Investigation of Mold Design and Process Parameters in Microinjection
Molding to Fabricate a Deformable Membrane Mirror
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy
in the Graduate School of The Ohio State University
By
Ahmed Salem El-Taleb
Graduate Program in Industrial and Systems Engineering
The Ohio State University
2013
Dissertation Committee:
Dr. Jose M. Castro, Dr. Allen Y. Yi, Co-Advisors,
Dr. Jerald R. Brevick
Copyright by
Ahmed Salem El-Taleb
2013
Abstract
Deformable membrane mirrors (DMMs) are often used for adaptive optics in the
fields of astronomy, laser communication, medical imaging, and industrial high energy
lasers. As light passes through an optical system (and a specimen), phase variations are
introduced resulting in wavefront distortion from an ideal spherical form. In order to
compensate for such phase variations, an equal but opposite phase change can be
introduced by using a DMM. The shape of the DMM is typically altered via an applied
electrostatic field, which controls the distortion of the mirror. The manufacture of
DMM’s today is a relatively expensive and time-consuming endeavor. The objective of
this research is to evaluate the technical feasibility of a new DMM design using plastic
materials, and the cost effective microinjection molding process.
The proposed design consists of three distinctive regions in the cross section of
the DMM. These three regions are the solid frame, microchannel, and mirror. The critical
optical features of the proposed design include the flatness and flexibility of the circular
mirror in the center of the DMM. This is accomplished by designing a thin ring microchannel
around the mirror. The thickness and depth of this microchannel are critical for successful
molding. This microchannel has 16 slots that are molded on the perimeter of the mirror to
add more flexibility (for subsequent electrostatic distortion control) and serve as reservoirs
ii
where the air can escape the mold cavity during the microinjection molding manufacturing
process.
During this research, the technical feasibility of the design is demonstrated using
both computer simulations as well as experiments. Specifically, a DMM with
microfeatures has been designed with the aid of a computer-aided engineering (CAE)
analysis program, Moldex3D. This was done, before any actual experiments were
conducted, to understand the flow behavior of the polymer melt in the mold cavity with
various processes and geometric parameters. For example, micro slots were investigated
to serve the dual purposes of venting channels in the mold cavity, and also as the
supporting mechanism for DMM mirror operation. The main concerns of microinjection
molding of a DMM part include: failure to fill the cavity due to premature solidification
(because of quick cooling due to small cavity thickness), air trapped in microinjection
mold inserts (because of inadequate venting), and limitation of the machine capacity
(clamping force and pressure).
In this research, a design of experiment technique was used to study the effects of
the controllable process variables of microinjection molding (such as packing pressure,
packing time, and injection speed) on DMM mirror surface quality. The goal of this study
was to identify the dominant processing parameters and the interactions among the
parameters using a systematic approach. The response surface methodology (RSM) was
used to approximate a stochastic function of input-output relations in a statistical model,
toward the goal of identifying the best feasible settings of the microinjection molding
iii
parameters to minimize the DMM surface variation. Finally, the microinjection molded
DMMs were tested using a Michelson interferometer to verify their optical performance.
The main contribution of this research was to evaluate the technical feasibility of
a new DMM design using thermoplastic materials, manufactured using the cost effective
microinjection molding process. Experiments and simulated flow patterns for various
DMM geometric parameters were compared, and different approaches for characterizing
the dimensions and the performance of the DMMs were investigated. A further
contribution of this research was the use of design of experiment techniques to determine
the micro injection molding process parameters that minimize the DMM mirror surface
variability.
iv
Dedication
This document is dedicated to my family.
v
Acknowledgments
I would like to acknowledge my country Libya for the financial support throughout my
PhD study in the United State of America through the Libyan-North American
scholarship.
I would like to express my sincere gratitude to my advisors Professor Jose M. Castro and
Professor Allen Yi for the continuous support of my PhD study and research, for their
patience, motivation, enthusiasm, and immense knowledge. Their guidance helped me in
all stages of my research and during the writing of this thesis. I could not imagine having
better advisors and mentors for my PhD study.
Besides my advisors, I would like to thank Prof. Jerald R. Brevick, for his invaluable help
on both academic and personal level, for which I am extremely grateful.
Professor Robert S. Brodkey has been very helpful as a graduate representative in my
committee; I’d like to express my gratitude for him.
I am very grateful to Mr. Joshua Hassenzahl of the ISE machine shop for providing me
advice and help with the experimental part of my research. I will also like to thank Dr.
Lei Li, Neil Naples and David Mccray for their help.
Last, but by no means least, I would like to thank all my family members and especially
my wife Faozea for her personal support and great patience at all times. My brothers and
sister have given me their unequivocal support throughout my studies.
vi
Vita
August 1966 ...................................................Born- Al- Baneia –Libya
March 1989 ....................................................B.Sc, University of Garyounis - Libya
April 1989 - May 1990..................................Petrochemical Company - Methanol
Maintenance Planning, El-Brega - Libya.
June 1990 - 2006........................................... High Voltage and Telephone,
Cables Company, Benghazi, Libya.
2004 -June 2006 .............................................M.Sc at university of Garyounis - Libya
July 2006 to May 2008................................. Lecturer, Engineering Faculty, Omar
El- Mokhtar University, El-Baida - Libya.
2009 to present ..............................................Graduate Student, Department of Integrated
Systems Engineering, The Ohio State
University.
Publications
Ahmed El-Taleb, Panpan Zhang, Lei Li, Jose M. Castro, Allen Y. Yi, “Mold design for
microinjection molding of deformable membrane mirrors,” ANTEC 2013 Paper 1590025
Fields of Study
Major Field: Industrial and Systems Engineering
vii
Table of Contents
Abstract .............................................................................................................................. ii
Dedication .......................................................................................................................... v
Acknowledgments ............................................................................................................ vi
Vita ................................................................................................................................... vii
Publications ..................................................................................................................... vii
Fields of Study ................................................................................................................. vii
Table of Contents ........................................................................................................... viii
List of Tables ................................................................................................................... xii
List of Figures ................................................................................................................. xiii
Chapter 1: Introduction ................................................................................................... 1
1.1.
Motivation ........................................................................................................... 2
1.2.
Research Objective ............................................................................................. 3
1.3.
Dissertation Outline ........................................................................................... 4
Chapter 2: Background and literature review ............................................................... 5
2.1.
Definitions of microfeature molded parts ............................................................ 6
2.2.
Studying the microinjection molding process using CFD software packages ..... 6
viii
2.3.
Factors affecting the flow patterns ..................................................................... 10
2.4.
Fabrication of designed micro-parts ................................................................... 20
2.4.1.
Micro-part design features .......................................................................... 23
2.4.2.
The microinjection process optimization .................................................... 24
2.4.3.
Microinjection molding machines technologies advancement ................... 27
Chapter 3: Design and Process Analysis ....................................................................... 32
3.1.
DMM part design ............................................................................................... 32
3.2.
DMM microchannel design ................................................................................ 34
3.2.1.
The effect of microchannel thickness in filling the cavity .......................... 34
3.2.2.
Effect of microchannel length on cavity filling and mirror deformation.... 36
3.2.3.
Effect of microchannel thickness on flow .................................................. 39
3.3.
Effect of DMM mirror thickness on the flatness............................................... 44
3.4.
Mold insert fabrication ....................................................................................... 45
3.5.
Material selection ............................................................................................... 47
Chapter 4: DMM Test .................................................................................................... 50
4.1.
Geometry measurement of the part .................................................................... 50
4.2.
Surface variation measurement of the DMM part .............................................. 52
4.3.
Measuring DMM deflection using INSTRON machine .................................... 54
4.4.
Michelson Interferometer ................................................................................... 57
ix
Chapter 5: Processability study using Design of Experiments ................................... 61
5.1
Response Surface Method in Experimental Design ........................................... 61
5.2
Face Centered Composite Design Technique (FCC) ......................................... 62
5.3
Statistical Modeling............................................................................................ 65
5.4
Statistical Modeling of µIM process parameters to mold a DMM .................... 65
5.4.1
Performance measure selected .................................................................... 66
5.4.2
Microinjection molding process parameters ............................................... 67
5.4.3
Levels of the selected process parameters (factors) .................................... 68
5.4.4
The DOE matrix. ......................................................................................... 68
5.5
Statistical Test of the Data ................................................................................. 71
5.5.1
Test of significance ..................................................................................... 71
5.5.2
Checking the model adequacy (normal probability plot) ........................... 72
5.5.3
Effect of residuals experiment .................................................................... 73
5.5.4
Lack of fit test ............................................................................................. 75
5.5.5
Goodness of fit ............................................................................................ 75
5.6
Effect of the significant µIM parameters on the response ................................. 77
5.6.1
The main effect of packing pressure (X1) on the response ......................... 77
5.6.2
The main effect of packing time (X2) on the response ............................... 78
5.6.3
The main effect of injection speed (X3) on the response ........................... 79
x
5.6.4
The interaction effect of the factors on the response .................................. 79
5.6.5
Response surface analysis ........................................................................... 81
5.7
Optimization using the statistical model ............................................................ 85
Chapter 6: Conclusions and Recommendations for Future Work ............................ 86
6.1.
Conclusions ........................................................................................................ 86
6.2.
