysis software to optimize
cooling lines and cycle time. Both experimental validation studies and industrial
use have validated the adequacy and usefulness of this portion of injection
molding simulation software. Shrink and warp analysis has by no means received
the same acceptance. Numerous companies have conducted investigations of
shrinkage and warpage predictions on simple plaques, disks, and ribbed plates.
Very few published studies have included simulation and experimental verification
on more complex parts.
The causes of discrepancies between simulation and experimental results
include uncertainty in the experimental process variables, the measured
responses, the material property data, and the inherent inaccuracy of the
simulation models themselves. These shortcomings in process modeling are
not likely to be solved soon. Ideally, extracting useful information from
these models requires a methodology that takes the inherent inaccuracies
into account.
Tolerance Evaluation Methodology
Overview of Methodology
Our research explores using process simulation in tolerance feasibility
studies. The research uses simulation to explore the effects that process
conditions have on dimensional accuracy for a given part geometry and material.
Using estimates of process parameter variation from experts, the methodology
will provide an estimate of feasibility for each critical to function dimension
on a part. This methodology relies on the predictive capabilities of process
simulation to quantify dimensional changes due to injection molding process
variation. This is justified for the following reasons:
- Experimental validation of part geometry and process design is desirable
but is not feasible or cost effective in most time-to-market critical applications.
- Whereas simulation may not accurately predict dimensional distortion
in absolute magnitude, several studies have shown that the accuracy of predicting
changes in dimensions due to process variation is more reasonable (Post,
1991, Beiter, 1993).
Figure 4 shows an outline of the methodology. The first step requires establishing
the processing window for the part and selecting process set points from
within the window. Next, based upon available information, an engineer estimates
the variation in each process set point due to the practical limits of process
control (process noise). Then, a fractional factorial simulation experiment
computes part distortion for various sets of process parameters. Analysis
of the results indicates the sensitivity of the change in dimensions with
respect to changes in individual process variables. This sensitivity, coupled
with the assigned tolerances, characterizes the criticality and feasibility
of holding each dimension.
Process Set Points and Noise
A change in process variables affects the actual dimensions of a molded
part. Several studies have shown that the most critical process variables
are melt temperature, mold temperature, injection time, and packing pressure.
Other variables such as polymer material properties, mold steel, and machine
type are fixed by other criteria and therefore are not considered as variables
in this study. To maximize the usefulness of this approach, designers should
consider the analysis before mold manufacturing. Design and process engineers
commonly use process simulation and experienced opinion to estimate the
process set points pk. Filling simulation enables
the selection of appropriate factor levels for each of the four significant
variables. Modification of these variables (factors) in filling simulation
establishes a window within which the part is easily molded. Choosing values
for each pk from within this window supplies the
process set points for the simulation experiment.
Due to less than perfect process control, process set points vary over a
range. Calculation of the deviation ranges requires estimations
of the process noise 
pk
for each pk. Estimates of process noise for the
four factors should come from knowledgeable sources. The injection molding
machine manufacturer should supply information regarding the control of
their machine. If controls were added subsequent to the machine purchase,
then the controls supplier should have the desired information. However,
the manufacturer may be the most appropriate source of information. In many
cases the manufacturer can obtain printouts directly from the machine indicating
process variations from the set point. The set points and the outer limits
of the process control become the factor levels for a fractional factorial
experiment.
Simulation Analysis
Using an orthogonal array permits efficient comparison of the individual
factor effects of each process parameter on critical to function dimensions
(Phadke, 1989). Table 1 shows typical values for three levels of the four
major process factors. In this case, we have chosen process factor levels
that correspond to estimated process variation, not levels that correspond
to a typical process window. In principle the process factor levels could
reflect either range. The simulation produces an estimation of the final
part geometry as a function of the experimental factor levels.
Sensitivity Analysis
The process simulation analysis yields a set of process factor effect graphs.
Note that the actual dimension 
(predicted by
simulation) corresponds to a target dimension xj,
where i denotes the level of process parameter pk.
We define a sensitivity, 
, as the effect
of a change in process parameter pk on a dimension
xj as:
(8)
j =1 to n dimensions
k =1 to q process parameters
where
(9)
(10)
Note that this definition for utilizes the
maximum variation in dimension xj over the process
range. We are interested in characterizing the overall effect on of the q process parameters. If we
assume a linear distribution in the variation of the pk's,
and that the pk's vary independently, one such
measure is:
(11)
j =1 to n dimensions
k =1 to q process parameters
where 
pk is an
absolute limit of error. In general, this estimate is highly conservative.
