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Deformation control for mask image projection based stereolithography process

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Deformation control for mask image projection based stereolithography process

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DEFORMATION CONTROL FOR MASK IMAGE PROJECTION BASED
STEREOLITHOGRAPHY PROCESS

by

Kai Xu

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)

May 2016

Copyright 2016 Kai Xu

ii

Acknowledgements
I would like to extend heartfelt gratitude and appreciation to those who helped me
in all aspects during my PhD study, without their help, it would be impossible for me to
complete my doctoral research.
First and foremost, I am deeply indebted to my PhD advisor, Professor Yong Chen,
who literally taught me how to do research. I am sincerely thankful for his guidance,
understanding, support, patience, caring, encouragement and advice. It is he who
exemplified and taught me how to think through the problem, analyze the problem and to
be an independent researcher. The valuable advice he has given me is not only beneficial
for my research, but will also have profound impact on me as a person. I am honor and
grateful to have him as a wonderful mentor.
I am extremely grateful for Professor Behrokh Khoshnevis for all the guidance, help
and support he has given me during my PhD study. I really enjoyed his courses, which
are full of wisdom from his life experiences. As a distinguished inventor, he really
exemplifies what a great and resourceful researcher is all about, which is quite inspiring
to me.
I owe my deepest gratitude to Professor Qiang Huang for his generous help and
support for providing IR camera and 3D scanner for my research; I cannot imagine I can
complete the research without these valuable tools. Besides, I am thankful to him for his
constructive and valuable suggestions for my research. It is also from his course that I
learned how to do design of experiments, which is very helpful for my research.
iii

I owe special thanks to my other committee members for all the constructive
suggestions, comments and encouragement they offered. Especially, I would like to thank
Professor Wei Wu for his willingness to be my committee member. His pleasant
personality is really inspiring. Special thanks go to Professor L. Carter Wellford, who is
very nice and willing to help me on my FEA simulation research even I am no longer in
his FEA class. I also would like to thank Professor Jernej Barbic for his valuable
comments and encouragement for simulation and reverse compensation in my research. I
am really grateful to all my committee members.
I am grateful to have an internship experience at EnvisionTec. Inc., which largely
expanded my knowledge in additive manufacturing field. I owe special thanks to Mr. Al
Siblani, the CEO of EvnisionTec Inc., for offering me this valuable opportunity. I am
really grateful to Alexandr Shkolnik, CTO of EnvisionTec Inc. and my advisor during the
internship, for all the guidance, support and help. I also want to thank Vandam, Huong
Ma, Chetan Bhadrashette and Ankur Agarwal for being friends and teaching me the
technique details during my internship.
I am really lucky to do research in a lab that is full of support, help, encouragement
and fun. The lab is just like a family, where we share the joy, and offer help and
encouragement whenever needed, and I can always gain positive energy. First, I would
like to thank Chi Zhou, who is a great role model both in doing research and life. He
offered me lots of help and encouragement, which I am very grateful. I also want to thank
Yayue Pan, Yongqiang Li and Xuejin Zhao for being good role models, and for all the
help they have given to me in my research and life. I owe my gratitude to Professor
iv

Zuyao Yu for his encouragement. Special thanks go to Jing Zhang, Xiao Yuan, who not
only offered me help in my research, but also took care of me when I was sick, and they
are good partners to work with. I am grateful to have Tsz-Ho Kwok, Xuan Song,
Dongping Deng, Pu Huang, Huachao Mao, Xiangjia Li, Jie Jin and Zhengcai Zhao as the
same research group, who offered me great support both in doing search and life,
especially, I want to thank Tsz-Ho Kwok for his contribution and collaboration of part of
my research. Besides, I want to express my gratitude to Matthew Petros, Payman Torabi,
Hadis Nouri, Xiang Gao, Behnam Zahiri, Aref Vali, Amir Mansouri for all the support
and help they have given me. I will cherish the moments of working with them forever.
I would like to thank Yuan Jin, He Luan, Yanqing Duanmu and Jizhe Zhang for
their help and collaboration for doing research. I want to express my gratitude to
Professor Shinyi Wu for her encouragement and caring, and Mr. Leu-Yang Eric Huang
for his help.
I would like to extend my deepest gratitude and respect to Professor Dequn Li and
Professor Huamin Zhou, my advisors during my Master's study back in China. They are
very supportive of me for my decision to apply for PhD study at Unites States. They
offered me lots of encouragement, suggestions, help and caring, before and during my
PhD study. Words cannot express my gratitude for their advice and encouragement.
Lastly, and most importantly, I would like to sincerely thank my wife, Wenzhen
Zhu, my parents, my sisters and my parents in law, who always stand by my side no
matter what happens, without their unselfish love, constant support and understanding, it
would not be possible for me to complete my PhD study. I am forever indebted to them.
v

Table of Contents
Acknowledgements ............................................................................................................. ii

List of Tables ................................................................................................................... viii

List of Figures .................................................................................................................... ix

Abstract................. ............................................................................................................ xv

Chapter 1 Introduction ...................................................................................................... 1
1.1 Research Background and Motivation....................................................................... 1
1.1.1 Additive Manufacturing...................................................................................... 1
1.1.2 Stereolithography.................................................................................................4
1.1.3 Deformation in Mask Image Projection Based Stereolithography Process.........7
1.2 Hypotheses............................................................................................................... 14
1.3 Research Scope........................................................................................................ 17
1.3.1 Research Process and Research Content........................................................... 17
1.3.2 Research Methodology...................................................................................... 20

Chapter 2 Path Planning Method & Exposure Strategies on Reducing Deformation ..... 24
2.1. Mask Image Planning of MIP-SL........................................................................... 25
2.1.1 Principle of Pattern-based Mask Image Planning Method................................ 26
2.1.2 Overview of Pattern-based Mask Image Planning Method......................... 28
2.1.3 Examples of Exposure Patterns......................................................................... 32
2.2 Exposure Patterns and Parameters........................................................................... 33
2.2.1 Isolated Cube Pattern......................................................................................... 33
2.2.2 Loop Structure Pattern....................................................................................... 35
2.2.3 Weave Structure Pattern.................................................................................... 36
2.3 Pattern-based Mask Image Planning Study for MIP-SL.......................................... 37
2.4 Experimental Setup.................................................................................................. 40
2.5 Experiment Results and Discussions........................................................................42
2.5.1 Test Case 1.........................................................................................................42
2.5.2 Test Case 2.........................................................................................................44
2.6 Concluding Remarks................................................................................................ 55

Chapter 3 Curing Temperature Study and Exposure Strategies on Reducing
Deformation in MIP-SL Process ....................................................................................... 57
3.1 Temperature Distribution Study of Cured Parts with Single Layer......................... 58
3.1.1 Calibration of IR Camera and Assumptions of Measurement...........................59
3.1.2 Experiment Design and Setup........................................................................... 60
3.1.3 Temperature Distribution.................................................................................. 61
vi

3.1.4 The Effect of Layer Thickness.......................................................................... 63
3.1.5 The Effect of Shapes and Sizes......................................................................... 64
3.2 In-Situ Monitoring of Temperature Evolution in MIP-SL Using IR Camera.......... 65
3.2.1 Experimental Design......................................................................................... 66
3.2.2 Temperature Evolution in Consecutive Layers................................................. 67
3.2.3 One Building Cycle Analysis............................................................................ 69
3.2.4 Temperature Variation Study within One Layer............................................... 70
3.2.5 Verification of the Effects of Layer Size and Thickness on Temperature........ 72
3.3 Curing Temperature by Varying Exposure Time.....................................................74
3.3.1 Experiment Design............................................................................................ 75
3.3.2 Exposure Time Effect on Curing Temperature................................................. 76
3.4 Curing Temperature by Varying Grayscale Values................................................. 80
3.4.1 Grayscale Level Exposure Study.......................................................................81
3.5 Curing Temperatures by Varying Mask Patterns..................................................... 86
3.5.1 Curing Temperature Study................................................................................ 87
3.6 MIP-SL Curing Strategies for Curl Distortion Control............................................90
3.6.1 Curing Strategy Using Grayscale Exposure...................................................... 90
3.6.2 Curing Strategy Using Mask Pattern Exposure................................................. 92
3.7 Physical Experiments and Results............................................................................93
3.7.1 Physical Experiments........................................................................................ 93
3.7.2 Experimental Results......................................................................................... 94
3.8 Concluding Remarks................................................................................................ 95

