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                    INJECTION MOLDING
                           David D. Gill, Thomas A. Dow, Alex Sohn
                          North Carolina State University, Raleigh, NC


The objective of this research is to study the process of replicating precision optics using
injection molding. The technology to produce optical devices for the communication and
photonics industries must allow high volume production of thin, highly transmissive, and
environmentally stable (uniform properties throughout a range of temperature and humidity)
components at low cost and high speed. The details of the current technology and methods used
in industry are typically closely held and research that reveals a greater understanding of the
processes involved and creates new replication methods is needed. This research must include
an investigation of the replication of nanometer-sized optical features and a determination of the
transfer function between the shape of the mold and that of the molded lens.


To address the research goals, a series of experiments have been carried out on a laboratory-scale
Nissei hydraulic injection molding machine at the Precision Engineering Center at North
Carolina State University. This machine has a 6.2cm3 shot volume and a 14mm screw that
allows very thin optics to be produced in a single cavity mold while still staying within common
design practices regarding the ratio of shot volume to screw volume. The available mold
clamping force is 69 KN with a maximum injection pressure of 175 MPa. The tie-bar spacing is
102mm. The machine has an integrated mold heating and cooling system that employs water as
the heat transfer medium. The parts replicated to date have been single and double cavity parts
approximately 1800mm2 in area with varying thicknesses below 350µm.

A series of diamond turned aluminum and hard-copper mold inserts have been fabricated and
thousands of optical components have been created. The mold inserts were populated with
optical features representing many different shapes, aspect ratios (depth divided by width), sizes,
f numbers, and groupings that are common in micro-optical devices. An example mold insert is
shown in Figure 1 with a representative cross-section and detailed information about each of the
features in the mold. The features included in this copper insert are a spherical lens, a spherical
Fresnel lens, a blaze diffraction grating, and a lenticular (cylindrical lens) array. Non-optical
features are also included for the purpose of studying the effects of aspect ratio and shape. These
non-optical features include a wedding cake structure and grooves of various geometries. The
features range in overall depth from 300nm to 600µm, have aspect ratios between 0.026 and
0.87, and contain both rounded and sharp corners in various combinations. Several of the
features are also included to reveal any replication effects due to different widths and depths of
features that have the same aspect ratio.
               Figure 1. Mold Insert with Optical Features and Their Dimensions

The features were designed to be measured using stylus profilometry, interferometry, scanning
probe microscopy, and optical transmission tests. The copper mold insert is fitted into a
diamond turned aluminum mold cavity as shown in the lower left hand corner of Figure 1 and
mounted in the injection molding machine. Because this insert is circular, it can be mounted in
the mold cavity with the mold features located at different positions with respect to the polymer
flow as it enters through the sprue and proceeds to fill the mold cavity.


Experiments are being conducted with the molds described above to investigate the effects of
different molding variables on the replication of optical features. Nine variables or factors were
chosen for this study due to their importance in general purpose injection molding. A design of
experiment was developed for the nine factors and initial high and low values were determined
for each factor using Atohaas Plexiglas VLD poly(methyl methacrylate) (PMMA). The factors
and their high and low values are given in Table 1.
                Table 1. Injection Molding Factors for Design of Experiment
                                  Factor                      Low        High
                  Polymer Temperature (deg F)                 470         523
                  Mold Temperature (deg F)                    120         176
                  Injection Pressure (MPa)                     88         175
                  Injection Speed (cm^3/s)                    5.85         13
                  Cooling Time (s)                             0           10
                  Hold Time (s)                               0.35       1.89
                  Hold Pressure (MPa)                         5.6          14
                  Screw Rotation (RPM)                        20.5        205
                  Feature Position (deg)                      0, 90, 180, 270

The high and low factor values for the first eight factors were determined as the minimum and
maximum values at which the optical features could be replicated with reasonable fidelity. The
features must be replicated well enough to be measurable so that test will make known any
correlation between molding factors and replication fidelity. To determine the low values of the
factors, all factors were initially set to low values and then individual factors were lowered in a
stepwise manner until the part was no longer acceptable. The factor was left at the lowest
acceptable value and the process was repeated with the next factor. At several points during this
search, all of the factors were reset to the initial low values to assure that the factor values
determined previously were not preventing the later factors from reaching their potential low.
By this process, acceptable low values were found for each factor. The high values were
determined by the limits of the molding machine except for the polymer temperature and the
cooling and hold times. The high polymer temperature is a high temperature for this polymer,
but not so high as to cause polymer degradation. The high cooling time was chosen as the
maximum that would be desirable in a production setting. The high hold time was determined as
a time longer than was necessary for the sprue to freeze, at which point the polymer in the part is
cut off from the pressure being exerted by the injection ram. The ninth factor is feature position.
The mold insert is circular and is designed so that it can be rotated in the mold. This allows the
features to be placed at different locations in the mold with respect to the polymer flow direction.
This factor was chosen to be incremented through 360 degrees in 90 degree intervals.

A combination of all of the factors with each factor set to one of its extreme values is called a
treatment. Using these maximum and minimum values, a design of experiment was developed,
which reduced the number of treatments from 1024 (testing each factor at both of its values
against every other condition in the table) to 32 by making the following assumptions: the factors
do not interact and the effects of the factors vary linearly between the high and low value given
in the table. Through statistical analysis of the chosen 32 treatments, it was shown that two
variables in the test were not constrained by the first assumption and could interact without
compromising the test results. Injection speed and injection pressure were chosen as the
variables most likely to interact. In the experiment, each treatment consisted of the production of
more than 100 parts to allow the process to reach equilibrium. Five of the final 25 parts were
collected and 3 of those 5 were measured, the extra 2 parts being backups in case of handling
damage during removal from the mold or during the measuring process. The measured parts
were then compared to measurements of the mold features to reveal the linkage between
injection molding process factors and feature replication fidelity.

Each replicated feature is compared to the matching mold; however, the method of quantifying
that measurement is different for each feature type. For example, Figure 2 shows an
interferometer measurement of a spherical lens feature in the mold and its replicated PMMA
lens. The lens can be compared to the mold by measuring the mean radius of a sphere fit to the
data, the error in overall feature height, the chi squared value showing the deviation from the fit
sphere, and by subtracting the corresponding errors in the mold from these replication errors.
The sphere can also be tested for optical transmission using optical tests such as the Air Force
Targets, error in focal length, and dispersion of a beam at the focal point. The Fresnel can be
measured with the same techniques as the spherical lens with the additional measurement of step
height at each of the zone changes. Sharp features such as the blaze grating and V-shaped
grooves are measured for PV error, feature edge form, and face angle and flatness. The
lenticular array can be measured for the radius of curvature of each cylinder and error in the
replication of the height of the peaks between the cylinders. On all features, analysis of both the
feature itself and the array of features is important. For example, the shape of each peak in the
blaze grating is important, but it is the form of all of the peaks together that causes the grating to

Through this experiment a greater understanding of the relationship between injection molding
factors and the replication of precision optical features is being developed. Through this
understanding, it will be possible to better predict the moldability of optical features in new

                         Mold                                     PMMA Lens

  Figure 2. Interferometer Measurement of the Error in the Spherical Lens for the Mold and a
                                  Replicated PMMA Lens
The authors wish to acknowledge the support of this research by the National Science
Foundation (grant #9908223, Dr. K. P. Rajurkar, Program Director)

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