Most process variable distributions more closely resemble a normal, rather
than a linear, distribution. If we consider the pk's
as statistical bounds or uncertainties, another method of estimating the
combined effects of processing error on the deviation range is:
(12)
j =1 to n dimensions
k =1 to q process parameters
For this example we adopt the so-called 6-sigma approach and assign six
times the standard deviation for each pk.
Criticality Analysis
Manipulation of the results obtained from the experiment establishes a set
of critical dimensions. The critical nature of a dimension is a function
of both the prescribed tolerance tj required and
the sensitivity of a dimension to varying processing conditions. A dimension
that has a tight tolerance and experiences large dimensional instability
due to process variations will go out of tolerance more readily than a dimension
with loose tolerances and smaller variations. We define criticality, 
, as the relative likelihood that a dimension
xj will exceed a prescribed tolerance limit:
(13)
A criticality greater than one indicates a critical dimension, or a dimension
which cannot hold its tolerances. Any criticality greater than one indicates
that the tolerancing scheme is not feasible. Possible solutions include
loosening the tolerances, changing the process set points, or modifying
the design to make the CFD's more insensitive to manufacturing variations.
Results
An initial test of the methodology used the geometry shown in Figure 4.
A flow analysis indicated the process set points for the experiment and
parts were molded near this set point. Estimations of process control for
the injection molding machine enabled us to run a fractional factorial experiment
over the process control window using C-Mold. Results of this fractional
factorial indicate the deviation in dimension over the control window for
each factor (melt temp, coolant temp, pack pressure, inject time). Addition
of the factors using Equation 11 (Figure 5, C-band) and Equation 12 (Figure
5, D-band) indicate the tolerance band estimated by simulation. Shown also
in Figure 5 are measurements from molded parts.
Expectations were that the measurements would fall within the D-band. The
fact that some points fall outside of the D-band is most likely due to errors
in estimation of machine control, measurement errors, as well as errors
in the predictive capabilities of the simulation software. Obtaining estimation
of machine control using data taken directly from the machine instead of
estimations will improve results. Measurement errors will have less effect
as distortion increases.
Another result of this ongoing research is a computer program that automatically
runs C-Mold through warpage for a user defined array of process variations
for the four factors varied in this research. The program works off of an
initial process file and runs in an xterm window.
Conclusions and Future Work
This paper proposed a methodology for using process simulation in evaluating
the feasibility of a tolerance scheme. The methodology involved the use
of simulation to quantify the dimensional errors due to process variations
and estimate sensitivities. First, we defined target dimensions, deviation
ranges, and dimensional error in injection molded parts. We then outlined
the steps in using the process simulation to compute the sensitivity of
each dimension to process variation. Given a variational range (noise) of
each process parameter, process simulation can estimate the total variation
(deviation range) on the critical to function (CFT) dimensions as a result
of process variation.
The paper defined criticality for each dimension as the ratio between the
deviation range and the specified tolerance. If any dimension has a criticality
greater than one, the injection molding machine will not be able to economically
produce this part to the designers specification. Hence, the designer must
loosen the tolerances, change the process set points, or modify the design
to make this dimension more insensitive to manufacturing variations. Thus
the proposed methodology helps designers evaluate the feasibility of his
or her specified tolerances and avoid costly redesigns.
This methodology is a first step towards an integrated tool for designing
plastic parts with robust dimensional control. Ongoing experimental work
seeks to validate the feasibility and generality of the proposed approach.
Our future work includes the application of simulation to generate design
and tolerancing guidelines for a family of parts.
Acknowledgments
The authors would like to thank Eaton Corporation and the NSF/ERC for Net-Shape
Manufacturing for supporting this work. Partial support also came from the
NSF Division of Design and Manufacturing.
References
- Bralla, J. G., Ed. (1986), "Handbook of Product Design for Manufacturing",
New York, NY, McGraw-Hill
- Phadke, M. S. (1989), "Quality Engineering Using Robust Design",
New Jersey, NY, Prentice Hall
- Post, S. (1991), "Verification of Warpage Simulation in Injection
Molding", Columbus, OH, The Ohio State University
- Rosato, D., DiMattia, D., and Rosato, D. (1991), "Designing with
Plastics and Composites", New York, NY, Van Nostrand Reinhold
- Rosato, D., and Rosato, D. (1986) "Injection Molding Handbook",
New York, NY, Van Nostrand Reinhold
- Walsh, S. F. (1992) "Shrinkage and Warpage Prediction for Injection
Molded Components", ANTEC proceedings, Vol. 38
Figure 1. Injection molded part distortion
Figure 2. Flowchart of the Methodology
Figure 3. Experiment Levels
Figure 4. Experimental Part
Figure 5. Experimental Results