Recommendations for Future Work ................................................................... 88
References ........................................................................................................................ 90
xi
List of Tables
Table 1: Simulations results for a rectangular cavity with various thicknesses............... 34
Table 2: Simulation results of various microchannel widths length. ............................... 37
Table 3: Positions measured thicknesses on the DMM solid frame. ............................... 51
Table 4: Positions measured thicknesses on the DMM mirror. ....................................... 52
Table 5: Probability Matrix of FCC Design with three factors [3-5]............................... 64
Table 6: Effect of melting temperature on the packing pressure ranges. ........................ 67
Table 7: Extreme values of the controllable variables ..................................................... 68
Table 8: List of experimental runs ................................................................................... 69
Table 9: Regressed coefficients of statistical model. ....................................................... 70
Table 10: Test of significance. ......................................................................................... 71
Table 11: ANOVA results of the developed model. ........................................................ 75
Table 12:Goodness of fit measures. ................................................................................. 76
Table 13: Residuals of experimental vs. predictions from statistical model. .................. 76
Table 14: Values of the controllable variables that minimize the surface variation ........ 85
xii
List of Figures
Figure 1: Schematic showing hesitation effect of the melt flow in micro-ribs................ 13
Figure 2: Modified Cross viscosity models #2 for COC-Topas-5013 S [53]. ................. 18
Figure 3: Pressure-Volume-Temperature (PVT) curves for COC-Topas-5013S [53]. ... 18
Figure 4: Study sequence of a manufacturing process. ................................................... 25
Figure 5: Microinjection molding cycle time. ................................................................. 25
Figure 6: Two main microinjection molding units. ......................................................... 27
Figure 7: The back flow systems in microinjection molding [2]. .................................... 28
Figure 8: Microinjection molding machine (LD30EH2). ................................................ 29
Figure 9: Two-stage V-Line plunger injection for plasticizing and injection [2]. ........... 30
Figure 10: Solid models of original and current designs. ................................................ 32
Figure 11: Detail drawing of DMM with detail C showing the three sections. ............... 33
Figure 12: The simulation results of a rectangular part with thickness of 100 µm (5.11
mm of cavity length was filled). ....................................................................................... 35
Figure 13: The simulation result of a rectangular part with at thickness of 500 µm (the
entire cavity filled). ........................................................................................................... 36
Figure 14: Stress strain curve for several COC-Topas 5013 [56]................................... 37
Figure 15: The DMM part with filling length of 2 mm (the cavity isn't filled). .............. 38
Figure 16: The DMM simulated deformation with filling length of 2 mm. .................... 39
xiii
Figure 17: Case # 1: comparison of DMM simulation results vs. real part with a
microchannel thickness of 500 µm. .................................................................................. 40
Figure 18: Case # 2: comparison of DMM simulation results vs. real part with a
microchannel thickness of 350 µm. .................................................................................. 41
Figure 19: Case # 3: comparison of DMM simulation results vs. real part with a
microchannel thickness of 250 µm. .................................................................................. 42
Figure 20: Case # 4: comparison of DMM simulation results vs. the real part with a
microchannel thickness of 100 µm (the new design of DMM). ....................................... 43
Figure 21: DMM deflection with various mirror thicknesses.......................................... 45
Figure 22: Microinjection molding insert. ....................................................................... 46
Figure 23: Microinjection molding insert detail drawing. ............................................... 46
Figure 24: Previous MFI results for Topas-COC-5013S vs. other OSU materials. ....... 47
Figure 25: MFI results for Topas-COC-5013S vs. other Topas product [56]. ............... 48
Figure 26: Surface variation and thicknesses positions for measurements. ................... 50
Figure 27: The Mitutoyo SURFTEST SV-3100 contact profilometer. ........................... 53
Figure 28: Surface variation and thicknesses positions for measurements. ................... 53
Figure 29: Schematic of deflection setup Measurement of DMM part. ......................... 54
Figure 30: DMM model under pressure of 4.75 mm in the center. ................................. 55
Figure 31: DMM model under pressure of 4.5 mm in the center. ................................... 56
Figure 32: DMM wavefront change measurement setup................................................. 57
Figure 33: Pinhole schematics and the effect on processed image [52]. ......................... 58
Figure 34: Schematic of the voltage applied to the DMM. ............................................. 58
xiv
Figure 35: DMM device interference patterns under 300 volts and 6 Hz sine wave. ..... 59
Figure 36: Face centered composite design using three selected factors [52]. ................ 63
Figure 37: The response measurement (i.e experiment run # 2). .................................... 66
Figure 38: Normal probability plots of residuals. ............................................................ 72
Figure 39: Plot of residual versus the order of run data................................................... 74
Figure 40: Plot of residual versus the predicted value of the model. ............................... 74
Figure 41: The model fitting curve of the experimental response. .................................. 77
Figure 42: Effect of each factor significant to the response. ........................................... 78
Figure 43: The interaction effect of the Xl X2 on the DMM surface deviation. .............. 79
Figure 44: The interaction effect of the X2X3 on the DMM surface deviation. .............. 80
Figure 45: Response surface plot of packing, pressure and time..................................... 81
Figure 46: Contour plot of packing, pressure and time. .................................................. 82
Figure 47: Response surface plot of packing pressure and injection speed..................... 83
Figure 48: Contour plot of packing pressure and injection speed. .................................. 83
Figure 49: Response surface plot of packing time and injection speed. .......................... 84
Figure 50: Contour plot of packing time and injection speed.......................................... 84
Figure 51: Suggested new DMM design (half cross section) .......................................... 89
xv
Chapter 1: Introduction
In recent decades, there has been an increasing demand for small and even micro
scale parts fabrication; this trend towards miniaturization makes micro-electromechanical-systems (MEMS) of growing importance. MEMS are versatile, and can be
used for multiple applications, including mechanical, optical and electronic products and
devices. Examples of MEMS devices include micro sampling cells, micro heat
exchangers, micro pumps, biochips and optical grating elements. As demand grows for
larger production quantities of MEMS, lower cost and faster fabrication processes, along
with a wider range of materials, need to be developed. Any fabrication processes should
demonstrate significantly high production rates, quality and enhanced performance,
creating capabilities for the mass production of MEMS and miniaturized parts
incorporating microfeatures with various materials.
One MEMS product, a deformable membrane mirror (DMM), is an optical device
whose shape or position can be altered with an applied voltage. The thin membrane on
the DMM is deformed electro-statically by applying a voltage to the electrodes of the
actuators positioned under the membrane. As light passes through the microscope's
optical system and the specimen, phase variations are introduced, resulting in the
wavefront distortion from the ideal spherical form. In order to compensate for such phase
1
variations, an equal but opposite phase change is introduced by using a deformable
membrane mirror.
1.1. Motivation
Plastic microinjection components, which are smaller than 1 mm in overall
dimension and thicknesses of the order of several microns, will be useful in future digital
imaging and MEMS technologies. With the development of the micro-injection molding
(µIM) technology, new machines have been introduced that are specially designed for the
fabrication of miniature components/parts that contain micro features. In microinjection
molding, the thickness of the microchannels on the surface of the mold insert is very
small compared with the mold cavity for macro-scale products. Hence, more power must
be provided by the injection molding machine to ensure a successful micro-part.
Therefore, the limitation of machine power and the resistance to flow of the polymer
injected into the micro cavity must be carefully evaluated to manufacture high-quality
parts by micro-injection molding. To decrease the viscosity of the polymer requires high
molding temperatures. However, excessively high temperatures have some negative
consequences, such as residual stresses and warping of the part surface.
The challenge, in this research, is to design the part so it can be successfully
molded. There are two specific problems to overcome: air venting and the freezing of the
molten polymer. Firstly, the difficulty that arises in microinjection molding is the
incorporation of venting for the trapped air in the mold. Since the part contains
microfeatures, air vents are difficult to manufacture at a scale smaller than the micron
size. In some cases, the air vents are of the same size, or even larger, than the
2
microfeatures. Therefore, some microfeatures cannot have air vents. As a consequence,
the trapped air during the injection process creates a back pressure that prevents the melt
polymer from completely filling the mold cavity. Secondly, the problem of the cavity not
being filled because of quick freezing of microstructures needs consideration. Even
though thermoplastics do not have a high thermal conductivity, which is the capability of
the material to transfer heat within itself by conduction, the molten polymer still freezes
relatively quickly due to the extremely small thickness in the mold cavity. Thus, the
surface-area-to-part-volume ratio is large, allowing for the relatively fast transfer of heat
from the molten polymer to the mold. The flow patterns with different process parameters
in the microinjection molding cavity were studied to guide the design of the mold
geometry to be machined. For this purpose, we used the CAE injection molding
simulation software Moldex3D.
1.2. Research Objective
The main objective of this research is to evaluate the technical feasibility of a new
DMM design using plastics materials manufactured using the cost effective micro
injection molding process. Specifically to evaluate the design to enable more mirror
flexibility, and also flatness under load, compare real experiments with simulated flow
results at various DMM geometric parameters, identify different techniques that best
measure the quality that characterize the DMM parts, and investigate the effect of varying
process parameters on the quality of the DMM parts.
3
1.3. Dissertation Outline
This dissertation consists of six chapters:

Chapter 1 gives an introduction and discusses the motivation and objectives of the
research.

Chapter 2 describes the background of the study, and a literature review.

Chapter 3 discusses the experimental setup and design methods to manufacture the
DMM part.

Chapter 4 describes the methods established to evaluate the quality of DMM parts.

Chapter 5 discusses, in detail, the design of experiment used to study the µIM process
parameters on the surface quality of the DMM mirror.

Finally, Chapter 6 contains general conclusions, recommendation and a discussion of
potential future work.
4
Chapter 2: Background and literature review
The rapid development of Micro Electro Mechanical Systems (MEMS) is driving
a trend toward product miniaturization. Related to this trend is an increase in
multipurpose products which can be used for multiple applications, including mechanical,
optical and electronic products and devices. Many devices with micro features such as
micro sampling cells, micro heat exchangers, micro pumps, biochips and optical grating
elements, have been successfully fabricated, many using injection molding.
A type of MEMS, called a deformable membrane mirror, is used for adaptive
optics [7, 8], confocal microscopy [9], two-photon microscopy, and ophthalmology [10].
Electro-statically controlled deformable membrane mirrors were first proposed in the
1970s and have recently become available for wavefront control in optic systems for
various applications [11].The use of adaptive optical components can be found in the
areas of astronomy (ground-based telescopes) [12], laser communications (switching and
coupling) [13], medical imaging (particularly ophthalmology) [14], and the industrial use
of high energy lasers (precision focus, cutting, and welding) [15]. Using DMM in
confocal microscopes provides the ability to obtain 3D images. Unfortunately, the
resolution of such microscopes is greatly affected by the specimen’s optical properties.
The image quality can be compromised due to optical irregularities introduced by spatial
variations in the refractive index of the specimen. Such problems become more
5
predominant when imaging deep into thick biological specimens, making it difficult to
observe cells and their processes in their natural environment. This necessitates the
observation of such specimens in the unnatural surroundings of microscope slides.
A DMM mirror can move back and forth with an imposed voltage. The thin
membrane is deformed electro-statically by applying a DC voltage to electrode actuators
positioned under the membrane and above the circular frame. As light passes through
microscope's optical system and the specimen, phase variations are introduced, distorting
the wavefront from the ideal spherical form. In order to compensate for such phase
variations, an equal but opposite phase variation is introduced by using a DMM.
2.1. Definitions of microfeature molded parts
There are several classifications of micro-parts fabricated by microinjection
molding process which can be found in literature, as reported below:
A. Parts having a weight of less than 1 mg or being a fraction of a polymer pellet that
is approximately spherical in shape and 3 mm in diameter.
B. Conventionally sized parts with microstructures having a thickness typically
around 100 µm.
C. Parts having any dimensions with tolerances in micrometer range, typically
between 2 and 5 µm.
2.2. Studying the microinjection molding process using CFD software packages
The process design of microinjection molding determines a number of processing
parameters such as injection pressure, packing pressure, melt temperature, barrel
6
temperature, mold temperature, filling time, packing time, cooling time, cycle time,
clamping force, injection speed and injection stroke. In this process, the micro-part is
irregular in geometry and has a different thermal history during the injection process
cycle. There are many numerical simulation methods to simulate the microinjection
molding process to predict a final product with micro-features, which is crucial for
precise operations in the process. Many variables in microinjection molding process, such
as high pressure and shear rate, quick cooling, and micro-scale part geometry have an
impact on the flow of the polymer melt. As a result, the following issues in simulation of
injection molding process must be taken into consideration due to the change in geometry
of micro-parts:
1) High heat transfer of polymer melts inside the microinjection molding cavity is
due to the flow phenomenon, which are mass and volume of the polymer melt in
the cavity.
2) The molten polymer quick cooling caused by higher shear stress that comes from
the friction near the mold cavity surface.
3) Different rheological polymer flow behavior in microinjection molding cavity.
4) The mold cavity surface property effect on the viscosity of the molten polymer.
There were many CAE software packages developed for the purpose of injection
molding process flow simulation in the filling of the cavity. These software packages are
used in academia and industry for process simulation of conventional injection molding.