Chapter 4 Curl Distortion Simulation and Reverse Compensation in MIP-SL .............. 97
4.1 Finite Element Model............................................................................................... 97
4.2 Geometric Model....................................................................................................101
4.3 Physics Settings...................................................................................................... 106
4.3.1 Modeling of Layer by Layer Dynamic Building Process................................ 106
4.3.2 Initial Conditions Settings............................................................................... 108
4.4 Entities Selection.................................................................................................... 108
4.5 Boundary Conditions............................................................................................. 110
4.6 Material Properties................................................................................................. 111
4.7 Mesh....................................................................................................................... 111
4.8 Simulation of Part Removal from Constraint Process........................................... 112
4.9 Deformation Alignment to Find the Optimal (Actual) Deformation..................... 114
4.9.1 Rigid Transformation...................................................................................... 116
4.10 Reverse Compensation......................................................................................... 119
4.11 Materials Properties Effects on Curl Distortion................................................... 122
4.11.1 Simple Bar Test Case.................................................................................... 123
4.11.2 Test Part with Holes...................................................................................... 124
4.12 Concluding Remarks............................................................................................ 126

vii

Chapter 5 A Reverse Compensation Framework for Shape Deformation in Additive
Manufacturing................................................................................................................. 128
5.1 Related Work of Reverse Compensation in Additive Manufacturing................... 128
5.2 Overview of Compensation Framework................................................................ 130
5.3 Correspondence and Deformation..........................................................................133
5.3.1 Establish Correspondence between Models.................................................... 134
5.3.2 Capture the Deformation of Physical Model................................................... 136
5.4 Compensation Calibration...................................................................................... 137
5.4.1 Using Offset Models for Calibration............................................................... 138
5.4.2 Compensated Profile........................................................................................141
5.5 Test Case 1 – 2.5D Freeform Shape.......................................................................142
5.5.1 Comparisons of Deformation Before and After Compensation...................... 143
5.6 Test Case 2 – 3D Freeform Shape..........................................................................145
5.6.1 Measurement Error of 3D Scanner.................................................................. 146
5.6.2 Artificial Markers Design................................................................................ 147
5.6.3 Deformation Calculations................................................................................ 148
5.6.4 Deformation of Offset Models and Analysis...................................................150
5.6.5 Reverse Compensation.................................................................................... 153
5.6.6 Deformation Comparisons...............................................................................154
5.7 Concluding Remarks.............................................................................................. 156

Chapter 6 Conclusions and Recommendations for Future Research ............................ 157
6. 1 Answering the Research Questions/Testing Hypotheses...................................... 157
6. 2 Contributions and Intellectual Merit..................................................................... 159
6. 3 Limitations and Future Work................................................................................ 160

References........................................................................................................................163

viii

List of Tables
Table 2.1. Curl distortion results using isolate cube pattern exposure ............................. 44
Table 2.2. Measurements of length AB in the benchmark test part .................................. 47
Table 2.3. Results using different exposure strategies ...................................................... 47
Table 2.4. Factors and levels for the isolated strcutrue pattern ........................................ 52
Table 2.5. Design matrix and AB dimension data ............................................................ 53
Table 2.6. Factorial estimated contrasts ............................................................................ 53
Table 3.1. Dimensions and building parameters of test cases .......................................... 67
Table 3.2. Comparisons of the exposure time effects ....................................................... 80
Table 3.3. Comparisons of the grayscale exposure effects ............................................... 84
Table 3.4. Grayscale effects on curing time ..................................................................... 85
Table 3.5. The maximum temperature after applying mask patterns ............................... 90
Table 3.6. Curl distortion of test parts .............................................................................. 95
Table 4.1. Material properties in simulation ................................................................... 111
Table 4.2. Simulation results of simple bar test case: curl distortion ............................. 123
Table 4.3. Simulation results of test part with holes: curl distortion .............................. 125
Table 5.1. Deformation comparisons before and after compensation for test case 1 ..... 144
Table 5.2. Deformation comparisons before and after compensation for test case 2 ..... 155
ix

List of Figures
Figure 1.1. Applications of 3D printing in medical fields. ................................................. 3
Figure 1.2. Micromirror device. .......................................................................................... 5
Figure 1.3. An illustration of the MIP-SL process.............................................................. 6
Figure 1.4. Examples of deformation of fabricated parts in SLA process. ......................... 8
Figure 1.5. Deformation sources ....................................................................................... 10
Figure 1.6. Research goal and hypotheses ........................................................................ 16
Figure 1.7. Research process ............................................................................................ 18
Figure 1.8. Research methodologies ................................................................................. 20
Figure 2.1. An illustration of mask image exposure strategies. ........................................ 26
Figure 2.2. Decompose exposure of large region into exposures of small regions .......... 27
Figure 2.3. An illustration of internal volume and boundary of a given solid model ....... 30
Figure 2.4. An illustration of part boundary in the Z axis and related projection images 31
Figure 2.5. Exposure strategies with small features and large regions ............................. 31
Figure 2.6. Three exposure mask patterns ........................................................................ 33
Figure 2.7. Isolated cube pattern. ...................................................................................... 34
Figure 2.8. Pattern definition of loop structure ................................................................. 35
Figure 2.9. Mask images based on loop structure patterns ............................................... 36
Figure 2.10. Pattern definition of weave structure pattern................................................ 36
Figure 2.11. Workflow of part fabrication using defined exposure mask patterns. .......... 37
Figure 2.12. Algorithm of exposure mask pattern generating program ............................ 39
Figure 2.13. An example of using “Boundary Exposure Last” ........................................ 40
Figure 2.14. Test case 1 .................................................................................................... 43
x

Figure 2.15. Schematic of the measured curl distortion ................................................... 43
Figure 2.16. The benchmark part. ..................................................................................... 45
Figure 2.17. Shrinkage comparison .................................................................................. 46
Figure 2.18. Relations between Gap Sizes and shrinkage improvement .......................... 49
Figure 2.19. The effect of Iteration Number on Gap Size = 7 .......................................... 49
Figure 2.20. The effect of Iteration Number on Gap Size = 8 .......................................... 50
Figure 2.21. Shrinkage improvement of loop structure patterns ...................................... 51
Figure 2.22. Half-normal plot of location effects ............................................................. 54
Figure 2.23. Half-normal plot of dispersion effects .......................................................... 54
Figure 3.1. The IR camera used in study .......................................................................... 58
Figure 3.2. In-situ temperature monitoring using IR camera in MIP-SL ......................... 58
Figure 3.3. Test cases of different shapes and sizes. ........................................................ 60
Figure 3.4. The setup of making single layer of resin ...................................................... 60
Figure 3.5. Workflow of one-layer experiments ............................................................... 61
Figure 3.6. A built single layer test case .......................................................................... 61
Figure 3.7. The maximum temperature of a circle with R=3" .......................................... 62
Figure 3.8. Temperature distribution along the X axis in the circle of R=3” ................... 62
Figure 3.9 Thickness measurements at some sampling points in a built circle layer ....... 63
Figure 3.10. The temperature differences between overlapping areas of five test cases .. 64
Figure 3.11. In-situ monitoring of the free-surface-based MIP-SL process ..................... 66
Figure 3.12. Dimensions of a built part. ........................................................................... 67
Figure 3.13. Schematics of sample points and a curing region ........................................ 67
Figure 3.14. Temperature plot at cursor 1 in test case 1 ................................................... 68
Figure 3.15. Building sequence in MIP-SL process ......................................................... 69
xi

Figure 3.16. Temperature plot of a building cycle at cursor 1 .......................................... 70
Figure 3.17. Temperature at 4 sample points .................................................................... 71
Figure 3.18. Temperature at 3 sample points (cursors 2- 4) ............................................. 72
Figure 3.19. Mean temperature plot in test cases 1, 2 and 3 ............................................. 72
Figure 3.20. Mean temperature in test cases 1 and 4 ........................................................ 74
Figure 3.21. Workflow of testing various exposure time ................................................. 76
Figure 3.22. Curing temperature using exposure time 5 s ................................................ 77
Figure 3.23. Curing temperature using exposure time 15 s .............................................. 78
Figure 3.24. Curing temperature using exposure time 45 s .............................................. 79
Figure 3.25. Comparisons of the maximum curing temperatures using exposure time ... 80
Figure 3.26. Examples of grayscale mask images ............................................................ 81
Figure 3.27. Curing temperature using grayscale 130 ...................................................... 82
Figure 3.28. Curing temperature using grayscale 160 ...................................................... 83
Figure 3.29. Curing temperature using grayscale 190 ...................................................... 83
Figure 3.30. Curing temperature using grayscale 220 ...................................................... 84
Figure 3.31. Grayscale effects on curing temperature ...................................................... 85
Figure 3.32. Grayscale effects on curing time .................................................................. 85
Figure 3.33. Mask pattern 1 .............................................................................................. 86
Figure 3.34. Mask pattern 2 .............................................................................................. 86
Figure 3.35. Mask image for entire region ....................................................................... 87
Figure 3.36. Curing temperature of exposure time 10 s ................................................... 88
Figure 3.37. Curing temperature of exposure time 25 s ................................................... 89
Figure 3.38. Curing temperature of exposure time 40 s ................................................... 89
Figure 3.39. Curing temperature of using grayscale 190 .................................................. 91
xii

