ADVANCED DESIGN GUIDELINES
TO ASSESS FILLABILITY
Douglas C. Mehl
The Ford Motor Company
Kurt A. Beiter
The Ohio State University
Kosuke Ishii
Stanford University
Introduction
Background to Fillability
Thickness determination in injection molding is a critical manufacturability
concern because it directly affects the entire part geometry and requires
what we call a whole-part analysis. Whole-part analysis is generally more
complex than design guidelines for isolated features such as bosses and
holes. To determine a nominal wall thickness in injection molded parts,
a designer must consider strength, weight, amount of material, cost, production
rate, dimensional stability, etc. In the design process, the designer will
conceptualize a shape to meet the functional requirements. Typically, thickness
is determined just after the designer determines the general shape. At this
stage in the design, there are very few tools to assist the designer in
determining nominal wall thickness. There are useful tools that are available
downstream in the design process, such as cost models and structural analysis,
but iterations in nominal wall thickness later in the design stage can often
cascade into major tooling and design changes. Effective fillability evaluation
requires incorporating the effects of flow length, part thickness and geometry,
process, and material properties.
Current Fillability Guidelines
Designers can perform a detailed fillability analysis with injection molding
process simulation., However, an accurate process simulation requires detailed
geometry and a time investment that the designer cannot always afford. The
available fillability design guidelines applicable to preliminary part design
are limited.
A major issue in injection molding part design is determining nominal wall
thickness. Typically the nominal wall thickness is specified after the general
shape of the part is determined and before the details of the features are
determined and gating scheme is specified as late as just before the tool
is cut. Often, many designers arrive at nominal thickness values by using
values from previous designs without considering the application, material,
processing conditions, part cost, etc. There are general nominal wall thickness
guidelines available from various material suppliers. Thickness guidelines
consist of nominal wall thickness ranges for specific materials, and general
rules on wall thickness variations.
Georgia Gulf has developed the "flow ratio" to determine potential
combinations of gating schemes and wall thickness. More sophisticated thickness
guidelines include flow length versus thickness curves. Material suppliers
develop these curves for families of material within their company. GE Plastics
has developed a set of curves accessible in their Engineering Design Database
(EDD). These curves have been developed using an internal code to simulate
flow at various pressures and melt temperatures. These curves only provide
an estimation of flow length. Achievable flow length of a plastic can vary
significantly over material, process, and geometry. Using different geometry
or even gating a part in different locations will alter the achievable flow
length of the polymer. Flow length versus thickness curves do provide a
method for accessing information quickly, but only on a relative scale unless
the intended geometry resembles the spiral mold used to generate the data.
Spiral flow information is easy to obtain using empirical tests and can
provide useful information on how a specific resin will flow under the flow
and cooling conditions of a molding application.
Standard flow length verses thickness curves are adequate to capture variations
in process, but not geometry and gating schemes. Velocity is an important
parameter that can incorporate geometry effects. Standard flow length versus
thickness curves confound two important factors that melt front velocity
can capture. 1) How injection rate affects flow length. Injection rate contributes
to maximum flow length via machine capacity, gate size, possible shear heating,
and shear thinning, and 2) how spiral mold size affects flow length. Companies
developed variations to the spiral mold, such as disc flow, to approximate
real life situations better than the spiral mold.
Our Approach
To address the shortcoming in preliminary whole-part design guidelines,
and more specifically, to develop wall-thickness guidelines that quantify
material, process, and geometry issues, this paper proposes the use of charts
that utilize non-dimensional techniques as a starting point in developing
empirical models. Non-dimensional relationships can incorporate the important
geometric, process, and material parameters that correspond to the physics
of the process. Solutions to real problems involve a combination of analysis
and experimental information. Dimensional analysis seeks a mathematical
model that is simple enough to yield an applicable solution, yet capture
the essence of the physical behavior. The injection molding process involves
many parameters. Using conventional methods with dimensional values would
require an excessive number of experiments to characterize the relationships
among parameters and more importantly an excessive number of charts to represent
the data to designers. Charts using non-dimensional, or near-non-dimensional
relationships with appropriate parameters can characterize relationships
among parameters very effectively. One method of formulating dimensionless
numbers is using the Buckingham Pi Theorem (Krantz, et al., 1971). The Buckingham
Pi Theorem is a statement of the relation between a function expressed in
terms of dimensional parameters and related functions expressed in terms
of non-dimensional parameters. Using the Buckingham Pi Theorem allows us
to develop the important non-dimensional parameters quickly and easily.