In the literature these products are often cited: CADMOULD, SIGAMA, MoldFlow, and
Moldex3D. Some investigated the filling process of the multi-fiber connector in
7
microinjection molding process in which the prediction of the weld line was done and the
cavity numbers were optimized [21-22]. In other studies, microinjection molding was
investigated along with the process-ability to produce a micro-part with 100 μm diameter,
and the results revealed the correlation between the processing conditions and processing
ability [23-24]. In reference [27], MoldFlow and C-Mold were used to simulate the
microinjection molding process of a micro gear with 150 μm diameter in 2.5D/3D to
analyze the weld line position, injection pressure and injection speed distribution during
the process. In reference [28] CADMOULD was used to simulate the 2.5D/3D
microinjection molding process to test the micro structures with ribs and corners. These
results showed that 2.5D simulation is hard to describe the polymer melts flowing as well
as the filling behavior in ribs and corners [29]. Simulations of the microinjection molding
process, as in the example [30] implemented studies for the microinjection molding
process by MoldFlow and C-Mold as well as a self-coded package. The simulation results
from these packages detailed the filling processing phase of the micro gear with 120 μm
diameter, in which the simulation was carried out for three different polymers:
Polypropylene (PP), polyamide (PA) and Poly-oxy-methylene (POM) These simulations
were based on the Taguchi design of experiment technique, which was significant in
achieving the processing parameters on filling performance [31-32]. With the software
package MoldFlow Plastic Insight (MPI), the molding process of a micro columns array
(with a diameter of 200 μm and height of 300 μm for one column) was simulated. The
Hypermesh software processed 3D model mesh elements of the micro-part [33]. The
simulation was carried out for all the microinjection molding filling process as well as the
8
shrinkage and warpage of the micro-part. The main purpose of any numerical simulation
is to improve the replication fidelity of the microinjection molding parts, and is calculated
by the equation below by optimization of the injection molding process parameters.
Equation 1
RF stands for replication fidelity, ΩC is the geometry domain of cavity, ΩP is the
geometry domain filled by polymer. The weights of the molded parts are used to
characterize the replication fidelity of microinjection molded parts as a quantitative
measurement. It is not accurate, but rather economical, as compared to the use of some
very expensive equipment to measure the geometry dimension of the micro-parts, such as
scanning electron microscopy (SEM). The part weight is fixed after the packing phase.
After the simulation of the filling and packing processes of injection molding in the Flow
3D module of MPI, the packing time influence on the part weight from simulation and
experiments had consistent results from both activities. From the results, it was
discovered that the higher the part weight, the better the filling of the microstructures.
The weight of the molded part can influence the replication fidelity of micro-part. The
Moldex3D software successfully developed the 3D simulation of the microinjection
molding process by analyzing the temperature history and distribution in the micro
features during microinjection molding. However, the research works based on special
software packages did indicate that the simulation software based on conventional
injection molding process can supply the characteristic analyses for microinjection
molding process. However, the simulation software was not able to precisely predict the
flow behavior of polymer melts in microinjection molding process, which results from
9
the fact that the mathematic model and boundary conditions were designed for fluid
dynamics at macro scale.
According to the above literature regarding the microinjection molding process
simulations, it is found that with CFD software packages, the numerical simulation can
be more precise than the case with special software packages based on traditional
injection molding process. After all, the special software packages cannot realize the
quantitative analysis for the microinjection molding process, since there are still many
unclear phenomena and mechanisms for micro-parts, especially in such comprehensively
complex processing conditions. Therefore, the improvement of modeling in physics and
mathematics for micro-parts will be the key issue to resolve in order to produce better
numerical simulation results.
2.3. Factors affecting the flow patterns
A considerable amount of research has focused on the numerical and
experimental investigation of flow behavior of the polymer materials [20-26] and the
applications of the MEMS devices [19]. In addition, the process factors are of significant
importance and have therefore been studied by many researchers. In general, the process
factors studied are melt and mold temperature, injection speed/rate, injection and holding
pressures, and cooling time. With the development of microinjection molding
technology, new machines were introduced that were specially designed for the
fabrication of miniature components or parts with microfeatures. New process factors
were considered, such as the shot size and the small forward movement of the injection
10
plunger for controlling the holding pressure [27], in an attempt to improve the process
performance.
The main factors investigated by researchers are melt and mold temperature,
injection speed, and injection pressure, due to their direct effects on the melt flow in
conventional injection molding. Many researchers have studied the importance of those
factors in microinjection molding mentioned in [27]. The main conclusions from these
studies are that high melt and mold temperatures, and high injection speed have a positive
effect on the melt flow in micro-cavities. However, when comparing the magnitude of the
influence of these factors on the melt filling quality the reported results are not consistent.
Some reports indicated that a high mold temperature above the glass transition
temperature of polymers (or close to their melt temperature) is the most important factor
for improving the replication capability of microinjection molding. Other researchers [3436], came to the conclusion that the injection speed melt temperature or holding
pressures, were the most influential factors. Such discrepancies in their findings could be
explained by the fact that the studies were carried out under different experimental
conditions. For example, different polymers and test structures were used. At the same
time, it should be noted that although high settings of the considered process factors
could improve the melt flow in micro cavities, this could also have a negative effect on
injection molded components. For instance, a high mold temperature may result in
temperature-induced defects on micro features [37], and could also increase the cycle
time and the processing cost due to the need of additional heating and cooling devices
[38]. Besides process parameters, the geometric configuration of final part is also a factor
11
affecting melt filling results in microinjection molding. For example some researcher
investigated the effect of the distance between micro features and the gate of the mold
tool on the melt filling depth [36]. The result showed that micro channels near the end of
the flow path would be better filled. Also, the study showed that the angle of the micro
features and the direction of the melt flow could result in different filling depth [34],
although the effect of these factors depends strongly on the polymers used to replicate the
features. Another study [39] also provided very useful information for the design of tools
and components that incorporate micro features.
There are many factors that can influence the capabilities of microinjection
molding to fabricate the DMM part with a microfeature. One of them is aspect ratio of a
molded part. The aspect ratio is defined as the ratio of a part’s longer dimension to its
shorter dimension. The achievable aspect ratio in replicating micro features is one of the
most important characteristics of the microfeature fabrication process and constitutes a
constraint in the application of conventional injection molding. The achievable aspect
ratio is also limited by the geometry of the microfeature, the polymer type, and the
process parameters. The literatures suggested that the critical minimum dimensions
which can be replicated successfully by microinjection molding are mainly determined
by the aspect ratio.
12
Figure 1: Schematic showing hesitation effect of the melt flow in micro-ribs.
In addition to geometry and aspect ratio, a physical phenomenon called the
hesitation effect has to be taken into account in microfeatures as opposed to macro parts.
To understand the hesitation effect, consider the flow pattern throughout the mold cavity
filling as shown in the Figure 1. The hesitation effect is common when an injection
molded part contains different thicknesses. The polymer melt first enters the cavity from
the gate, and the front of the flow reaches the thin ribs. There is insufficient injection
pressure to fill these thin ribs, as the melt takes an alternative route along the thick
section of the mold cavity.
The melt that just entered the thin section sits losing heat until the rest of the mold
cavity is filled. When the mold is almost completely filled, the full injection pressure is
available to fill the thin micro-ribs but the material is almost frozen, and the thin microribs will not be filled. This problem is caused by the hesitation effect at the filling stage.
If the melt continues to flow at a nearly uniform rate, there is no difficulty in filling the
thin section. To fill the cavity, it is required for the melt polymer to have proper
temperature, pressure, and injection speed. The melt tends to flow more easily into
13
cavities with relatively low resistance areas that have greater cross sections, while the
flow speed slows at the entrance of microfeature. The result is that the melt freezes in the
microfeature cavity because the filling time of the cavity is usually greater than the
cooling time of the microfeature. It was recommended in the literature that injection
molded parts with higher aspect ratio microstructures have larger thicknesses in which a
quick filling of the cavity allows the filling of the microfeature before part cooling starts.
In addition, the literature shows that in unidirectional flow, the depth of the filling in
microchannels is sensitive to the channel length. In this study, a commercial CAE
analysis program, Moldex3D, has been adopted as the analysis tool in the simulation of
the flow phenomena of polymer melt inside the mold cavity. The polymer melt [39] is
assumed to be Ellis modeled as a visco-elastic fluid, which provides both a power law
and Newtonian flow model in equation 1:
*
Equation 2
+
Where 1/2 is the shear stress at which the viscosity is 50% of the Newtonian limit, 0, and
-1 is the slope in the power law model. The corresponding relationship between flow
rate in equation 2 and pressure for viscous flow between two parallel plates is:
*
(
)+
Equation 3
Where Q is the flow rate, H is the thickness of the cavity, W is the cavity width, ∆P is the
pressure drop, L is the length of the cavity, and other coefficients are from the Ellis
model. The change in the bulk temperature which was analyzed by equation 3 at the melt
front is:
14
̅
[
*
(
]
)+
Equation 4
Where  is the density, Cp is the specific heat,  is the thermal diffusivity of the polymer
melt, ∆P is the pressure drop, R is the radius, L is the length in each portion of the cavity,
Tmelt and Twall are the upstream melt and mold wall temperatures, and ∆t is the time step
between process updates.
The shear rate is modeled as:
̇
[
(
)
]
Equation 5
In microinjection molding, the thickness of microchannels on the surface of the
mold insert is very small compared with the mold cavity for conventional products [25].
For a polymer filling into a cavity channel of thickness (t) with average injection velocity
Vi, the shear strain rate of the polymer on the average is defined as:
̇
Equation 6
And its shear stress, which is the resistance to deformation, can be expressed as:
̇
Equation 7
Where  is the viscosity of the polymer, and is a function of temperature. These
equations reveal that the average shear strain rate of the polymer in the micro-injection
15
molding is thousands of times greater than that of conventional injection molding, in
order to achieve the same injection speed of the polymer. Additionally, the filling
resistance (shear strain rate) of the polymer in microinjection molding is markedly higher
due to the low thickness of the microchannels. Hence, more power must be provided by
the injection molding machine to ensure a successful micro-injection molding. Even so,
the limitation of the machine power and minimization of deformation resistance of the
polymer injected into the micro cavity must be addressed in order to create the desired
high-quality part with the microinjection molding process. Obtaining a relatively low
viscosity in the polymer one direct method is to keep the polymer at a high melting
temperature and mold temperature.
To fill the microfeatures in the part successfully with minimum injection pressure,
the mold temperature must be greater than the glass transition temperature (Tg) of the
polymer used. This fact demonstrates that the mold temperature greatly influences the
mold ability to produce a part with microfeatures. However, an excessively high mold
temperature will have some negative consequences such as residual cavities and warping
of the part surface. The vacuum cavity is another defect originally generated by the
shrinkage of the polymer, and is formed by the remainder of the gas at high pressure. The
additional creation of air pockets within the mold is caused by an excessive increase in
the temperature of the polymer. The high temperature increment due to the shear strain
rate and mold temperature affects the flowability through the gate to the mold cavity.
Other main reasons behind the failure to fill the cavity in microinjection molding
include venting of the trapped air and quick cooling of the polymer melt. Firstly, since
16
the part contains microstructures, air venting is difficult to manufacture at a scale smaller
than the micron size. The air vents are of the same size as the microstructures or may be
even bigger. Therefore, some microfeatures do not have air venting. As a consequence,
the trapped air during the injection process creates a back pressure that prevents the
polymer melt from completely filling the mold cavity. Secondly, the quick freezing of
microstructures that prevents the cavity from being filled needs consideration when
injection molding a part in order to keep the polymer melt from freezing until the mold
cavity is completely filled. Even though thermoplastics do not have a high value of
thermal conductivity, a property dictates the capability of the material transfer heat within
itself by conduction; the polymer melt still freezes relatively quickly due to the extremely
small thickness in the mold cavity. Thus, the ratio between surface areas to part volume is
large, allowing for the relatively fast transfer of heat from the molten polymer to the
mold. However, this problem can be solved by raising the temperature of the mold close
to that of the molten polymer, during flow, with subsequent fast cooling.