Figure 3.40. Curing temperature of grayscale 255 for 40 s .............................................. 92
Figure 3.41. Curing temperature of mask pattern exposure.............................................. 93
Figure 3.42. Exposure strategy using mask patterns......................................................... 94
Figure 4.1. Elastic domain and boundary conditions ........................................................ 98
Figure 4.2. Workflow of creating geometry of layers in COMSOL ............................... 102
Figure 4.3. Input STL of test case ................................................................................... 103
Figure 4.4. Sliced image of one layer ............................................................................. 104
Figure 4.5. Boundary contours of one layer ................................................................... 104
Figure 4.6. Topology of loops......................................................................................... 105
Figure 4.7. Creation of one layer in COMSOL .............................................................. 106
Figure 4.8. Final geometry of one layer .......................................................................... 106
Figure 4.9. Geometry of 10 layers in COMSOL ............................................................ 106
Figure 4.10. An illustration of dynamic building process .............................................. 107
Figure 4.11. Selection of all domains ............................................................................. 109
Figure 4.12. Selection of all domains in two layers ........................................................ 110
Figure 4.13. Mechanical boundary conditions ................................................................ 111
Figure 4.14. Meshing using tetrahedron ......................................................................... 112
Figure 4.15. Warping after removing constraint ............................................................. 113
Figure 4.16. Symmetric boundary conditions settings.................................................... 114
Figure 4.17. Simulation of curl distortion for simple bar ............................................... 115
Figure 4.18. An illustration of non-symmetry constraint ............................................... 116
Figure 4.19. Simulation result applying non-symmetry constraint................................. 116
Figure 4.20. Two point sets: A and B ............................................................................. 117
Figure 4.21. Illustration of rigid rotation ........................................................................ 117
xiii

Figure 4.22. Curl distortion after rigid transformation ................................................... 119
Figure 4.23. Reverse compensated model ...................................................................... 120
Figure 4.24. Reversed geometry created in COMSOL ................................................... 120
Figure 4.25. Meshing of reverse compensated geometry ............................................... 121
Figure 4.26. Simulated deformation of reverse compensated geometry ........................ 121
Figure 4.27. Actual curl distortion after reverse compensation. ..................................... 122
Figure 4.28. Effects of materials on curl distortion of simple bar test case .................... 124
Figure 4.29. Rectangular test part with holes ................................................................. 124
Figure 4.30. Curl distortion for test part with holes ........................................................ 125
Figure 4.31. Effects of materials on curl distortion of test part with holes..................... 126
Figure 5.1. Computational framework to reduce deformation. ...................................... 131
Figure 5.2. Models with no salient feature points ........................................................... 134
Figure 5.3. Cross-parameterization of two models with 35 artificial markers ............... 135
Figure 5.4. Sample points and correspondence. ............................................................. 137
Figure 5.5. Offset models and physical built parts ......................................................... 140
Figure 5.6. Comparisons of deformation of models with no offset and offsets.............. 141
Figure 5.7. Compensated profile. .................................................................................... 142
Figure 5.8. Compensated STL model ............................................................................. 143
Figure 5.9. Comparisons of deformation before and after compensation....................... 143
Figure 5.10. Comparison of physical built parts ............................................................. 144
Figure 5.11. Testcase 2 – 3D freeform shape ................................................................. 145
Figure 5.12. Standard test part for accuracy study.......................................................... 146
Figure 5.13. Scan result of test part for accuracy study. ................................................. 147
Figure 5.14. Scan model of baseline part ........................................................................ 149
xiv

Figure 5.15. Comparison of baseline nominal model and scan model compensation .... 150
Figure 5.16. Nominal offset models of test case 2 .......................................................... 151
Figure 5.17. Physical built parts of offset models .......................................................... 151
Figure 5.18. Deformation using offset models ............................................................... 152
Figure 5.19. Compensation ............................................................................................. 153
Figure 5.20. Physical parts comparisons......................................................................... 154
Figure 5.21. Deformation of built part with compensation ............................................ 155
xv

Abstract
Based on a Digital Micromirror Device (DMD), Mask Image Projection based
Stereolithography(MIP-SL) uses an area-processing approach by dynamically projecting
mask images onto a resin surface to selectively cure liquid resin into layers of an object.
Consequently, the related additive manufacturing process can be much faster with a
lower cost than the laser-based Stereolithography Apparatus (SLA) process. However,
the part built in MIP-SL process has deformation after building, which may be attributed
to several reasons. First, the volumetric shrinkage takes place during the phase change
process when liquid monomers are converted to solid polymer. Second, heat will be
generated since the photopolymerization is an exothermic process, and thermal shrinkage
is resulted when the curing layer cools down. Third, SLA is a layer-by-layer dynamic
building process, in which current curing layer is restricted by the layers solidified below,
therefore residual stress builds up. Moreover, the material used in MIP-SL process is
acrylate resin, which has much larger shrinkage when it is solidified than the epoxy resin
widely used in SLA process. As a result, the deformation of built part in MIP-SL is more
obvious than that built in traditional SLA process.
In this research, we address the deformation problems in MIP-SL process from two
approaches. The first approach is based on using different exposure strategies. The
shrinkage related deformation control method has been studied and verified using
physical experiments, besides, the curing temperature during the photopolymerization
process has been investigated, and exposure strategies have been designed to reduce part
xvi

deformation. The second approach tries to reduce deformation through reverse
compensation of input geometry based on the deformation calculation, which can either
be done by using simulation or physical measurement. Finite Element Analysis(FEA) has
been adopted to model and simulate the MIP-SL building process based on the curing
temperature calibrated, and reverse compensation computational framework based on
physical measurements has been investigated and applied to reduce deformation of
fabricated part in MIP-SL process.
For the shrinkage related deformation control method, an exposure strategy is
investigated based on mask patterns by decomposing the exposure of a large area in one
layer into several exposures of smaller areas in several layers, instead of curing the whole
layer in one exposure. A mask image planning method and related algorithms have been
developed for the MIP-SL process. The planned mask images have been tested by using a
commercial MIP-SL machine. The experimental results illustrate that our method can
effectively reduce the deformation.
In the curing temperature studies, test cases of curing layers with different shapes,
sizes and layer thicknesses have been designed and tested. The experimental results show
that the temperature increase of a cured layer is mainly related to the layer thickness,
while the layer shapes and sizes have little effect. The curing temperatures of built layers
using different exposure strategies including varying exposure time, grayscale levels and
mask image patterns have been studied. The curl distortion of a test case based on various
exposure strategies have been measured and analyzed. It is shown that, by decreasing the
xvii

curing temperature of built layers, the exposure strategies using grayscale levels and
mask image patterns can effectively reduce the curl distortion.
COMSOL Multiphysics software has been used to simulate the curl distortion of
part built in MIP-SL. The dynamic layer-by-layer building process of MIP-SL has been
simulated using birth and death technique. The curing temperature calibrated for each
layer has been incorporated as thermal load into the FEA model. The curl distortion
simulation result has the same trend with that of the physical built part. Based on the
simulation result, a reverse compensation method has been applied on a simple test case
to show the effectiveness of reducing curl distortion.
A general reverse compensation computation framework based on physical
measurements is presented to reduce the complex deformation in additive manufacturing
process. A novel method is presented for identifying the optimal correspondence between
the deformed shape and the given nominal CAD model. By studying relations of offsets
and deformation for each point, the reverse compensated CAD models can be calculated.
The intelligently modified CAD model, when used in fabrication, can significantly
reduce the part deformation when compared to the nominal CAD model. Two test cases
have been designed to demonstrate the effectiveness of the presented computation
framework.
1

Chapter 1 Introduction
1.1 Research Background and Motivation
1.1.1 Additive Manufacturing
Additive Manufacturing(AM), also known as 3D printing, Rapid Prototyping,
Direct Digital Manufacturing, Layered Manufacturing and Freeform Fabrication [1], etc.
has become increasingly popular nowadays and even been considered as a disruptive
technology that is bound to revolutionize the manufacturing industry [2]. Previously, the
traditional manufacturing methods that prevail in the manufacturing industry can be
categorized into two aspects: subtractive manufacturing [2] and near net shape
manufacturing [3]. In subtractive manufacturing processes, the undesired portions are
removed from the bulk, such as machining, drilling, milling and lathing, etc., which
produce waste and expensive tools and machines are needed. While in the near net shape
manufacturing processes, such as injection molding, casting and forging, etc., the mold or
tool is required which is expensive and time-consuming to make. Unlike the traditional
manufacturing, AM process builds part by depositing/adding materials on desired
positions in a layer-by-layer sequence, which can be considered as the opposite of
subtractive manufacturing process and produces little or no waste [1]. Specifically, AM
process requires the input of 3D model (STL) of build part, which is then sliced into
many thin layers by using slicing software. The cross-section region of each layer is
traced, and consequently built, by 3D printer. The platform moves a certain distance to
recoat a new layer. This building cycle is repeated until the final layer is completed. As
2