The functional relation among the independent, dimensionless parameters
must be determined experimentally.
Charts thus obtained allow designers to determine feasible geometry and
gating schemes without resorting to detailed process simulation programs.
The power of this approach is that it incorporates manufacturability concerns,
specifically fillability characteristics, into the preliminary stages of
geometry synthesis. The designer will be able to start with a feasible preliminary
design and more efficiently generate a detailed geometry without unnecessary
iteration.
Research Focus
Our research focus includes only a part of the fillability portion of wall
thickness guidelines. Fillability guidelines include quality issues during
the filling stage such as short shots, material degradation and burning,
knit lines, splay, and jetting. Our research specifically encompasses short
shots and knit lines. Our research seeks to develop a model that will aid
in determining a minimum nominal wall thickness in the geometry synthesis
stage of design by considering material, pertinent process parameters, and
gating scheme.
To obtain an accurate filling model that applies to the generic injection-molded
part, we must look at the physics of the process, or how the filling is
affected by the interdependent geometry, process, and material parameters.
The fillability model that we are proposing is flow length as a function
of velocity, viscosity, and part thickness (Equation 1).
(1)
The velocity parameter is a primary reason why information from the standard
flow length versus thickness charts cannot be extrapolated to generic geometries.
Velocity can affect the physical process by reducing the viscosity from
increased shear-rate, increasing the polymer temperature from shear heating,
and reducing the polymer time in the mold, thus not allowing boundary layers
to form to reduce the effective thickness. Typical flow length versus thickness
curves contain information about viscosity in the form of representative
curves at specified melt temperatures. However, viscosity is also a function
of shear-rate. Thus, using viscosity in a fillability chart would incorporate
the affects of shear-rate and melt temperature. Previous research has found
thickness to be the dominant factor in determining achievable flow length.
An empirical chart based on Equation 1 will capture affects of process and
geometry on flow length. Thus, such a chart will allow designers to extrapolate
information to any generic geometry or even different gating schemes on
a part.
Dimensional Analysis
To represent the information from Equation 1, we use dimensional analysis
to formulate dimensionless numbers that can characterize the relationships
among parameters in a compact form. The fillability model will use the dimensionless
numbers as a starting point. Empirical data will determine a more precise
relationship among the filling parameters.
We used the Buckingham Pi procedure to determine the initial dimensionless
parameters. First we state all the parameters involved while listing the
primary dimensions of each (Table 1). For simplicity we combined viscosity
and density into a kinematic viscosity parameter which eliminates mass,
a primary dimension, from the analysis, but will not change the outcome
of the dimensional analysis. Previous research has found variable-density
effects to not have a significant influence on the spiral flow-length (Hieber,
1994), so we are actually only dividing the viscosity by a material constant.
We arbitrarily select the repeating parameters of t and V.
The analysis for the first dimensional group is as follows:
(2)
L: a+b+1 = 0 (3)
T: -b = 0 (4)
b = 0, a = -1 (5)
Therefore, the first non-dimensional group is:
(6)
We determined the other dimensionless parameter using the same procedure:
(7)
L: a+b+2 = 0 (8)
T: -b-1= 0 (9)
b = -1, a = -1 (10)
The second non-dimensional group is:
(11)
Equation 11 takes the form of the inverse of the Reynolds Number (Osborne
Reynolds, 1880) which is a measure of the inertial forces to the viscous
forces. Initially, the Reynolds number was used as a criterion to determine
the state of flow, laminar or turbulent. Later experiments show that the
Reynolds number is a key parameter for other flow cases as well.