It is essential to understand the flow behavior of a polymer melt with different
process parameters on the injection molding cavity of the designed DMM part before the
process actually begins. In this study, a CAE analysis program, Moldex3D, has been
adopted as the analysis tool for simulating the flow phenomena of the polymeric melt
inside the mold cavity during the process. The Moldex3D simulation indicates the weld
line and air trap, decides the optimal runner design and gating locations, and selects the
proper settings for melt and mold temperature, filling time, flow rate profile, injection
pressure profile, and history of important process variables during filling phase.
17
Figure 2: Modified Cross viscosity models #2 for COC-Topas-5013
[http://www.moldex3d.com].
Figure 3: Pressure-Volume-Temperature (PVT) curves for COC-Topas-5013S
[http://www.moldex3d.com].
At the packing step, the simulation can decide the packing pressure and amount of
time necessary to prevent over-packing, estimates volumetric shrinkage distribution,
18
clamping force and history of important process variables. At the filling stage, both
polymer melt and air are assumed to be incompressible. The COC-Topas-5013S as
material selected to fabricate the new DMM design. The polymeric melt of COC-Topas5013S is assumed to behave as a generalized non-Newtonian material, where the
viscosity data shown in Figure 2 are fitted to modify cross viscosity law models #2.
Figure 3 shows the Pressure-Volume-Temperature (PVT) data are fitted to the modified
PVT traits. The modified cross viscosity law models #2 uses the following equations:
Equation 8
Equation 9
Where  is the is the material viscosity, ́ is a shear rate,
represents the zero shear rate
viscosity, * represents the critical shear stress (roughly characterizing transition shear
stress from the Newtonian range to the pseudo-plastic region), and n (where 0 < n <1)
represents the shear rate sensitivity, where 1-n roughly characterizes the slope of the line
over the pseudo-plastic region in the plot. Viscosity is a decreasing function of
temperature. The temperature time superposition principle of viscoelasticity describes the
dependence of viscosity on temperature. The viscosity and shear rate curves are divided
into three regions (Newtonian, pseudo-plastic, and Newtonian behavior) on a log plot of
() versus log (γ˙). Firstly, for sufficiently low shear rate values (that is, log (γ˙) ≤ 102
1/sec), viscosity becomes independent of the shear rate, in that the material exhibits
19
Newtonian behavior. Secondly, if 102 ≤ log (γ˙) ≤ 105, the dependence of log ( ) on log
(γ˙) is non-linear and decreasing (this is pseudo-plastic behavior, as can be seen on Figure
2). Finally, for log (γ˙) ≥ 105,  has a power law dependence on γ˙. As γ˙ increases
beyond 105 the viscosity curve levels off, and the material tends to have Newtonian
behavior again.
2.4. Fabrication of designed micro-parts
Using the microinjection molding process is not the same as conventional
injection molding, where many concerns or manufacturing issues are considered in the
product design phase. Very little of this has been done so far for the microinjection
molding process. The focus of this research is the study of the process capabilities of the
microinjection molding, specifically the issues we are interested in microinjection
molding are:
1. Which is the smallest and maximum size of the desired product?
2. Which is the achievable aspect ratio for the microfeatures?
3. What should the design of the venting channel be in order to remove the air pockets
from final product?
Until recently, there has been no consolidated approach towards the design for
fabric-ability of parts with microfeatures. In the designing phase there are considerations
such as the geometry of the part, the positioning of the mold cavity, and mold inserts
features such as the tolerance and surface finish of the designed part. There are many
studies that have suggested techniques to evaluate the complexity of injected parts with
respect to replication and ejection [40-41]. However, the overall small dimensions of
20
microinjection molding produced parts do not always allow the use of the above
mentioned techniques. In the following discussion, the design parameters affecting the
overall quality of a microinjection molding molded part are evaluated.
An important consideration in mold cavity design is related to the large surfaceto- volume ratio of many micro-parts, which leads to the fast cooling of the polymer melt.
Despite the fact that polymers usually have a low thermal conductivity, the injected
polymer rapidly cools on the tool wall and the mold cavities could not be filled
completely as a result. As a consequence of the thin walls and large surfaces of microparts compared with their volume, the temperature of the material in the mold adapts to
the cavity temperature very quickly. The evacuation of the air from the mold cavity is
another important issue for the evaluation of the quality of produced micro-parts, in that
it is necessary to prevent compression-induced defects (air pockets) from forming in the
produced parts. If the cavities contain microfeatures that are so small that they cannot be
vented in the standard way through the parting plane, it is necessary to develop a system
dedicated to the evacuation of the air from the cavity. Some applications in literature note
the creation of a vacuum in the mold [42-43]. In microinjection molding it is difficult to
design the cooling system due to the dimension of the mold. The cavity insert is located
within a small area, which means that the temperature variation across the molded part
should be expected (depending on the mold geometry) [44]. In any case, according to
literature, if it is desired to keep the mold temperature above the glass temperature (Tg) of
the polymer, then it is not required to control the mold cooling and the amorphous
material behaves like a glassy solid (brittle and hard). For temperatures greater than Tg,
21
polymers have the flexibility and ability to undergo plastic deformation without
encountering fracture, which is a property of polymers that is difficult to control using
polymer technology. The ejection of the part is another important aspect to consider in
mold insert design for micro-parts. A factor that affects ejection is the orientation of the
polymeric chain for the injected part after cooling, because this affects the observed
shrinkage direction [45]. A useful geometrical method that obtains a successful ejection
consists of the use of draft angles in the mold. A positive draft angle (an angle greater
than 0.25º) has been successfully used for the ejection of microinjection molding parts
[46]. The use of the mold inserts is another typical application of the conventional
injection molding process, and becomes very crucial in microinjection molding when, for
example, micro-cavities for micro-sampling cells applications are realized and then fitted
in the main mold body. The main objective of using a micro-injection mold with
changeable inserts/removable cavities comes from the ability to test different micro-part
geometries without discarding the basic structure of the mold designed for microinjection
molding [47]. The use of micro-injection molds with removable inserts reduces the
overall cost of setting up the process. There are a number of iterations in the finalized
production of the mold design during which the parts are ejected and more changes in
mold design are made [48]. The concept of replaceable or removable mold inserts can be
applied in the design of the mold for different applications and the efficiency of the
micro-part is greatly improved. For any new design, prototyping is more easily achieved
when mold inserts are used in cases where there are no clear design steps available. This
is because the need for recreation of the entire mold is reduced, which in turn reduces
22
time and costs. In addition, the advantages of using inserts are related to the material with
which they can be manufactured. For instance, an aluminum insert is different from a
mold made from steel, and the use of it can depend on the available manufacturing
technology and costs of doing so. Another concern in injection molding technology is the
measurement of injection pressure in the mold cavity, which is the topic for many
researchers. In the literature, many proposed methods to measure the injection pressure in
the mold cavity, through the use of piezoelectric force transducers that are located behind
the injection pin or through the use of a miniaturized quartz sensor that directly measures
the injection pressure in the mold cavity, applied at the end of the spruce [49].
2.4.1. Micro-part design features
One of the main objectives related to the design of a microinjection molding part
is the dimension reduction of the produced part due to the induced shrinkage/warping that
affects the stability of the shape. The warpage comes from the non-uniformity of the
shrinkage induced by the mold thermal variation complexity [44]. The prediction of the
microinjection molding part warping is important due to their relatively large surface area
in comparison to their thickness.
There are many proposed techniques mentioned in literature for decreasing the
effect of shrinkage, such as:

Increasing cooling time affects the thermal equilibrium in the mold cavity, which
results in a uniform product [44], but increases the cycle time of the process.

Higher value of packing pressure increases the stresses in the molded part [48].
23
Other concerns that must be considered are geometrical parameters such as the
aspect ratio, which was mentioned earlier, and the microfeature position from the gate.
The filling-time-to-pressure parameter [49] was introduced to explain the dependence of
the area filled to the distance from the gate where the polymer melt enters the mold
cavity. This parameter was measured and, compared with the injection rate for different
thicknesses, indicated that a pressure drop was required to fill the microfeature cavity.
Additionally, this resulted in the formation of shear stresses.
2.4.2. The microinjection process optimization
At first, the microinjection molding technology was intended as a modification to
conventional injection molding technology [51]. In the conventional injection molding
process known more specifically as the reciprocating screw process, polymer materials
are melted and injected into mold cavities through a screw-barrel system. However, there
are limitations related to the reduction of screw dimension for constructive problems.
Moreover, cycle times are usually longer than necessary when using a conventional
machine for micro injection molding. In this research, a DMM with microfeatures was
designed through the aid of a computer aided engineering (CAE) analysis program,
Moldex3D-R10, to simulate the flow phenomena of a polymeric melt inside the mold
cavity during the microinjection molding process. In any process, it is most desirable to
optimize productivity with high quality and less cost. Achieving this objective for any
process may be investigated by the steps shown in Figure 4.
24
Figure 4: Study sequence of a manufacturing process.
Figure 5: Microinjection molding cycle time.
25
Understanding the cycle time in the injection molding process is very important.
The cycle time of the µ process as shown in Figure 5 consists of a mold closing with a
clamping force for a few seconds, a step which depends on the specifications of the
machine. In the filling stage, the material begins in the form of granules stored in a
hopper, which are then transferred to a plasticizing unit. This unit contains a screw
surrounded by heaters, so that polymer granules liquefy. The plunger of the injection unit
then retracts, takes in the molten material, and performs the injection with a set speed and
distance over a specific period of time. It then switches over to packing (or holding) the
material at a constant pressure for a certain time to compensate for material shrinkage.
For a set cooling time, the material solidifies in the mold insert, and at the end, the mold
opens so the part can be ejected and the cycle is repeated.
Studying and optimizing µ process parameters, especially for high aspect ratio
microfeatures, are essential for producing parts with an acceptable quality level. There
are many variables that affect the part quality, such as the mold insert design for the
specific part, the molding machine performance, the polymer material to be used, and the
processing conditions. The µprocess has a set of advantages that makes it applicable
with a potential for future developments, such as:
1. Wide spread use of various thermoplastics and the potential for full automation
with short cycle times.
2. Cost-effectiveness for mass-production processes, especially for disposable
products.
3. Accurate shape replication and good dimension control.
26
4. Low maintenance cost of capital equipment.
2.4.3. Microinjection molding machines technologies advancement
The two main process units in microinjection machines are the reciprocation and
the V-Line two-stage injection processes as shown in Figure 6.
a. Microinjection reciprocating screw
plasticizing unit.
[http://www.dc.engr.scu.edu]
b. Microinjection V-Line two stage
(plasticizing and injection).
[http://www.plustech-inc.com]
Figure 6: Two main microinjection molding units.
During injection with the V-Line two-stage machine, the plasticizing screw’s
rotation time and movement is less than that of the reciprocating machine. This is
because the screw has only one function, which is plasticizing, where each polymer pellet
goes through the same thermal exposure and the material is distributed in a uniform
polymerization melt with stable density due to the screw’s lack of retraction. After
plasticizing, the material is fed into the injection unit, which then gets injected it into the
mold. In contrast, the reciprocating screw continuously rotates and has two functions
(plasticization and injection) that lead to instability in thermal distribution of the polymer
27
melt. Additionally, the polymer’s metered feeding is not of a constant density because of
the retraction in the screw.
a. Check ring in reciprocating
b. The screw close the back flow in
screw system
V-Line two stages system
Figure 7: The back flow systems in microinjection molding
[http://www.plustech-inc.com].