manifested by the building process, AM process eliminates the needs for mold and tools,
thus it can be much cheaper and faster to fabricate small batch of parts. Besides, it is very
flexible and can build parts with complex features easily, which may pose great challenge
and would be costly for traditional ways of manufacturing.
Due to its unique characteristics and advantages, AM has drawn growing concerns
from both academia and industry. Many novel AM processes have been developed as
more efforts have been spent on them during the recent decades. Based on the layer
forming mechanism, AM processes can be put into several categories [4]:
(1) Projection – based, such as Stereolithography(SLA), Selective Laser
Sintering(SLS), Selective Laser Melting(SLM), Electron Beam Melting(EBM), etc.
(2) Nozzle – based, such as Fused Deposition Modeling (FDM), inkjet 3D Printing
(3DP), and Contour Crafting (CC), etc.
(3) Others, such as Laminated Object Manufacturing (LOM), etc.
Each process has its corresponding material(s) to work with. The materials that can
be built in AM processes are including but not limited to polymers, plastic film, metals
and metal alloys, ceramics, and concrete, etc. More materials are being explored and
added for AM processes.
AM processes have been widely used for fabricating customized products in many
fields. Originally, they are mainly used for building prototypes for visualization purpose;
however, advances over the decades have made it possible for AM processes to direct
manufacturing of increasing number of end products or tools. For example, some
companies use AM processes to fabricate highly customized products for patients in
3

medical fields, such as hearing aid shell [5], teeth aligner [6], prosthetics [7], and 3D
printed custom insoles [8], etc., as shown in Figure 1.1. It has been reported that GE is
preparing to use AM process to manufacture complex jet parts [9], and EOS Inc. uses its
3D printer to directly fabricate metal mold with optimized conformal inner cooling
channels that can produce better quality plastic parts than the molds fabricated by
traditional way of manufacturing [10], etc. AM processes are playing an increasingly
important role in our daily life.

(a) (b)

(c) (d)
Figure 1.1. Applications of 3D printing in medical fields. (a) Hearing aid shell [5]; (b) teeth
aligner [6]; (c) prosthetic hand [7]; (d) 3D printed custom insoles [8]
4

Despite many obvious advantages of AM process, it has its own disadvantages
when compared to traditional ways of manufacturing. It has low accuracy since the built
part has deformation, low surface quality and weak mechanic properties, which are
intrinsic in the layer-by-layer building process. Many research have been conducted/are
being conducted trying to overcome these drawbacks, including developing new
processes and materials, process modeling and control [11], etc. The goal of this research
is to investigate methods to control the deformation during AM process to increase the
accuracy of built part. Specifically, mask image projection based stereolithography
process has been selected as the target process to work on. The deformation sources for
AM processes are firstly outlined, and effective process planning methods have been
designed to reduce deformation. Finite Element Analysis has been adopted to simulate
the deformation of built part. Reverse compensation based on measurement method has
been presented to further increase part accuracy.
1.1.2 Stereolithography
Stereolithography Apparatus (SLA) is one of the first projection-based additive
manufacturing processes that have been developed for directly building physical objects
based on digital models. Stereolithography is a photopolymerization process, in which
small liquid monomers are cross-linked to large polymer under light exposure. In the
SLA process, parts are fabricated layer by layer by using a laser beam with appropriate
power and wavelength to selectively cure liquid photosensitive resin into solid. A three-
Dimensional (3D) Computer-aided Design (CAD) model (e.g. a STL file) defines the
surface boundary of the object. Based on them, the 3D CAD model is sliced into a set of

2D layers, which are then processed by the computer for controlling the tool path of the
laser beam [12].
Recent developments of digital devices, such as Liquid Crystal Display (LCD) and
Digital Micromirror Device (DMD), provide the capability of simultaneously and
dynamically controlling the energy input of a whole area. The use of such devices in
developing novel Mask Image Projection Based Stereolithography process (MIP
been recognized as an important research direction for future AM development. DMD is
a reflective spatial light modulator that can digitally control the direction of the reflected
light on each micromirror, thus make it turned on/off. An example of DMD is shown in
Figure 1.2. The DMD device consists of millions of micromirrors as shown in Figure
1.2(a), the status of which can be switched at very high frequency (approximately 5000
Hz). Detailed structure of each mic
tilted +/- 10 degree, which can reflect the light either onto or away from the screen. The
light intensity can be controlled by Pulse Width
Figure 1.2. Micromirror device. (a)
(a)
2D layers, which are then processed by the computer for controlling the tool path of the
Recent developments of digital devices, such as Liquid Crystal Display (LCD) and
Digital Micromirror Device (DMD), provide the capability of simultaneously and
dynamically controlling the energy input of a whole area. The use of such devices in
ng novel Mask Image Projection Based Stereolithography process (MIP
been recognized as an important research direction for future AM development. DMD is
a reflective spatial light modulator that can digitally control the direction of the reflected
light on each micromirror, thus make it turned on/off. An example of DMD is shown in
Figure 1.2. The DMD device consists of millions of micromirrors as shown in Figure
(a), the status of which can be switched at very high frequency (approximately 5000
z). Detailed structure of each micromirror is shown in Figure 1.2(b); the mirror can be
10 degree, which can reflect the light either onto or away from the screen. The
light intensity can be controlled by Pulse Width Modulation (PWM) [13-
evice. (a) Micromirror array; (b) detailed structure of micromirrors
(b)
5
2D layers, which are then processed by the computer for controlling the tool path of the
Recent developments of digital devices, such as Liquid Crystal Display (LCD) and
Digital Micromirror Device (DMD), provide the capability of simultaneously and
dynamically controlling the energy input of a whole area. The use of such devices in
ng novel Mask Image Projection Based Stereolithography process (MIP-SL) has
been recognized as an important research direction for future AM development. DMD is
a reflective spatial light modulator that can digitally control the direction of the reflected
light on each micromirror, thus make it turned on/off. An example of DMD is shown in
Figure 1.2. The DMD device consists of millions of micromirrors as shown in Figure
(a), the status of which can be switched at very high frequency (approximately 5000
(b); the mirror can be
10 degree, which can reflect the light either onto or away from the screen. The
-15].

ailed structure of micromirrors
6

The basic idea of the MIP-SL is to use mask images generated from the sliced
shapes of a CAD model to directly cure 2D layers [16-24]. An illustration of the MIP-SL
process is shown in Figure 1.3. When the building process starts, the DMD chip projects
the mask image of a sliced layer onto the liquid resin surface to selectively cure resin at
desired regions. After one layer is cured, the platform moves down to prepare another
layer of liquid resin. The process repeats until the 3D object has been built. In such a
process, note that a whole layer can be cured by just one exposure. Hence the building
speed can be greatly improved. For the MIP-SL process, several mask image planning
methods have been developed [25-28].

Figure 1.3. An illustration of the MIP-SL process
There are two types of photopolymer systems, acrylate chemistry and cationic
photopolymerization, in the SLA process [12]. Acrylate chemistry polymerizes via a free-
radical mechanism while cationic photopolymerization undergoes ring-opening reactions
7

in the presence of cationic photoinitiators. Epoxy resin, the widely used photopolymer in
the SLA process, is based on cationic photopolymerization and can be cured by
ultraviolet (UV) light. In comparison, acrylate resin requires less energy input to start the
photopolymerization process. Since it can be cured by both UV and visible light, acrylate
resin is commonly used in the commercially available MIP-SL systems, such as the V-
Flash system from 3D Systems Inc. (Rock Hill, SC) and the Ultra system from
EnvisionTec Inc. (Dearborn, MI).
Ever since the invention of SLA process, many variants have been developed, and
many improvements have been made. Compared to other AM processes, SLA has high
resolutions, surface finishes and speed. Recently a breakthrough has been made to
dramatically increase the building speed (up to 100 times faster than current available
SLA process) in SLA [29]. SLA has wide range applications in many fields, such as
medical parts (hearing aid shell, teeth aligner, implants, etc.), jewelry, electronics, etc.
1.1.3 Deformation in Mask Image Projection Based Stereolithography Process
Although the MIP-SL process has good properties such as fabrication resolution [28]
and speed [29, 30], the parts it builds have deformation after removing supported
structures. This deformation leads to tolerance loss, making it unacceptable to fabricate
assembly features. Suppose patients wear a customized hearing aid or teeth aligner
fabricated by SLA process, a slight deformation exist in the fabricated part would make it
an unpleasant experience for them.
8

Deformation is a common and fundamental problem in SLA process and shared in
all other AM processes. Some examples of deformation of fabricated parts are shown in
Figure 1.4.