The resulting dimensional analysis tells us that:
(12)
or
(13)
The non-dimensional parameters can characterize a physical relationship
only through an empirical model via experiments and simulations. The analysis
produces two dimensionless parameters, a normalized flow length and a normalized
viscosity. The flow length is normalized by the thickness and the viscosity
is normalized by the geometry and process, or the thickness and velocity.
As results show in later sections, the empirical data calls for slight modifications
to the normalized flow length parameter.
Experimental Focus
Our approach in this study is to develop a fillability model utilizing non-dimensional
techniques as a starting point for an empirical model that quantifies the
material, process, and geometry factors. To quantify the fillability model
(Equation 1), we are using a full-factorial experiment with factors that
essentially control the velocity, viscosity, and thickness.
We selected the parameters for the full-factorial experiment using information
from previous studies and knowledge from the injection molding field. Thickness
is a variable that can act as an independent parameter. Thickness is widely
used in industry, often as the only parameter that controls ultimate flow
length. Injection rate combined with thickness will be the primary parameters
that control velocity. The viscosity will be a function of shear-rate and
temperature. We can control the viscosity in the filling process by varying
the injection rate, melt temperature, mold temperature, and type of material.
We eliminated mold temperature as a factor from the experiment through testing
each factors sensitivity to flow length over the process window using simulations.
Spiral Mold Design
The range of flow rate, velocity, and thickness constrain the spiral mold
geometry. The flow rate should be between 0.5 and 4.0 in3/sec.,
a range for a typical injection molding machine. A typical PVC part thickness
specified by the Geon molding handbooks range from 0.060" to 0.125".
The flow velocity in most applications, calculated by (flow rate/melt front
area), is typically in the range of 2 to 5 in./sec. A typical spiral mold
generates too high of a velocity for practical applications; therefore,
we must use a mold with a larger cross-sectional area. A mold of width one
inch will allow the melt-front area to range from 0.060 to 0.125 in2
under the typical thickness range. Figure 1 shows the cavity of the spiral
mold consisting of three inserts of thickness 0.060", 0.0925",
and 0.125" and a total flow length of 30".
Design of Experiments
To characterize the fillability model, we ran a full-factorial experiment
with thickness, material, melt temperature, and ram speed as variables.
The mold temperature was set at a constant 100F. Thickness and melt temperature
contain three levels, ram speed contains four, and material contains two
(Table 2). We used two grades of rigid PVC from The Geon Company in the
experiment; 87241 general purpose injection molding compound, and M-3700,
a newer generation higher flowing injection molding compound.
Experimental Results
Developing the Fillability Model
Using dimensional analysis techniques (such as the Buckingham Pi Theorem)
to formulate dimensionless numbers can serve as a starting point for formulating
an analytical predictive model. Figure 3 shows the experimental data plotted
as flow length versus a dimensionless number, which we call the Fillability
Number (see Dimensional Analysis Section), is essentially a function of
process (Equation 14). The thickness dependence is eliminated from the denominator
because the velocity term is defined as the flow rate over the melt front
area where the melt front area is the melt front width multiplied by thickness.
The experimental data shows that the Fillability Number can capture the
effect of variations in viscosity and velocity from changes in melt temperature
and ram speed. Observing Figure 2, as the thickness increases, there becomes
more scatter in each thickness-dependent curve. Second order interactions
between melt temperature and thickness show that as the thickness increases,
flow length becomes more sensitive to melt temperature.
Incorporating the effect of thickness in the y-axis allows us collapse the
three curves. The dimensional analysis suggests to use flow length divided
by thickness as the other dimensionless parameter, however, the dimensionless
number could not collapse the three different thickness curves into a single
curve. The experimental data suggests to divide the flow length by the square
of thickness to collapse the data. The M-3700 material shows less scatter
than the 87241 material (Figure 3). As the curves both materials suggest,
the fillability model characterizes the 87241 material and M-3700 on two
distinctly different curves, however, the curves have similar slopes.