The back flow prevention check ring in the reciprocating screw system is shown
in Figure 7a. In contrast, back flow is minimized at the V-Line two-stage process prior to
injection with the screw pushing forward to trap the molten material outside of the
plasticizing unit as seen in Figure 7b. On the other hand, the V-Line's metered volume is
equal to the filling volume and there is reliable control of the injection speed and
maximum pressure is achieved. This makes the V-line two-stage process preferable,
particularly for precise injections.
28
Figure 8: Microinjection molding machine (LD30EH2).
The desired goal of this research is to produce DMM with tight tolerances, low
weights and micro features. Because of these requirements, the Sodick Plustech MicroInjection Molding machine model LD30EH2, as shown in Figure 8, was used. This
model has a hybrid direct pressure clamping system that can leverage a maximum
clamping force of 30 Tons and a maximum mold thickness of 150 mm. An alternating
current servo motor control ejector system is used to eject the part. The plasticization and
injection units have high speed and an overall high pressure injection capability. The
plasticizing screw diameter is 18 mm, with a 16 mm plunger diameter and a 70 mm
plunger stroke. The maximum injection pressure for the machine is 267 MPa. The
injection unit has a 250 mm/sec maximum injection speed with a 370 rpm maximum
screw revolution and a maximum of 230 mm injection unit stroke. The Sodick Plustech
29
microinjection molding machine utilizes a two-stage V-Line plunger injection system for
plasticizing and injection, as shown in Figure 8. Further details are shown below in
Figure 9.
Figure 9: Two-stage V-Line plunger injection for plasticizing and injection
[http://www.plustech-inc.com].
The plasticizing unit starts with a hopper that holds the raw plastic granules and
feeds them into the barrel in a uniform manner. The plastic is melted in the barrel using
the heaters surrounding the V-LINE plasticizing screw. The screw functions to both
transfer the material and melt the pellets to homogeneous properties in the injection
chamber. The screw remains stationary during the material transfer which minimizes the
axial wear and ensures that each pellet is exposed to the same heat profile. As the screw
melts and mixes the pellets and pushes the melt into the injection chamber, the melt
pushes back the injection plunger to a set position. This set position is set by the user
through a process monitor screen attached to the machine controller. A linear encoder
detects the plunger position in a certain increment. After the injection chamber is filled, a
30
hydraulic cylinder pushes the screw forward approximately 1.5mm abutting it firmly
against the check ring and sealing the injection chamber. This sealing eliminates any
backflow of material during the injection step. After the injection chamber is filled and
sealed, the plunger drives forward at the speed and pressure that were input to the
controller as process parameters. There is a pressure sensor which monitors the injection
pressure as the plunger injects the shot precisely into the mold cavity to create the part.
31
Chapter 3: Design and Process Analysis
3.1. DMM part design
The DMM part was originally designed [8] as shown in Figure 10A with a thin
deformable membrane at the center with a target thickness of 50 µm; the circular solid
frame surrounding the thin membrane had a 2 mm thickness. It was found that the
minimum thickness that allowed for complete filling of the center disk was 125 µm.
Figure 10: Solid models of original and current designs.
The overall diameter of the part is 40 mm because the mold assembly used can
only accommodate that circular inserts diameter. Figures 10B and 11 show the details of
the new design. Notice that the part consists of three sections with different thicknesses,
as shown in detail C of Figure 11. The three sections are the solid frame, microchannel
and mirror. The part has a circular solid frame that is 2 mm thick (region #1). The part
32
slopes down to a circular microchannel (region # 2) that has a thickness of 100 µm and a
surface length of 0.93 mm. Sixteen molded slots are distributed evenly along the
perimeter of the circle to add more flexibility to the thin membrane as well as to allow for
venting.
Figure 11: Detail drawing of DMM with detail C showing the three sections.
Each slot is an isosceles trapezoidal dimensioned with a height of 0.5 mm, an
inner width of 0.4 mm, and an outer width of 0.6 mm (see detail A of Figure 11). To
improve the flexibility, the dimension of the slot increases to an inner width of 1.91 mm
and an outer width of 2.11 mm (keeping the same height). The center section (region #
3), consists of a circular disk with a thickness of 500 µm and a diameter of 21.1 mm.
33
3.2. DMM microchannel design
The main characteristics considered when designing DMM parts are the flexibility
of the mirror and its flatness under loading. In our design, the main factor affecting the
flexibility is the geometry of the microchannel, which includes the thickness and the
length of the channel. For increased flexibility, it is desired to have as thin as feasible
microchannel with the largest width. The flatness of the mirror is mainly a function of the
mirror's thickness. These factors are discussed in detail below.
3.2.1. The effect of microchannel thickness in filling the cavity
In studying the microchannel geometry, the ratio of the length per thickness is
crucial towards filling the overall cavity, for this purpose many simulations were carried
out using a rectangular part with the dimension 100 mm x 40 mm (Length x Width) with
different thicknesses. As a note, these simulations were merely exploratory, as they were
carried out before any final design changes and recommendations were carried out. The
results of some simulations shown in Table 1 indicate that with a thickness of less than
100 µm, there is no filling at all and the L/t ratio is inversely proportional to filling length
of the overall cavity.
Thickness of rectangular
cavity (µm)
70
100
200
300
500
The L/t
ratio
1428
1000
500
333
200
Filled length
(mm)
0
5.11
28.78
53.63
100
Table 1: Simulations results for a rectangular cavity with various thicknesses.
34
At a 100 µm thickness (shown in Figure 12) only 5.11 mm of the cavity was
filled, even though the maximum injection pressure of the machine was reached. For
larger thicknesses (particularly those greater than or equal to 500 µm) the part was
completely filled, as shown in Figure 13. As a result, the minimum thickness of the
microchannel to fill at least part of the cavity was determined to be 100 µm. when L/t
ratio decreases the microchannel surface length increases, which concludes the
importance of this ratio, the microchannel length will be discussed in the next section.
Figure 12: The simulation results of a rectangular part with thickness of 100 µm (5.11
mm of cavity length was filled).
35
Figure 13: The simulation result of a rectangular part with at thickness of 500 µm (the
entire cavity filled).
3.2.2.
Effect of microchannel length on cavity filling and mirror deformation.
To test the feasibility of the new DMM design, the effect of microchannel length
on the fill patterns and mirror deflection was analyzed using Moldex3D [53] for flow
analysis and ANSYS Workbench [57] for stress analysis. . The DMM was modeled with
various microchannel lengths. However, we kept the thickness at 100 µm. For the stress
analysis, we fixed the DMM, and applied a pressure of 2887 Pa on the mirror. The
maximum stress and strain are located on the region of the slots in the microchannel
region.
36
Figure 14: Stress strain curve for several COC-Topas 5013 [56].
Simulated microchannel
length (mm)
Cavity filling
status
Simulated deflection
(µm)
Maximum stress
(MPa)
0.5
1.0
Filled
Filled
56
92
6.93
8.93
1.5
Not filled
130
11.23
2.0
Not filled
158
15.89
3.0
Not filled
224
17.61
Table 2: Simulation results of various microchannel widths length.
The maximum stress values are shown in Table 2 and are found to be less than the
yield stress of the COC-Topas 5013 S polymer, which is 46 MPa (as shown in Figure 14).
From the results on table 2, we can conclude the following:
a. For complete filling at the maximum fill pressure allowed in the machine, the
microchannel surface length should not exceed 1 mm, in other words the L/t
ratio of the DMM microchannel should not exceed 10.
37
b. The flexibility of the mirror is directly proportional to the microchannel surface
length.
c. Comparing the maximum stress predicted with the material yield stress on Table
2 shows that the DMM under a pressure of 2887 Pa on the mirror is still in the
elastic region.
Figure 15: The DMM part with filling length of 2 mm (the cavity isn't filled).
38
Figure 16: The DMM simulated deformation with filling length of 2 mm.
As an example, of the analysis done, the simulation results of the DMM with
microchannel surface length of 2 mm are shown in Figures 15 and 16. Figure 15 shows
the simulated prediction that the part will not completely fill. Figure 16 shows the
predicted deformation under a pressure of 2887 Pa on the mirror with the same
microchannel surface length. The maximum deformation is seen at the center of the
DMM part with a value of 158 µm.
3.2.3.
Effect of microchannel thickness on flow
Various cases of the new DMM design with different microchannel thicknesses
were simulated and compared to experiments. The simulation results are shown below in
Figures 17 - 20 as cases #1 to #4, respectively. The Moldex 3D simulation results are
39
indicated by the color spectrum with the red region representing the start of melt flow
into the cavity, and the dark blue representing the end of filling (EOF).
Figure 17: Case # 1: comparison of DMM simulation results vs. real part with a
microchannel thickness of 500 µm.
In Figure 17 (case#1) the microchannel thickness 500 µm, allows the melt to flow
directly through the microchannel. The EOF is opposite to the gate location. The picture
40
of the real part shows the EOF location with the burn mark from the trapped air, caused
by the lack of venting channels in the mold.
Figure 18: Case # 2: comparison of DMM simulation results vs. real part with a
microchannel thickness of 350 µm.
For cases #2 and #3 shown in Figures 18 and 19, the microchannel thickness is
decreased to 350 and 250 mm, respectively. As a result, the EOF region shifts towards
41
the middle of the part. The burn mark from the trapped air in the pictures for the real part
confirms the shift.
Figure 19: Case # 3: comparison of DMM simulation results vs. real part with a
microchannel thickness of 250 µm.
In the selected DMM part design, which is shown in Figure 20 (case #4) below,
the microchannel thickness is 100 µm. The melt flows through the path with less
42
resistance at region #1 (which has a thickness of 2 mm). The flow front goes around the
part and enters regions #2 and #3, as shown in Figure 20, from the end opposite to the
gate position. The EOF region shifts closer to the gate location, allowing the air to escape
the mirror region into the slots, thus no burn marks are present on the molded part.
Figure 20: Case # 4: comparison of DMM simulation results vs. the real part with a
microchannel thickness of 100 µm (the new design of DMM).
43
Based on the progression of the EOF regions shown in Figures 17-19, we can
conclude that the air escaped the mirror region into the slots. Therefore, the revised mold
design with the trapezoidal slots provides a two-fold advantage. Firstly, this design gives
more flexibility to the mirror. Secondly, the slots work as venting channels for the air to
escape through. Using Moldex3D it is possible to identify a microchannel thickness to
improve thin membrane quality as shown in these previous Figures 17-20.
3.3. Effect of DMM mirror thickness on the flatness
The flatness of the DMM mirror is one of the required characteristics for the
DMM part. In order to investigate the flatness of the mirror, the geometry of the
microchannel (indicated by region # 2 in Figure 20) is kept fixed with a thickness of 100
µm and a length of 0.93 mm, while applying a pressure of 2887 Pa on the mirror at the
center of the DMM part with various thicknesses of 300, 500 and 700 µm.
44
Figure 21: DMM deflection with various mirror thicknesses.
From the simulation results shown above (Figure 21), the DMM deformation is
inversely proportional to the mirror thickness. On the other hand, the flatness is
proportional to the thickness. A compromise had to be made between flexibility and
flatness, thus a thickness of 500 µm was selected for the new DMM design.
3.4. Mold insert fabrication
To mold the deformable membrane mirror, the mold insert shown in the Figures
22-23, was made from aluminum 6061substrate, which has a brinell hardness of 95 and
compression strength of 276 MPa.
45
Figure 22: Microinjection molding insert.
Figure 23: Microinjection molding insert detail drawing.