Figure 1.4. Examples of deformation of fabricated parts in SLA process. (a) Letter H diagnostic
part [31]; (b) U-shaped part [32]; (c) rectangular bar
(a)
(b)
(c)
9

Figure 1.4(a) shows a "Letter - H" diagnostic part widely used for accuracy study in
SLA process [31]. The solid line denotes the nominal model, while the deformed shape is
illustrated in dash line, from which we can find the physical built part is deformed with
bending and shrinkage. Similar to Figure 1.4(a), U-shaped part (nominal undeformed
model is shown in solid line) is bended after fabrication (shown in dash line), which is
better illustrated in the cross-section view of A-A [32] in Figure 1.4(b). Figure 1.4(c)
demonstrates a physical built part in MIP-SL process, in which the nominal part of a
rectangular bar is shown in dashed line. The side view of the object is shown for a better
illustration. From the figure, it can be clearly seen the left and right sides, denoted as A
and B respectively, curl up. The physical built part is no longer flat. This kind and other
types of deformation exist for parts built in MIP-SL process and other AM processes.
Stereolithography is a complex chemical reaction process, in which liquid
monomers are cross-linked into solid polymer under light exposure [12]. The deformation
source comes from several aspects, as summarized in Figure 1.5. First, intrinsic
volumetric shrinkage takes place when liquid resin is converted to solid polymer.
Different resin have different volumetric shrinkage rate. The liquid resin used in MIP-SL
process is acrylate resin, which has larger shrinkage than epoxy resin commonly used in
laser-based SLA process, thus deformation in MIP-SL process is more challenging than
that in conventional SLA process [33, 34]. Second, photopolymerization process is an
exothermic reaction process, in which heat will be generated and thermal shrinkage can
be involved in the process when the curing layers cools down [32, 35]. Some research
have been reported on using IR camera to study the curing temperature in MIP-SL
10

process [36, 37]. Third, the additive manufacturing processes built part on a layer-by-
layer basis, the shrinkage of current layer is restricted by underlying layers, consequently,
tensile stress builds up in the current shrinking layer, while compressive stress is
generated on the underlying layer that restrict it [32, 38]. Besides, the nonuniformities of
light source and material properties also contribute to deformation since these
nonuniformities lead to nonuniform curing rate of resin and nonuniform shrinkage as a
result[33, 38]. Moreover, variants of MIP-SL process and hardware setup may play roles
in the final deformation. Generally, MIP-SL process can be categorized into two types:
constrained-surface and free-surface, which exerts different constraints on the curing
layer during building process [12, 30].

Figure 1.5. Deformation sources [12, 30, 32-38]
Part accuracy is one of the major drawbacks that limit the application of SLA and
other AM processes. Extensive research has been conducted to improve part accuracy in
the SLA process. Some of the previous researches try to reduce deformation from process
planning aspects, specifically to explore different building styles that can reduce the
internal stresses during building. For example, many build styles based on different laser
beam scanning patterns have been developed and used in the commercial machines from
11

3D Systems Inc. (Rock Hill, SC), such as Tri Hatch, WEAVE, STAR-WEAVE, and
ACES [39]. Huang and Lan [40] investigated the influence of three types of path
scanning: scanning in only one direction (X, or Y), scanning in X direction in odd layers
and in Y direction in even layers, and profile scanning after finishing scanning the interior
region. Some other researchers employed Design of Experiments (DOE) to study effects
of key building parameters, and optimize them in order to reduce deformation of built
parts. Taguchi method has been employed [41, 42] to study effects of the combinations of
hatching style parameters, such as layer thickness, hatch and border overcure, hatch
spacing and fill spacing and cure depth, in order to find the optimum combination of
parameters leading to best accuracy of final parts. Narahara et al. [35] analyzed the
relation between the laser scanning and linear shrinkage of a single strand using
developed experimental equipment. Jayanthi et al. [43] studied the effects of process
parameters, such as layer thickness, hatch spacing, overcure, on curl distortion in
photopolymerization process.
To understand how deformation is formed, some researchers tried to use Finite
Element Method (FEM) and other modeling methods to simulate the SLA process.
Bugeda et al. [44] and Chambers et al. [45] developed a Finite Element Analysis (FEA)
program to simulate SLA deformation. The volumetric shrinkage was incorporated into
the model. Huang et al. [33] and Vatani et al. [38] considered heterogeneous material
properties in their simulation models. Some researchers considered the thermal effects
during the building process. Hur et al. [32] included the thermal cooling effects in the
FEA model to predict the related deformation in SLA. Tanaka et al. [46] simulated the
12

distortion in SLA by incorporating both thermal effect and polymerization shrinkage into
the FEA model. Rosen et al. [47] and Tang [48] used an analytical irradiance model to
simulate the laser-based SLA curing process. Koplin et al. [49] presented a material
model to incorporate elastic, viscous-elastic and viscous components to describe the
strain response in SLA process. Flach et al. [50] applied a simple shrinkage model to
simulate SLA process. There are also some research on the modeling and simulation of
other AM processes [51-62].
Based on the deformation result, some research has been conducted to improve the
part accuracy by compensating the part geometry. Huang et al. [63, 64] used reverse
compensation method to improve distortion or shrinkage of part built in laser-based SLA
based on the simulation results. Some research has been reported on compensating errors
through modifying slice file or STL surface [65, 66]. Recently, Huang et al. [67-71]
presented statistical approach to model and predict geometric deviation of parts built in
MIP-SL process, and compensate the geometry shape to improve part accuracy. Relative
little research on the geometry compensation reported in SLA or other AM processes,
since modeling and predicting SLA or AM processes is not an easy task. Similar
geometry compensation methods have been applied to reduce the springback effect in the
sheet metal forming process, in which the tool geometry is modified based on the FEA
simulation result of sheet metal spring back [72, 73].
MIP-SL is a novel stereolithography process based on using DMD chips to
selectively cure large area, which is quite different from the laser scanning used in
conventional SLA process. Besides, the material used in MIP-SL is acrylate resin, which
13

has larger shrinkage than epoxy resin used in conventional SLA. Thus the deformation
problem is more challenging than that in conventional SLA. However, little research has
been reported on reducing deformation of built parts in MIP-SL process. To fill the
research gap, the goal of this research is to reduce deformation of built part in MIP-SL
process.
There are several possible ways for reducing the deformation in the MIP-SL
process. For example, one effective way is to develop a liquid resin for MIP-SL that has
less shrinkage. In this research work, we first present novel exposure strategies to
intelligently set mask images during the building process such that less shrinkage will
occur to the built objects. Based on the curing temperature studies in MIP-SL, we further
explore additional exposure strategies by combining mask patterns with grayscale
exposures to lower down curing temperature of built layers and therefore reducing curl
distortion. In addition, similar to change the input light exposures, another idea is to pre-
modify the input CAD model to incorporate complex deformation sources to compensate
the shape deformation that may happen in the building process. This requires
measurement of deformation of built part, which can be done either by using a simulation
model capable of predicting deformation in MIP-SL, or by using physical measurement
tools such as CMM machines or 3D scanners. To this end, we develop a Finite Element
Analysis (FEA) model to simulate the curl distortion of part built in MIP-SL process.
Reverse compensation of the original CAD model based on the physical measurement is
also conducted to demonstrate the improvement of reducing curl distortion.
14

1.2 Hypotheses
The primary goal of this research is to improve accuracy of built part in mask image
projection based stereolithography process. As introduced in previous sections, the
deformation is one of the biggest and most critical problems in SLA and other AM
processes. Some research have been conducted to investigate methods to reduce
deformation in the conventional SLA process. However, little research work has been
conducted related to deformation control in MIP-SL process. Although MIP-SL process
has higher speed compared with conventional SLA process, the acrylate resin it uses has
much larger shrinkage than epoxy resin used in conventional laser-based SLA process.
Thus it would be more challenging to deal with the deformation control problem in MIP-
SL process. In order to improve the part accuracy in MIP-SL process, the following
question needs to be answered:
Primary research question:

Q1. How to reduce part deformation in the mask image projection based
stereolithography process?

To answer this question, the following hypotheses are investigated:

H1. Less deformation can be achieved by using process planning methods
(exposure strategies).
H2. Deformation can be reduced by using pre-modified part geometry approach.

Exposure strategies consist of several aspects, for example, the exposure strategies
can focus on the sequence of exposing different regions with the same layer, while they
15

can also refer to using different light intensities during the exposures. Exposure strategies
can have effects on reducing volumetric shrinkage as well as thermal shrinkage. Thus,
Hypothesis 1 can be further divided into 2 sub-hypotheses:

H1.1. Part deformation can be reduced by reducing shrinkage effect by using
exposure strategies.
H1.2. Part deformation can be reduced by lowering down curing temperature of
built layer.

For the second hypothesis, using pre-modified part geometry requires the
measurement of part deformation, and reversely modifies the geometry based on that.
The measurement of deformation can either be done by using Finite Element Analysis
simulation, or by using physical measurement tools such as microscope and 3D scanner.
Thus, it is further divided into the following two hypotheses:

H2.1. Reverse compensation based on Finite Element Analysis simulation can be
adopted to improve the part accuracy.
H2.2. Reverse compensation based on physical measurement can be used to
modify original part geometry, and improve the part accuracy.