The best fit model for the experimental data is of exponential form (Equation
15). The equation has two constants, C and k. Therefore, for
each material, two constants need to be empirically determined to characterize
a Fillability Model. Table 3 represents the t2 values,
and constants C and k. for each material.
Fillability Chart Application
Fillability Chart Capabilities
The Fillability Model will estimate a minimum nominal wall thickness based
on feasible gating schemes, material, and process window limits. The designer
can get a qualitative feel for which parameters are going to affect the
design by the chart's functional relationship. The designer can determine
a minimum thickness while adequately filling a part by varying the gating
scheme, material, and flow rate. The chart will allow for quick solutions
of minimum thickness while also giving designers a qualitative feel for
the gating scheme, thickness, material, and required flow rate for a part.
Assigning a gating scheme in the preliminary stages of design will allow
the designer to create features, such as bosses, ribs, holes, snaps, etc.
with knowledge of distance from gate, last-to-fill areas, etc.
Application Procedure
Following a certain series of steps using the fillability chart will allow
us to converge on a minimum nominal wall thickness.
Step 1: Select material for molding part.
Step 2: Specify desired flow rate from injection molding machine barrel
diameter and ram speed.
Step 3: Specify desired processing temperature.
Step 4: Specify initial gating scheme on part to determine required flow
length and melt front width.
Step 5: Determine shear rate from initial nominal thickness, flow rate,
and melt front width assuming no slip at the wall and a linear velocity
distribution (Equation 16).
Step 6: Determine shear-rate and temperature dependent viscosity using a
5-constant viscosity model.
Step 7: Calculate Fillability Number, FN (Equation 17).
Step 8: Use Fillability Model, or Fillability Chart to determine flow length
over thickness squared (Equation 18).
Step 9: Calculate minimum thickness using the required flow length.
Step 10: Repeat procedure using other candidate materials and gating scheme
until reaching a feasible solution.
Conclusions
The objective of the research presented in this document is to develop a
methodology for presenting fillability information to designers to aid in
determining nominal wall thickness of injection molded parts early in the
design stage. The fillability information includes material, process, and
geometry parameters that will aid the designer in determining process sensitivities,
and choosing gating schemes and material to determine minimum wall thickness.
This paper proposed using dimensional analysis techniques as a starting
point in composing a fillability model. The two steps in developing a fillability
model included: 1) Conducting experiments using a variable thickness, 1"
wide, spiral mold using 87241 and M-3700 grades of rigid PVC from The Geon
Company to compose an initial fillability model, and 2) model a 5"
wide plaque geometry in C-MOLD to test the fillability model's sensitivity
to different geometries.
The use of dimensional analysis techniques facilitated the formulation of
a proposed dimensionless fillability model using the parameters of velocity,
viscosity, and thickness. Dimensional analysis techniques proposed two dimensionless
parameters. The experiment used a customized spiral mold containing three
thicknesses, two materials, and the process settings of ram speed and melt
temperature to control the velocity, viscosity, and thickness parameters.
The experimental results suggested that one of the two dimensionless numbers
be modified to represent the empirical information in a fillability chart.
Acknowledgments
The authors would like to thank the GEON Vinyl Company, especially Dr. Clive
Copsey, and the NSF/ERC for Net-Shape Manufacturing for supporting this
work.
References
- Hieber, C.A., Chiang, H.H. (1994), "Spiral-Flow Analysis Including
Variable-Density Effects," Society of Plastics Engineers, 52nd Annual
Technical Conference, San Francisco, CA, pp. 102 - 107.
- Krantz, D., Luce, R., Suppes, P., and Tversky, A., (1971) Foundations
of Measurement, Volume 1, "Additive and Polynominal Representations".
Academic Press, Inc., San Diego.
Table 1. Dimensional Analysis parameters.
Figure 1. Spiral mold insert geometry.
Table 2. Full-factorial experimental array.
Figure 2. Flow length versus a dimensionless Fillability Number.
Figure 3. Fillability model comparison between 87241 and M-3700 materials.
Table 3. Fillability Model material constants and fit
for empirical data and simulations.