The designed mold insert was machined with a CNC ultraprecision machine
center (model 350 FG, manufactured by Moore Nanotechnology Systems incorporation).
The machined parts have micrometer dimension accuracy and nanometer surface
roughness. They can be used as optical molds without any extra polishing. After
46
fabricating the DMM surface on the mold insert using diamond turning, the
microchannels were machined using the broaching process. Finally, the machined mold
insert was installed in a mold base on the microinjection molding machine a flat insert
was used for the flat side of the DMM part.
3.5. Material selection
The polymer material selected for this part was Cyclic Olefin Copolymers (COC),
Topas-5013S. This grade of material is characterized by high flowability and excellent
optical properties.
Figure 24: Previous MFI results for Topas-COC-5013S vs. other OSU materials
[Eusebio D. Cabrera, thesis, 2010].
.
The high transparency of Topas-COC in the visible and near ultraviolet regions,
coupled with a refraction index of 1.53, makes this polymer attractive for optical
47
applications. Therefore, this polymer is suitable for the production of high-quality optical
components. These types of materials are recommended for applications such as optical
parts, lenses, and optical storage media as well as medical and diagnostic applications.
Topas-COC-5013S has a Young’s modulus of 3.2 GPa and a density of 1020 kg/m³ [56].
Figure 25: MFI results for Topas-COC-5013S vs. other Topas product
[http://www.topas.com/products-topas_coc ].
Melt flow index (MFI) is an ASTM test commonly used in industry to measure
how easily a molten thermoplastic polymer flows. MFI is given as the amount of molten
polymer mass, in grams, that flows through a capillary of a specified length and diameter
in ten minutes. Once the molten polymer reaches the prescribed temperature, it flows due
to pressure applied via prescribed weights. Melt flow rate is an indirect measure of
viscosity and molecular weight because high melt flow rate measurements correspond to
low viscosity and, in general, this means lower molecular weight. Previously, the melt
48
flow index for TOPAS-COC-5013S was studied by [8] and is shown in Figure 24, the
melt flow measurements were plotted against a normalized temperature, to make the
comparison meaningful. The normalized temperature is given by the following formula:
Equation 10
To and Tmax are the minimum and maximum melt temperature given from the
manufacturer. Different product data of the TOPAS company [35] are shown in Figure
25. Both Figures 24-25 clearly demonstrate that the selected material has the highest MFI
which conclude that TOPAS 5013S is the best material to fabricate the DMM part.
49
Chapter 4: DMM Test
There are several tests to ensure the performance of the DMM part such as:
measuring the dimensions, measuring the mirror surface profile, measuring deflections
due to load, and testing the optical properties using an optical interferometer.
4.1. Geometry measurement of the part
Figure 26 shows the DMM with three circular regions of different thicknesses
denoted by regions #1-3, and are the solid frame, microchannel, and mirror, respectively.
Figure 26: Surface variation and thicknesses positions for measurements.
The critical dimension of the DMM part is the microchannel ring thickness
(denoted by region #2 in Figure 20). However, it is difficult to measure this region
50
consistently and accurately. Because of the mold insert clamping force, the thickness of
the fabricated DMM part will vary in a consistent manner. Therefore, variations in the
measurements in region #1 and 3 will reflect variations in region #2. The measurements
of region #1 and region #3 are much easier to measure accurately and consistently using
the Mitutoyo electronic digital micrometer. Region #1, which is the DMM solid frame, is
designed for a 2 mm thickness, which is measured at four positions in Figure 26 that are
denoted by letters F to I. The arrow at the right shows the gate position. Region #3, which
is the DMM mirror, is designed with a 0.5 mm thickness, and is measured at five
positions in Figure 26 that are denoted by letters A to E.
Sample
#
1
2
3
4
5
µ
σ
Positions measures on the DMM part (mm)
Position Position
Position
Position
F
G
H
I
2.001
2.011
2.006
2.007
2.012
2.0074
0.0044
2.003
2.006
2.011
2.009
2.006
2.0052
0.0041
2.006
2.001
2.009
2.011
2.004
2.0062
0.00396
2.004
2.009
2.001
2.01
2.004
2.0056
0.00378
Average
Dimension
(µ)
2.0035
2.00675
2.00675
2.007
2.0065
2.0061
0.00146
Standard
deviation
(σ)
0.00208167
0.00434933
0.00434933
0.00496655
0.00378594
0.0039066
Table 3: Positions measured thicknesses on the DMM solid frame.
The average thickness and standard deviation have been calculated and compared
to the specified dimensions for the designed DMM part, as shown in Table 3 - 4. Tables 3
and 4 both show the five repeated measurements at each position at different locations of
the DMM fixture and mirror. Comparisons were made between the DMM part measured
dimensions and the designed dimensions. The results of the comparisons show a
51
difference of 6.1 µm in region # 1 and a difference of 22.6 µm in region # 3. The
measurement results show no large standard deviation between the readings in each
region, where the largest standard deviation calculated was equal to 0.00619 (a very
small deviation). This concludes that the DMM surface is almost completely flat.
Sample
#
1
2
3
4
5
µ
σ
Positions measures on the DMM part (mm)
Position Position Position Position
Position
A
B
C
D
E
0.517
0.518
0.517
0.522
0.514
0.522
0.518
0.531
0.52
0.531
0.525
0.519
0.532
0.523
0.529
0.518
0.518
0.531
0.518
0.523
0.52
0.523
0.531
0.522
0.524
0.5204
0.5192
0.5284
0.521
0.5242
0.0032
0.0022
0.00639
0.002
0.00661
Average
Dim.
(µ)
Standard
dev.
(σ)
0.5176
0.5244
0.5256
0.5216
0.5240
0.5226
0.00317
0.00289
0.00619
0.00508
0.00568
0.00418
0.00480
Table 4: Positions measured thicknesses on the DMM mirror.
4.2. Surface variation measurement of the DMM part
The surface variations of the DMM were measured by using a Mitutoyo
SURFTEST SV-3100 contact profilometer, as shown in Figure 27. Figure 28 shows the
diamond stylus moves across the DMM surface that results in a surface profile reading.
The part surface profile will not be symmetrical for many reasons, and the process
parameter variation will affect the DMM mirror surface quality.
52
`
Figure 27: The Mitutoyo SURFTEST SV-3100 contact profilometer.
Figure 28: Surface variation and thicknesses positions for measurements.
The surface variation will be taken as the distance between the farthest two points
on the surface profile. Surface variations will be measured in region #3 as shown in
Figure 28, as well as from point B to point C (in Figure 26) on the axis of the injection
53
gate (that is, from one end to the other end). The surface profile measurements show
some variations with different process parameters. For this reason, design of experiments
was applied to minimize the variation and will be demonstrated in detail in chapter 5.
4.3. Measuring DMM deflection using INSTRON machine
The DMM deflection was measured using the INSTRON set up, shown in Figure
29. The experiment set up consists of a DMM part clamped in a fixture using region #1 of
the DMM part. A contact point tool (see Figure 29) was created using a 5 mm diameter
cylindrical bar having a spherical end that will contact the DMM part.
Figure 29: Schematic of deflection setup Measurement of DMM part.
This DMM Contact Point is attached to the upper fixture of the INSTRON 5569
machine. The upper fixture of the INSTRON machine drives the contact Point
downward, applying a load to the center of the DMM mirror, which is indicated by
region #3. The INSTRON machine measures the deflection of the center of region #3 in
54
increments of 0.5 micrometers with the upper load limit being 100 grams. At each 0.5
micrometer increment, the INSTRON captures the force applied that caused the
deflection of the mirror. The resulting data is provided as table of force exerted vs.
vertical displacement.
Figure 30: DMM model under pressure of 4.75 mm in the center.
The DMM model shown in Figure 30 was developed to simulate the deflection of
the mirror under increased loads. In the model, the DMM solid frame is fixed and the
load is applied uniformly over a 4.75 mm circle in the middle of the DMM mirror.
55
Figure 31: DMM model under pressure of 4.5 mm in the center.
The model was simulated using ANSYS Workbench 13 [57]- 3D model with solid
element plane 82 and with 8 nodes. The results were plotted in Figure 31 and have been
compared with the INSTRON deflection measurements. The result of the comparison
clearly shows a consistency between the simulated numerical results and the observed
results in the INSTRON experiments. At the load of 100 grams, the applied force is
approximately 1 N, the INSTRON experimental deflection result is 134 m and the
simulated result of 136.24 m. The ANSYS Workbench simulation predicts the
56
INSTRON experimental deflection consistently and shows that the new design of the
DMM part is more flexible.
4.4. Michelson Interferometer
The wavefront change caused by the membrane mirror was measured using the
system shown in Figure 32. Such a system is a Michelson interferometer, which is
composed by a beam splitter, one flat mirror and the deformable membrane mirror. The
laser that was used is a He-Ne laser whose wavelength is 632 nm.
Figure 32: DMM wavefront change measurement setup.
The wavefront change measurement system works by first expanding the laser
beam to approximately 10 mm with a microscope objective lens, a 50 microns pinhole,
and another lens (L1). Figure 33 shows schematically the pinhole that will be used in the
image processing.
57
Figure 33: Pinhole schematics and the effect on processed image
[http://www.newport.com/Spatial-Filters/].
The front side of the DMM was sputter-coated with ~100 nm of gold (Au) in a
clean room at Nanotech West at The Ohio State University. Both two DMM devices
attached with tape were coated with gold shown in Figure 34. The coated surface can be
used as a reflection mirror surface as well as an electrode. Electrostatic voltage is applied
between the top electrode (top surface of the DMM) through the coated tape and bottom
electrode (bottom surface of the DMM fixture), as shown in Figure 34.
Figure 34: Schematic of the voltage applied to the DMM.
58
0.20 second
0.40 second
0.60 second
0.80 sec
Figure 35: DMM device interference patterns under 300 volts and 6 Hz sine wave.
The change in phase angle is obtained by comparing the wavefront of the light
reflected from the DMM surface with the wavefront of the light reflected from the flat
mirror. The reflected light from both surfaces is combined into a single wavefront and
captured by a camera. The resulting image is shown in Figure 35 in series time steps of
59
DMM deformation. The black and white fringes represent constructive and destructive
interference patterns, respectively. The deformation of the membrane mirror can be
calculated using the following equation:
Equation 11
Where d is the deformation,
is the wavefront phase change in radians, and
wavelength of the laser.
60
is the
Chapter 5: Processability study using Design of Experiments
Design of experiments (DOE) [3-6] begins with determining the objectives of an
experiment and selecting the process factors for the study. A DOE is the layout of a
detailed experimental plan prior to performing the experiment. The DOE also maximizes
the amount of data that can be obtained for a given amount of experimental effort. It is
common to begin with a process model, with several discrete or continuous input factors
that can be controlled and varied by the experimenter and one or more measured output
responses. The output response is assumed to be continuous. Experimental data are used
to derive an empirical (approximation) model linking the outputs and inputs. These
empirical approximations generally contain first and second-order terms.
5.1
Response Surface Method in Experimental Design
In DOE, the experiment is designed to allow us to estimate interactions and even
quadratic effects, and therefore gives an idea of the (local) shape of the response surface
we are investigating. For this reason, they are termed response surface method (RSM)
designs. The desirable features for response surface designs are [3-5]:A. Satisfactory distribution of information across the experimental region.
B. Fitted values are as close as possible to observed values (minimize
residuals or error of prediction).