The Framework of primary research goal and hypotheses are shown in the
following Figure 1.6.
16

Figure 1.6. Research goal and hypotheses
The first hypothesis is based on the deformation sources outlined before.
Volumetric shrinkage and thermal cooling effect are two major factors contribute to the
final deformation. To reduce deformation, the straightforward idea is to investigate how
to reduce the shrinkage effect, as well as lowering down curing temperature, during
building process. It is found in the research that by decomposing the exposure of entire
region in the layer into multiple alternative exposures of several smaller regions, the
shrinkage effect can be reduced. Besides, using grayscale level exposure instead of using
normal light, curing temperature of curing layer, measured by high-resolution IR camera,
is smaller.
The exposure strategies applied in Hypothesis 1 either change the sequence of
exposures of regions or use different light intensities, while maintaining the original
geometry of part, which can only have limited effects on reducing shrinkage. As
mentioned earlier, deformation sources are very complex in MIP-SL process. The pre-
17

modified geometry method in Hypothesis 2 addresses the problem the other way. It
incorporates all deformation sources and converts the deformation control problem to a
geometry design problem, specifically, it pre-modifies the original geometry of part in
such a way that the pre-modified shape can be cancelled out by the deformation during
and after building. More precisely, it takes advantage of the deformation and uses it as a
basis to modify the original geometry, instead of reducing deformation itself. The
ultimate goal is to make the final built part close to target geometry.
1.3 Research Scope
1.3.1 Research Process and Research Content
In this research, the goal is to reduce deformation of built part in mask image
projection based stereolithography process. To achieve this goal, two hypotheses have
been proposed: (1) Less deformation can be achieved by using process planning methods
(exposure strategies); (2) Deformation can be reduced by using pre-modified part
geometry approach. The research content is focused on the verification of these two
hypotheses, while the research procedure is to verify these two hypotheses one by one,
which is shown in Figure 1.7.
As stated before, the first hypothesis tries to reduce deformation through developing
intelligent exposure strategies, which targets on reducing shrinkage during MIP-SL
process. There are two aspects of shrinkage: volumetric shrinkage that happens when
liquid resin is converted to solid polymer, and thermal shrinkage, which is involved
during the exothermic photopolymerization process. In Chapter 2, we first propose the
pattern-based mask image planning methods and outline the principle to design valid
18

mask patterns, then design and implement three types of mask patterns based on it.
Physical experiments applying these mask patterns on selected test cases have been
conducted to verify the effectiveness of these patterns. Statistical analysis has been
applied to find out the significant factors that have effects on reducing deformation of
mask patterns.

Figure 1.7. Research process
Chapter 3 presents the exposure strategies aiming at reducing thermal shrinkage.
The curing temperature distribution and evolution during MIP-SL process is studied by
using in-situ IR camera. Effects of layer thickness, curing region sizes and shapes on
curing temperature are investigated by conducting designed experiments. Besides, the
curing temperatures of built layers are studied using different exposure strategies
including varying exposure time, grayscale levels and mask image patterns. Based on the
curing temperature studying results, different exposure strategies, such as using grayscale
19

levels and mask image patterns, have been designed. Physical experiments show that curl
distortion can be effectively reduced by decreasing the curing temperature of built layers
when applying designed exposure strategies.
The second hypothesis plans to use pre-modified geometry method to compensate
deformation of built part in MIP-SL process. To reverse compensate the deformed model,
the deformation needs to measured. There are two approaches to measure the
deformation: one is to use FEA simulation to predict deformation, while the other is to
use physical measurement tools such as CMM or 3D scanner. Chapter 4 presents the pre-
modified geometry method based on FEA simulation. Reverse compensation is
conducted after the deformation is predicted. COMSOL Multiphysics FEA software
package is adopted to simulate deformation of built part in MIP-SL process. The
deformation of built part can be modeled as structural mechanics problem, where the
shrinkage during the building process can be considered as loads. The material behavior
of each layer is assumed to be linear elastic. The curing temperature calibrated in Chapter
3 is included as thermal load for each layer. To model the layer-by-layer dynamic
building process, the birth and death technique is applied to activate the building layers
step by step. Test cases have been selected to go through the simulation process to
demonstrate the capability of FEA simulation framework. Reverse compensation has
been conducted on a simple rectangular bar test case to show the effectiveness of using
compensated geometry.
In Chapter 5, the pre-modified geometry approach based on physical experiments
and measurements is presented. A general reverse compensation computation framework
20

based on physical experiments to reduce deformation of built parts is introduced.
Corresponding points between nominal and deformed shapes are found by applying
cross-parameterization using feature points. By studying relations of offsets and
deformation for each point, the reverse compensated models can be calculated. Two test
cases have been selected to demonstrate the effectiveness of the presented computation
framework. The final compensated STL models are built and compared with original
models. It is found that the compensated models can greatly reduce the shape
deformation for both test cases.
1.3.2 Research Methodology
This research is conducted based on three types of methodologies: analytical
research, experimental research and developmental research, as shown in Figure 1.8.

Figure 1.8. Research methodologies

21

These three types of research methodologies are not independent, but rather
correlated with each other. For example, the deformation problem was firstly analyzed by
identifying the deformation sources, exposure strategies were designed and implemented
using a developed algorithm. Physical experiments were conducted to verify the
effectiveness of designed exposure strategies, which in turn lead to further analysis of
finding optimal exposure strategies and their corresponding defining parameters.
1.3.2.1 Analytical research
The analytical research is mainly focused on the following aspects: investigate the
problem, analyze the problem, and formulate or model the problem. Specifically as
follows:
(1) Investigate the problem. In this research, the goal is to reduce deformation of
built part in MIP-SL process. The deformation sources were firstly investigated, which
provide basis for following research efforts. Besides, for the pattern – based exposure
strategies to work, the design principle of valid mask patterns was investigated.
(2) Analyze the problem. For pattern – based exposure strategies, analysis of
different types of mask patterns and effects of their defining parameters was conducted.
Curing temperature distribution during single layer as well as continuous layers building
process was analyzed. Relations between curing time and different grayscale levels was
also analyzed.
(3) Formulate or model the problem. In the Finite Element Analysis of deformation,
the deformation problem was modeled as structural mechanics problem with shrinkage
22

included as load. Dynamic layer-by-layer building process and part removal process were
also modeled.
1.3.2.2 Experimental research
Experimental research refers to conduct physical experiments to study the problem,
and verify effectiveness of proposed methods, which can be illustrated as:
(1) Study problem. Physical experiments are very useful to help investigating and
understanding the problems. In this research, physical experiments were designed to
study the curing temperature distribution and evolution during building process, relations
of curing temperature and curing time related to exposures using different grayscale
levels, and effects of layer thickness and shape on curing temperature. It was also
conducted to study the suitable marker size to help establish correspondence between
different models in the reverse compensation study.
(2) Verify effectiveness of proposed methods. Physical experiments were designed
with selected test cases to verify the effectiveness of exposure strategies using different
types of mask patterns, different grayscale levels, and that of the proposed reverse
compensation methods.
1.3.2.3 Developmental research
Developmental research is to develop tools to assist analytical or experimental
research, which can be categorized as:
(1) Algorithms. An algorithm was designed and implemented to generate flexible
exposure mask patterns. Correspondence between deformed model and nominal model
23

was established by using a developed algorithm. An algorithm was presented to calculate
reverse compensation.
(2) Computational framework. Reverse compensation computational framework
based on physical experiments and FEA simulation have been designed and implemented.
24

Chapter 2 Path Planning Method & Exposure Strategies on
Reducing Deformation
In this chapter, a mask image planning method for the MIP-SL process is presented
for reducing the shrinkage and related deformation in the fabricated objects. The basic
idea of the approach is to generate different exposure mask patterns on each layer, similar
to the scanning or build styles developed for the laser-based SLA process. Even though a
lot of research has been done for the scanning-based SLA process, we did not find
literatures that reported related efforts for the projection-based MIP-SL process. Similar
to the scanning strategies as studies in the SLA process, it is critical to identify
appropriate mask image exposure strategies. Three different exposure strategies have
been studied in our research. The related mask patterns, as well as their defining
parameters, are characterized. More exposure strategies can be generated by exploiting
the possible combinations of the defining parameters in each pattern. A software system
has been developed that can plan mask images with desired mask patterns for any given
CAD model. Two test cases have been designed to verify and investigate the effects of
proposed mask patterns exposure strategies. Statistical analysis has been applied to
identify the most significant parameters in the explored exposure strategies. The
experimental results provide the guidance on choosing the optimum combinations of
these parameters for achieving the best accuracy of built parts.
25

2.1. Mask Image Planning of MIP-SL
There are several possible ways for reducing the shrinkage in the MIP-SL process.
For example, one effective way of reducing the shrinkage is to develop a liquid resin for
MIP-SL that has less shrinkage. Another way is to modify the CAD model to compensate
the shrinkage-related shape deformation that may happen in the building process. The
approach considered in this chapter is to intelligently set mask images during the building
process such that less shrinkage will occur to the built objects.
A simple example to illustrate our approach is given in Figure 2.1. For a given CAD
model as shown in Figure 2.1(a), a slicing plane related to the model is shown in Figure
2.1(b). The mask image of the sliced layer is shown in Figure 2.1(c). Currently both
research and commercial MIP-SL systems [16-28] are directly using such a mask image
in building a related layer. Since no mask patterns are applied, the shrinkage of the layer
is large if the projected area is large. Alternatively, one exposure strategy is to use a solid
boundary with square patterns as shown in Figure 2.1(d) to cure the layer. For such a
projection image, all the cured areas are small and, more importantly, separated.
Consequently, the shrinkage would be much smaller. This is similar to the use of a set of
scanning vectors instead of filling vectors in the SLA process to cure each layer in order
to reduce part shrinkage. Another exposure strategy that can be learned from the SLA
process is to project the internal portions first (refer to Figure 2.1(e)). After the internal
portions have been cured, a mask image related to the layer boundary can then be
projected to define the final shape of the layer (refer to Figure 2.1(f)). This is similar to
the use of border vectors in the SLA process. Such a strategy is called “Boundary
26

Exposure Last”. In the remaining of the section, the principle of setting such mask image
patterns is first discussed, based on which the steps of creating mask pattern exposure
strategies are summarized. Then three candidate patterns that are further investigated in
our research are presented.