61
C. Good lack of fit detection.
D. Internal estimate of error.
E. Constant variance check.
F. Transformations can be estimated.
G. Suitability for blocking.
H. Sequential construction of higher order designs from simpler designs.
I. Minimum number of treatment combinations.
J. Good graphical analysis through simple data patterns.
K. Good behavior when errors in-settings of input variables occur.
5.2
Face Centered Composite Design Technique (FCC)
For FCC shown in Figure 36, the sampling points are located at three different
levels for each random input variable. In order to make the specification of these levels
independent from the distribution type of the individual random input variables. The
three different levels of a Face-Centered Cubic (FCC) design are low (-1), middle (0) and
high (+1) coded settings for all factors that are the original form of the central composite
design.
62
Figure 36: Face centered composite design using three selected factors
[http://www.iue.tuwien.ac.at].
FCC designs provide high quality predictions over the entire design space, but
require factor settings in the range of the factors in the factorial part. The main FCC
design portions are:
A.
Center points
At the center point, the values of all random input variables have a cumulative
distribution function that equals P2 at level (0).
B.
Axial points
There are two points for each random variable located at the axis position, i.e., if
there are (n) random input variables then there are (2 * n) axis points. For the axis
points all random input variables except one have a value corresponding to the
center location as P2 at level (0) and one random variable has a value corresponding
63
to P1 for the low level point (-1) (or corresponding to P3 for the high level point
(+1)).
C.
Factorial points
In a central composite design there are 2n factorial points. For the factorial points,
all random input variables have values corresponding to permutations of P1 for the
lower factorial level and P3 for the higher factorial level.
Experiment
Number
Factor
Factor
Factor
X1
X2
X3
1
P1
P1
P1
2
P3
P1
P1
3
P1
P3
P1
4
P3
P3
P1
5
P1
P1
P3
6
P3
P1
P3
7
P1
P3
P3
8
P3
P3
P3
9
P1
P2
P2
10
P3
P2
P2
11
P2
P1
P2
12
P2
P3
P2
13
P2
P2
P1
14
P2
P2
P3
15
P2
P2
P2
16
P2
P2
P2
17
P2
P2
P2
18
P2
P2
P2
19
P2
P2
P2
20
P2
P2
P2
Fcc
Portion
Factorial Points
(8)
Axial Points
(6)
Center Points
(6)
Replicates.
Table 5: Probability Matrix of FCC Design with three factors.
64
5.3
Statistical Modeling
The most common empirical models that are fitted to the experimental data take
either a linear form or a quadratic form. The experimental optimization of a single
response is usually conducted in two phases or steps. The first phase consists of a
sequence of line searches in the direction of maximum improvement. Each search in the
sequence is continued until there is evidence that the direction chosen does not result in
further improvements. The sequence of line searches is performed as long as there is no
evidence of lack of fit. A simple first-order model is of the form:
Y = b0+b1X1+b2X2+….+bkXk+b12X1X2+b13X1X3+….
+bIkX1Xk+ b23X2X3 +….+b2kX2Xk+….+bk-1,kXk-1Xk
Equation 12
The second phase is performed when there is lack of linear fit in Phase I, and
instead, a second-order or quadratic polynomial regression model of the general form is
fit:
Y = b0+b1X1+b2X2+....+bkXk+b11(X1)2 +b22(X2)2+….
+bkk(Xk)2 + b12X1X2+b13X1X3+….+b1kX1Xk +
Equation 13
b23X2X3+….+b2kX2Xk + ….+bk-1,kXk-1Xk
5.4
Statistical Modeling of µIM process parameters to mold a DMM
The DMM part is analyzed using FCC design with full replication. . The steps
followed are:
a. Choice of the process parameters (factors)
b. Working ranges of the selected process parameters
65
c. Selection of the levels of process parameter.
d. Construction of the experimental design matrix
e. Molding with selected parameters.
f. Development of statistical models for the performance measures or
responses.
Each step will be elaborated on further.
5.4.1
Performance measure selected
PP-packing pressure
PT- packing time
IS- injection speed
22 µm
Figure 37: The response measurement (i.e experiment run # 2).
The DMM surface variation was chosen as a performance measure (response) due
to the importance of the flatness of the mirror surface. The flatness was measured using a
Mitutoyo SURFTEST SV-3100 contact profilometer. The surface profile readings were
66
done using a diamond stylus. The surface variation was measured between the farthest
two points on the surface profile as shown for example in Figure 37, for the second
experimental condition. Surface variation was measured along the DMM surface axis of
the injection gate from one end to the other for the twenty experiments of FCC design.
5.4.2
Microinjection molding process parameters
Previous to selecting the levels of the controllable parameters, a screening
experiment was conducted using full factorial design. As a result of this, the melting
temperature was found to be a major factor affecting the other process parameters levels.
The recommended melting temperature for COC-TOPAS 5013 was from 250 to 300 C˚
as shown in the table 6. For successful molding, the values of the packing pressures had
different ranges at these temperatures. The middle level of the melting temperature was
chosen to study the other process parameters.
Melting temperature (C˚)
Packing pressure (MPa)
250
175 - 200
275
100 - 130
300
65 - 85
Table 6: Effect of melting temperature on the packing pressure ranges.
The µIM process parameters that were chosen to vary in this study are:
A. The packing pressure (MPa).
B. The packing time (second).
C. The injection speed (mm/second).
67
The process parameters that were kept constant are:
a) Melting temperature of 275 C˚.
b) Cooling time at 30 sec.
c) Shot size at 26 mm.
d) Clamping force of 28.5 KN.
5.4.3
Levels of the selected process parameters (factors)
Table 7 summarizes the extreme levels of the factors studied. We found that if the
injection speed increases over 200 mm/s, the part will have burn marks on the surface, if
the speed is less than 150 mm/s, the cavity does not completely fill. A packing pressure
of more than 130 MPa causes flash. On the other hand, if the packing pressure is less than
100 MPa, the part does not completely fill.
Selected
Factor
X1- Packing pressure
MPa
X2- Packing time
Second
X3- Injection speed
mm/second
Units
Low Level
(-1)
100
High Level
(+1)
130
2
10
150
200
Table 7: Extreme values of the controllable variables
5.4.4
The DOE matrix.
With an FCC design, the axial points are located on the face of the cube for α = 1.
Since there are three factors, it is recommended to replicate 6 times in the center where
all the factors are of level (0). The number of experimental runs is calculated according to
the following equation:
68
Equation 14
Where N is the number of experimental runs, k is the number of selected factors
and
is the number of experimental replications in the center.
Experimental
Run
Number
1
Experimental
Random
Rank
18
Factor
(X1) Level
(MPa)
-1 (100)
Factor (X2)
Level
(sec.)
-1 (2)
Factor (X3)
Level
(mm /sec.)
-1 (150)
Response
(Y)
(µm)
38.1
2
19
+1 (130)
-1 (2)
-1 (150)
22.1
3
16
-1 (100)
+1 (10)
-1 (150)
27
4
13
+1 (130)
+1 (10)
-1 (150)
20
5
10
-1 (100)
-1 (2)
+1 (200)
45
6
14
+1 (130)
-1 (2)
+1 (200)
28
7
11
-1 (100)
+1 (10)
+1 (200)
23
8
3
+1 (130)
+1 (10)
+1 (200)
20
9
15
-1 (100)
0 (6)
0 (175)
30.5
10
20
+1 (130)
0 (6)
0 (175)
19.5
11
4
0 (115)
-1 (2)
0 (175)
31.7
12
6
0 (115)
+1 (10)
0 (175)
20.8
13
17
0 (115)
0 (6)
-1 (150)
21
14
7
0 (115)
0 (6)
+1 (200)
22
15
5
0 (115)
0 (6)
0 (175)
21
16
8
0 (115)
0 (6)
0 (175)
18.7
17
9
0 (115)
0 (6)
0 (175)
18.7
18
1
0 (115)
0 (6)
0 (175)
17.9
19
2
0 (115)
0 (6)
0 (175)
19.2
20
12
0 (115)
0 (6)
0 (175)
18.9
Table 8: List of experimental runs
69
Coefficient
Predicted µim
Statistical
Regressed
Parameters
number
Variables code
Model portions
Parameters
Value
1
Constant
Constant
bo
20
2
(X1)
bl
- 5.40
3
(X2 )
b2
- 5.41
4
(X3 )
b3
0.98
5
(X1)2
b11
3.5
6
(X2)2
b22
4.7
7
(X3)2
b33
0.00091
8
(XI * X2)
b12
2.9
9
(XI * X3)
b13
0.38
10
(X2 * X3)
b23
– 2.10
Linear
Quadratic
Interaction
Table 9: Regressed coefficients of statistical model.
Using the data in Table 8 as input in statistical software's MINITAB 16, the
statistical model was developed to obtain the estimation of the model factors represented
by X’s in terms of linearity, quadratic, and interactions to the response (Y). These
relationships are tabulated in Table 9. The fitted model for DMM surface variation can be
written as:
Y = 20 - 5.4 X1 - 5.1X2 + 0.98 X3 + 3.5 (X1)2 +4.7 (X2)2 +
0.00091(X3)2 + 2.9 X1X2 + 0.38 X1X3 – 2.1 X2X3
70
Equation 15
5.5
5.5.1
Statistical Test of the Data
Test of significance
The regressed model coefficients were tested for significance by using response
surface analysis in MINITAB 16 [54]. The calculated p-level for each coefficient is
shown in Table 10, From the table, it can be concluded that all coefficients are significant
when the p-level is smaller than significance level α =0.05.
* significance coefficient
Equation
Sum of
Degree of
coefficient
square
freedom
F - value
P - value
Model
970
9
11.81
0.0001 significant
X1
290
1
30.99
0.0001*
X2
290
1
27.54
0.0001*
X3
9.6
1
0.65
0.0980
(X1)2
66
1
2.56
0.00067*
(X2)2
1.1
1
9.86
0.00094*
(X3)2
35
1
0.062
0.99
(X1 * X2)
34
1
7.03
0.00074*
(X1 * X3)
62
1
0.12
0.55
(X2 * X3)
0.00023
1
3.75
0.0067*
Residual
29
10
9.41
Lack of Fit
23
5
4.72
Pure Error
5.4
5
1.1
Cor. Total
1000
19
Table 10: Test of significance.
71
0.067 not significant
The probability P of the factors X3, X32 and X1X3 were found to be greater than
significance level α =0.05. They are not significant to the response, but in this case the Pvalue of X3 is below 0.1 so, it is recommended [3 and 55] to keep the factor in the
developed statistical model.
5.5.2
Checking the model adequacy (normal probability plot)
The normal probability plot is a graphical technique for assessing whether or not a
data set is normally distributed. The data is plotted against a theoretical normal
distribution (shown in Figure 38) in such a way that the points should form an
approximate straight line.
Figure 38: Normal probability plots of residuals.
72
Departures from this straight line indicate departures from normality. Normal
probability plots were generated by using computer software MINITAB 16. It can be
seen from the plotted data that all residuals are normally distributed.
5.5.3
Effect of residuals experiment
The residuals from a fitted model are the differences between the responses
observed at each combination of explanatory variables and the corresponding prediction
of the response computed using the regression function. Mathematically, the definition of
the residual for the ith observation in the data set is written as:
ei = Yi - f(xi, βi)
Equation 16
Where Yi represents the ith response in the data set and xi represents the list of
explanatory variables, each set at the corresponding values found in the ith observation in
the data set. For the analysis of variance, two plots were drawn, one plot for residuals vs.
the order of data (Run sequence plots) shown in Figure 39 and another plot of residuals
vs. the value of a fitted response or predicted value (shown in Figure 40). Residuals
versus the order of data are an easy way to graphically summarize a variation in the data
set. If the data is not random, the model is not valid
73
Figure 39: Plot of residual versus the order of run data.
Figure 40: Plot of residual versus the predicted value of the model.
74
From the residuals plot, we can conclude that the model fits the data well. The
results from Figures 39-40, are satisfactory because of the randomness distribution of
residuals this verifies that the analysis of variance is the proper way to deal with the µIM
process parameters to produce DMM part.
5.5.4
Lack of fit test
The F-test and analysis of variance (ANOVA) shown in Table 11 were used to
test the adequacy of fit of the estimates. Based on α =0.05 the developed regressed model
fits the experimental data because of insignificant lack of fit (P-level = 0.067 > α =0.05).
Sum of,
Mean
DOF
Squares
Squares
F-values
Regression
9
970
111.128
11.81
0.000*
Linear
3
589.6
185.588
19.73
0.000*
Quadratic
3
380
113.618
12.08
0.001*
Interaction
3
98
34.177
3.63
0.053
Residual
10
94.08
9.408
Lack of Fit
5
23
15.529
4.72
0.067
Pure Error
5
5.4
3.287
1.1
Total
19
1064.08
Source
P- values
Table 11: ANOVA results of the developed model.
5.5.5
Goodness of fit
To obtain an indication of the predicted accuracy of the statistical model, using
MINITAB 16, R2 was determined. R2 adjusted is a modification of R2 that adjusts for the
number of terms in a model.
75
R2 - Multiple coefficient of determination
97 %
R2 - Adjusted
95 %
Table 12:Goodness of fit measures.
Experiment
number
1
Experimental
observation of DMM
surface variation
38.1
Fitted results from
the statistical
model
39.43364
2
22.1
22.13364
0.03364
3
27
27.70364
0.70364
4
20
21.90364
1.90364
5
45
44.44364
-0.55636
6
28
28.64364
0.64364
7
23
24.31364
1.31364
8
20
20.01364
0.01364
9
30.5
27.70545
-2.79455
10
19.5
16.90545
-2.59455
11
31.7
30.24545
-1.45455
12
20.8
20.06545
-0.73455
13
21
19.02545
-1.97455
14
22
20.58545
-1.41455
15
21
19.34636
-1.65364
16
18.7
19.34636
0.64636
17
18.7
19.34636
0.64636
18
17.9
19.34636
1.44636
19
19.2
19.34636
0.14636
20
18.9
19.34636
0.44636
Residual
1.33364
Table 13: Residuals of experimental vs. predictions from statistical model.
76
Figure 41: The model fitting curve of the experimental response.
The acceptable level of R2 and R2adjusted is above 80% [55]. The values are summarized
in Table 12. We can see that both R2 and R2 adjusted exceed the acceptable level. Table
13 and Figure 41 represent the residuals of the statistical model, it is clearly shown that
the model predicts the experimental values.
5.6
Effect of the significant µIM parameters on the response
Using Microsoft Excel 2007 software program the perturbation graph (Figure 42)
was plotted. The main effects of each factor neglecting the other two factors and
interaction effects for different significant process parameters on the response were
examined within levels between ± 1.0 through the design of experiments technique.
5.6.1
The main effect of packing pressure (X1) on the response
Keeping the other two factors (X2-packing time and X3-injection speed) at zero
levels and X1 at the different fixed levels -1, 0, and +1, the regression model will be
77
affected by the change in levels of X1, the curve denoted by letter A-A in Figure 42, is
significantly curvilinear form. It is seen that if the packing pressure increases, the DMM
surface deviation decreases until the level 0.97 then starts to increase.
Figure 42: Effect of each factor significant to the response.
5.6.2
The main effect of packing time (X2) on the response
Keeping the other two factors, Xl and X3, at zero levels and varying X2. The curve
denoted by B-B in Figure 42 shows the variation of packing time X2, the minimum is
around the coded value of 0.5. A nonlinear effect of packing time on the DMM surface
deviation is predicted.
78
5.6.3
The main effect of injection speed (X3) on the response
As shown in Figure 42, the injection speed was varied at different levels while
both other factors (X1and X2) are kept constant at zero level. The injection speed effect
on the predicted DMM surface deviation is smaller than for the other two factors.
5.6.4
The interaction effect of the factors on the response
The only two significant combination effects were between the factors (Xl.X2)
and (X2.X3) on the DMM surface deviation, shown respectively on Figures 43-44. In the
first interaction, the two factors Xl and X2 were varied at the coded levels ± 1, while
keeping the third factor X3 at fixed zero level. Secondly, the interaction between the X2
and X3 factors were varied at the ± 1 levels while keeping X1 at the zero level.
Figure 43: The interaction effect of the Xl X2 on the DMM surface deviation.
79
Figure 43 shows the two curves for the variation of packing time at ± 1 levels. At
a low level (-1) of packing pressure on the x-axis, the packing time has large difference
between DMM surface deviation. Furthermore, on the same graph we can see that the
packing time at the higher level (+1) of packing pressure has smaller difference between
DMM surface deviation which indicate that there is a very low interaction between
packing pressure and packing time. On the other hand, Figure 44 shows the two curves of
± 1 levels of injection speed. At the lower level (-1) of the packing time on x-axis shows
the higher level (+1) of injection speed which predicts higher value of DMM surface
deviation. However, at the higher level (+1) of packing time and same level of injection
speed the value of DMM surface deviation is low which indicates that there is high
interaction between packing time and injection speed.
Figure 44: The interaction effect of the X2X3 on the DMM surface deviation.
80
5.6.5
Response surface analysis
Design Expert statistical Software [55] was used to obtain three dimensional
response surface plots and their contours for each of the two selected factors on the
response, assuming the third factor is at zero level. Figure 45 shows the 3D-response
surface plot of the expected DMM surface variation as a function of packing pressure and
packing time, while Figure 46 shows the contour plot. The dark blue regions indicate the
preferred region for minimizing DMM surface variation.
Figure 45: Response surface plot of packing, pressure and time.
81
Figure 46: Contour plot of packing, pressure and time.
In Figure 47, the effect of packing pressure and injection speed on DMM surface
variation are given. The dark blue zone in the contour plot in Figure 48 indicates the
region where DMM surface variation is lower. The Figures 49-50 shows similar plots for
packing time and injection speed.
82
Figure 47: Response surface plot of packing pressure and injection speed.
Figure 48: Contour plot of packing pressure and injection speed.
83
Figure 49: Response surface plot of packing time and injection speed.
Figure 50: Contour plot of packing time and injection speed.
84
5.7
Optimization using the statistical model
Optimization was carried out using the desirability function approach to select the
optimum parameter level values that must be used in order to minimize the DMM surface
variation. The factor levels were kept coded between ± 1, the DMM surface variation
ranged between the minimum and maximum experimental results 18 and 45, and the
desirability equation applied the confidence interval of 95%. The three-dimensional
response surface plots and their contours represented in Figures 45-50 were examined to
predict the main objective. Design Expert software was employed to optimize the process
parameters by doing iterations to sets of solutions observed from optimum regions in the
three contour plots.
DMM Standard
Selected
Desirability
surface
error of
by
variation response
software
1
0.27
0.24
-0.18
18
0.59
0.95
selected
2
0.26
0.25
-0.17
18
0.59
0.95
3
0.26
0.24
-0.21
18
0.59
0.95
4
0.28
0.25
-0.12
18
0.59
0.95
Table 14: Values of the controllable variables that minimize the surface variation.
Solution Packing Packing Injection
number pressure
time
speed
The solutions were calculated and four of the best solutions were selected by the
software and are shown above in Table 14. The best solution for achieving the objective
of minimizing the surface variation of the DMM is to set the packing pressure to a value
of 119 MPa, the packing time to a value of 7 seconds, and the injection speed to a value
of 170 mm/sec.
85
Chapter 6: Conclusions and Recommendations for Future Work
This research evaluated the feasibility of a new DMM design using plastic
materials, manufactured via the cost effective micro injection molding process. The new
design consists of three distinctive regions in the cross section of the DMM, which are
the solid frame, microchannel, and mirror. The critical optical features characterizing the
performance of the new design include the flatness and flexibility of the circular mirror in the
middle of the DMM. To evaluate the different design alternatives, previous to machining the
die, flow simulation was performed using the CAE injection molding analysis program,
Moldex3D. . DOE techniques were used to study the effects of the microinjection process
control variables, such as packing pressure, packing time and injection speed on the
DMM mirror surface flatness.
6.1. Conclusions
Based on this study we can conclude that:
1. The DMM was successfully fabricated using COC-Topas 5013 via microinjection
molding.
2. The flexibility of the designed DMM part is affected mainly by the geometry of the
microchannel surrounding the mirror. Increased flexibility is achieved by decreasing
the channel thickness and increasing its width. However their values are limited by
86
melt premature solidification. The minimum thickness and largest width successfully
molded were 100 m and 1 mm, respectively.
3.
The flatness of the mirror surface improves by increasing the thickness. The selected
thickness was 500 m.
4. The slots in the microchanel besides increasing the flexibility of the mirror, act as
vents to allow for the air to escape from the cavity. Without the slots, it was not
possible to mold a good part.
5. Experimental results indicate that Moldex3D does a good job in predicting the
experimental fill patterns.
6. The thickness of the microchannel has a major influence on the fill patterns.
7. The study of the effect of microinjection molding parameters on the DMM mirror
surface flatness was done using RSM and FCC as DOE techniques. The process
parameters selected were packing pressure, packing time, and injection speed. The
experimental results were analyzed using MINITAB. The results of the statistical
analysis can be summarized as follows:
A. A second order regression model was found to be adequate to predict the surface
variation of the DMM mirror surface for the range of parameters selected. The
model is given below:
Y = 20 - 5.4 X1 - 5.1X2 + 0.98 X3 + 3.5 (X1)2 + 4.7 (X2)2 + 0.00091(X3)2 +
2.9 X1X2 + 0.38 X1X3 – 2.1 X2X3.
B. The packing pressure and time are the highest significant factors affecting the
mirror surface variation, while the injection speed had little effect. The surface
87
variation is directly proportional to the injection speed and inversely proportional
to the packing pressure and packing time.
C. There are two significant interactions between pairs of process parameters. The
first interaction is between packing pressure and packing time while the other
one is between packing time and injection speed.
D. The solution that minimizes the surface variation of the new DMM design is
obtained with a packing pressure of 119 MPa, packing time of 7 seconds, and
injection speed of 170 mm/sec.
6.2. Recommendations for Future Work
The Microinjection molding process is becoming of greater importance for the
fabrication of polymeric micro-parts. The research in this technology has increased
dramatically and it is important to focus future research on process control, new
materials, simulation techniques, and quality testing methods. Specifically, further work
can include the following areas of DMM design and fabrication:
a) Study different polymers with various mechanical properties to choose the
proper material in producing the DMM part.
b) Study the possible use of reacting systems that have a low initial viscosity and
then polymerize once the mold is filled. An example would be the use of
Reaction Injection Molding (RIM).
c) Use of a microinjection molding that allows for larger injection pressures and
tonnage, to allow the molding of thinner microchannels.
88
d) Development of a new design of DMM e.g. as shown in Figure 51, where the
thicknesses change gradually from 100, 230, to 500 µm. The new design has
to be investigated numerically and experimentally for the flexibility and
flatness of the DMM mirror.
Figure 51: Suggested new DMM design (half cross section)
e) Try coating the mold surface to promote slip to facilitate the flow.
89
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