Figure 2.1. An illustration of mask image exposure strategies. (a) An input 3D CAD model; (b) a
2D slicing plane related to the 3D model; (c) a sliced layer image; (d) a mask image based on a
defined mask pattern; (e) the internal portion of the mask image; (f) the boundary portion of the
mask image
2.1.1 Principle of Pattern-based Mask Image Planning Method
To reduce the part deformation in the MIP-SL process, the approach of alternatively
exposing different cross-sectional regions (or the volume) of the part in each layer is
explored. As well demonstrated in the SLA process, the larger the cross-sectional region
is, the more shrinkage it will have due to the factors such as the density difference
between solid and liquid, and the internal stress associated with the temperature increase
and decrease in the polymerization process. Thus, instead of curing the whole layer in
one exposure, an alternative curing strategy based on mask patterns is to decompose the
27

exposure of a large area in one layer into several exposures of smaller areas in several
layers. When all these smaller regions are cured, the whole volume of the CAD model
will be cured without leaving any voids that are uncured. Figure 2.2 presents a simple
example to illustrate the idea. Note that in both the SLA and the MIP-SL processes,
overcure is required in order for a newly cured layer to bond with previous layers. An
appropriate projection time can be set to ensure an exposed image at current layer i will
also cure the resins at the same position in the previous few layers (e.g. > 4 layers as
shown in Figure 2.2). Such small regions are denoted as exposure mask patterns in this
research.

Figure 2.2. A large region in one layer is decomposed into exposures of four small regions in four
layers
To develop an effective exposure strategy, it is desired to understand how the
exposure of a large region can be decomposed into multiple exposures of smaller regions.
As shown in Figure 2.2, suppose a cube whose cross-sectional region is A needs to be
cured. The cube has many layers with the same shape in each layer. If no exposure mask
pattern was applied on each layer, the same mask image A would be exposed in building
28

each layer. However, when adopting a mask pattern based exposure strategy, only 1/4 of
the cube will be exposed in each of the four layers. That is, A
1
can be exposed in the first
layer, A
2
in the second layer, A
3
in the third layer, A
4
in the fourth layer, and repeat the
patterns for the remaining layers. Note that the exposure of A
2
in the second layer will
cure the region A
2
in both first and second layers due to overcure (i.e. light will penetrate
several layers down). Similarly, the exposure of A
3
and A
4
will cure the related regions in
the bottom few layers. Hence, the whole volume of the cube will be cured completely
after iteratively exposing these four mask patterns. For the few layers that are the closest
to the top surface of the cube, the whole projection region (A) will still be used to ensure
the whole volume will be completely cured after the building process.
2.1.2 Overview of Pattern-based Mask Image Planning Method
The steps for decomposing the exposure of a larger region into the exposures of
smaller regions can be summarized as follows:
Suppose the internal area of a large region to be exposed in a layer is A
Internal
and the
maximum overcure layer number is N (N > 1).
For the ith layer (1 , i M M N    ), design the mask pattern such that the area
related to the designed pattern shapes are A
Internal_i
.
When building these M layers, A
Internal
and A
Internal_i
must satisfy:
_
1
( )
M
Internal Internal i
i
A A



 such that the area of A
Internal
can be cured. If not, the designed
patterns in these M layers are not valid because there will be voids that are not cured.
29

If yes, the designed patterns can be iteratively used for the internal volume of the
object to ensure all the layers will be properly cured.
It must be noted that the generated mask patterns based on the above steps can also
be applied in less than M layers, in order to cure the entire region. For example, for the
decomposition as shown in Figure 2.2, the larger region A is decomposed into 4 smaller
regions A
1
, A
2
, A
3
and A
4
. After applying these four mask patterns in four continuous
layers, the entire region is cured. However, it is also possible to apply 2, 3 or 4 mask
patterns iteratively in the same layer, and apply remaining patterns in the continuous
layers. However, the building time of the related exposing methods will be much longer
than the original exposure approach, although they may have some advantages on
reducing deformations (e.g. due to lower curing temperature). These kinds of exposure
strategies and a hybrid approach based on them will be further investigated in the future
work.
Note that the mask patterns should only be applied to the internal volumes of an
object. They should not be used for the part boundary since multiple exposures on the
boundary may adversely affect its surface quality. Consequently, it is important to
separately perform the mask image planning for the boundary and internal portions of an
object. Suppose a given CAD model is denoted as S and a boundary distance is given as r.
Offsetting S by r into a grown or shrunken version of S has been precisely defined for
point sets in Euclidean space E
2
or E
3
[74]. Suppose S shrunk by r is defined as S 
r
.
Accordingly the internal volume of S is I(S) = S 
r
(refer to Figure 2.3). The part
boundary of S is B(S) = S  I(S), where ‘ ’ is the subtraction between the two models.
30

Figure 2.3. An illustration of internal volume and boundary of a given solid model
Since only the internal volume of an object will be applied with the mask patterns,
neither the part boundaries (both in the XY and Z directions) nor small features will be
affected by the mask-pattern-based exposure strategy. This is further explained in more
details as follows.
(1) In addition to the part boundary in the XY axes (refer to an example in Figure
2.1(f)), the part boundary in the Z axis will also be fully exposed without applying mask
patterns. Figure 2.4 shows some layer examples based on the CAD model as shown in
Figure 2.1(a). For slicing layers that are adjacent to the planes of A, B, and C, the related
mask images after applying the square mask pattern are shown in the same figure. Note
that the pixels that are related to the part boundary B(S) are fully exposed. This can
ensure that built object will not have any uncured portions on its boundary.
31

Figure 2.4. An illustration of part boundary in the Z axis and related projection images
(2) For a given boundary distance r, any features that are smaller than a circle with
the radius r will not have any internal volume. Hence such features will be fully exposed
without considering any mask pattern. A small region is typically not problematic for
deformation since the shrinkages of such small features are quite small anyway. Applying
mask patterns only to a large volume inside the built object can be effective. An example
to illustrate the building of small features is given in Figure 2.5.

Figure 2.5. An illustration of the developed exposure strategy that differently handles small
features and large regions
A set of small features and three large regions are shown in Figure 2.5(a). For a
given offsetting distance, the computed internal volume I(S) is shown in Figure 2.5(b).
(a) (b) (c)
Small features
32

Hence only the pixels related to I(S) will be applied with the square mask pattern (refer to
Figure 2.5(c)). All the other pixels in Figure 2.5(a) are B(S) and will not be changed in
the computed projection images.
Hence, during the mask image planning process, all the pixels in a sliced image can
be classified into boundary pixels and internal pixels based on the idea of solid offsetting
[74]. Accordingly, the mask patterns will only be applied to all the internal pixels while
the boundary pixels will not be changed. The development of appropriate exposure
patterns for internal volumes will discussed as follows.
2.1.3 Examples of Exposure Patterns
Many exposure patterns can be defined as long as the aforementioned criteria in
Section 2.1.2 are satisfied. In this research, three types of exposure patterns are designed.
Their effects on reducing the shrinkage and related distortion in the MIP-SL process are
investigated. Figure 2.6 shows the three exposure patterns that are studied. The first
exposure pattern is designated as an isolated cube pattern, in which the large rectangular
region are decomposed into four cubes (refer to Figure 2.2). The second exposure pattern
is designated as a loop structure pattern, in which several loops are used for forming a
large rectangular region. The third exposure pattern is called a weave structure pattern, in
which a set of grid patterns are used for covering a large rectangular region. Detailed
definitions of these three mask patterns are described in Section 2.2. These three
exposure patterns represent the three connection types that may exist between the
subdivided regions, i.e. surface, volume and line connections. For each connection type,
33

there may be some other exposure patterns that will be further investigated in our future
work.

Figure 2.6. Three exposure mask patterns. (a) Isolated cube; (b) loop structure; (c) weave
structure
2.2 Exposure Patterns and Parameters
The three types of exposure mask patterns including the isolated cube pattern, loop
structure pattern, and weave structure pattern are defined as follows. The related
parameters to characterize each exposure mask pattern are also presented.
2.2.1 Isolated Cube Pattern
Isolated squares with different sizes can be defined in the isolated cube pattern.
Hence, for a given 2D mask image, only portions of the image that are related to the
defined cubes will be fabricated when building the 2D layer. The pattern description is
shown in Figure 2.7(a). In the text definition, the notation “#” denotes the area to be
cured, while “0” denotes the area that will not be cured.
(a) (b)
(c)
34

Figure 2.7. Isolated cube pattern. (a) Pattern definition with gap size of 5 pixels; (b) mask image
with gap size of 5 pixels; (c) mask image with gap size of 8 pixels
One of the main parameter that defines the isolated cube pattern is the Gap Sizes in
both the X and Y axes. As shown in Figure 2.7(a), the Gap Size in the X or Y axes is the
size (in pixels) between two neighboring small cured regions along the related direction.
Although different Gap Sizes can be set, the same value was used in our study by
assuming it is symmetry along the two directions. An example of a mask image based on
different Gap Sizes is given in Figure 2.7. In Figure 2.7(b), the Gap Size of 5 pixels is
used; in comparison, the mask image based on the Gap Size of 8 pixels is shown in
Figure 2.7(c). Both examples use a pattern size of 32×32 pixels.
Suppose the Iteration Number of the isolated cube pattern (N) is 4. As shown in
Figure 2.2, four consecutive layers (i, .., i+3) need to be exposed in order for the whole
region of a current layer i is cured. Within each layer, the cured squares are shifted to
another potion of the mask pattern that has not been cured in the previous three layers.
Each mask pattern can also be applied multiple times on continuous layers if the overcure
is big or the layer thickness is small, or it is acceptable to have uncured resin inside the
(a) (b) (c)

built object that will be fully cured during the p
suppose each exposure pattern is applied twice for two neighboring layers. The four mask
patterns will be applied for 8
cube pattern will be 8. In addition
Iteration Number also applies to other exposure patterns.
2.2.2 Loop Structure Pattern
Figure 2.8 shows the pattern definition of a
patterns as shown in Figure
in each exposure. That is,
cured area in mask pattern 1; similarly,
the thickness of cured areas in mask patterns 2, 3, and 4, respectively. An example of the
loop structure pattern is shown in Figure
example, a = 8, b = 8, c = 8
Fig
built object that will be fully cured during the post-processing process. As an example,
suppose each exposure pattern is applied twice for two neighboring layers. The four mask
patterns will be applied for 8 continuous layers. Thus the Iteration Number
will be 8. In addition to the isolated cube pattern, the defined notation of
also applies to other exposure patterns.
Loop Structure Pattern
shows the pattern definition of a loop structure pattern. In the four mask
patterns as shown in Figure 2.8, parameters a, b, c, and d describe the sizes of cured loops
in each exposure. That is, a defines the number of pixels in a row and in a column of the
cured area in mask pattern 1; similarly, b, c, and d defines the number of pixels related to
ckness of cured areas in mask patterns 2, 3, and 4, respectively. An example of the
loop structure pattern is shown in Figure 2.9 to illustrate the defined parameters
a = 8, b = 8, c = 8, and d = 8 for a pattern size of 32×32 pixels.
Figure 2.8. Pattern definition of loop structure
35
processing process. As an example,
suppose each exposure pattern is applied twice for two neighboring layers. The four mask
Iteration Number of the isolated
, the defined notation of
. In the four mask
describe the sizes of cured loops
defines the number of pixels in a row and in a column of the
defines the number of pixels related to
ckness of cured areas in mask patterns 2, 3, and 4, respectively. An example of the
parameters. In the
for a pattern size of 32×32 pixels.

Figure
2.2.3 Weave Structure Patter
Figure 2.10 shows the pattern definition of a
Figure
In this exposure pattern, a weave
types of weave-structures are shifted to different potions of a region. Hence the whole
volume will be cured when the mask images based on the four patterns are applied
continuously. For the defined
adopted to characterize the pattern design. The

Figure 2.9. Mask images based on loop structure patterns
Weave Structure Pattern
shows the pattern definition of a weave structure pattern
Figure 2.10. Pattern definition of weave structure pattern
In this exposure pattern, a weave-structure region is cured in each laye
structures are shifted to different potions of a region. Hence the whole
volume will be cured when the mask images based on the four patterns are applied
continuously. For the defined weave structure pattern, a parameter denoted
adopted to characterize the pattern design. The Gap Size is defined as the number of
36
weave structure pattern.

structure region is cured in each layer; and four
structures are shifted to different potions of a region. Hence the whole
volume will be cured when the mask images based on the four patterns are applied
, a parameter denoted as Gap Size is
is defined as the number of
37

pixels in the X and Y axes of uncured square area. In the example pattern as shown in
Figure 2.10, a Gap Size is set as 8 for the defined weave structure pattern. A larger gap
size means smaller regions will be cured in each layer. Figure 2.6(c) presents a mask
image example based on the defined weave structure pattern.
2.3 Pattern-based Mask Image Planning Study for MIP-SL
Figure 2.11 shows the workflow of fabricating a simple cube using the specified
mask patterns.

Figure 2.11. Workflow of part fabrication using defined exposure mask patterns
For a given CAD model that is saved in the STL format, a software system will
slice the model into a set of 2D layers based on a given layer thickness. The exposure
mask patterns to be used for the internal volume can then be specified by the user.
Accordingly, a set of modified 2D mask images will be automatically generated. The
mask images will then be sent to the MIP-SL machine. The building parameters, such as
the exposure time for each layer, can also be set by the user. The physical object defined
38

by the CAD model is built after all the 2D layers have been cured in the building process.
Finally, its accuracy and deformation are measured in order to understand the effects of
the used mask patterns.
The slicing of a 3D model into a set of 2D layers has been extensively studied
before. As discussed before, modifying the sliced images based on given mask patterns
needs to consider the types of pixels in a given projection image. That is, no mask pattern
should be used for the boundary pixels in the X, Y and Z axes. Based on a given CAD
model S and a given thickness r, a 3D offsetting operation based on the Layered Depth-
Normal Images (LDNI) can be used to compute the CAD model of S 
r
[74]. Accordingly,
the sliced images of S 
r
based on the same layer thickness can be used for identifying the
inner and boundary pixels of S. As discussed in Section 2.1.2, the boundary pixels will
not be modified; while the defined mask patterns will be used in modifying the internal
pixels (refer to an example in Figure 2.4). The algorithm for adding desired exposure
patterns in sliced layers of a given CAD model is shown in Figure 2.12.
For each layer to be processed, the algorithm will also check whether the layer will
use the exposure strategy of “Boundary Exposure Last”. That is, the inner regions can be
cured first before the part boundary is to be cured. This is similar to the scanning strategy
adopted in the SLA process by using hatching vectors first before applying border vectors
in the end. If the layer requires “Boundary Exposure Last”, the algorithm will generate a
mask image with only the inner region of the original sliced layer after applying the
desired mask pattern. An additional mask image with only the boundary pixels of the
original sliced layer will be generated. An example of setting “Boundary Exposure Last”
39

is shown in Figure 2.13. Accordingly, when building the layer, the MIP-SL system will
expose the resin surface twice, first using mask pattern in inner region and then mask of
boundary. A side effect of using “Boundary Exposure Last” is that the building process
will be even slower compared to projecting one mask image that combines both boundary
and inner pixels.

Figure 2.12. Algorithm of exposure mask pattern generating program

40

Figure 2.13. An example of using “Boundary Exposure Last”
A mask image planning testbed has been developed using C++ programming
language with Microsoft Visual C++ 2005. The program can automatically generate 2D
mask images with different exposure patterns for a given 3D model. A general
architecture based on defining desired exposure mask patterns as individual INI files is
adopted. As shown in Figures 2.7, 2.8 and 2.10, a user can easily use notations of ‘#’ and
‘0’ in a text editor to define the exposure mask patterns to be used. The size of each ‘#’
and ‘0’ is 1×1 pixel. The mask pattern can thus define a region of 32×32 pixels or some
other sizes. Besides mask patterns, the user can also specify the boundary thickness, the
layer range to apply the mask patterns, whether to use “Boundary Exposure Last”, etc.
2.4 Experimental Setup
A commercially available MIP-SL system, the Ultra machine [24] from
EnvisionTEC Inc. (Dearborn, MI), is used in physical experiments. The Ultra machine
accepts mask images that are defined as BMP or PNG files. For each mask image, a
related exposure time needs to be specified. In this research, experiments using an
41

isolated cube pattern are first conducted to verify the effectiveness of applying mask
pattern exposure strategy on reducing distortion. Then, experiments based on the three
exposure mask patterns as described in Section 2.2 are performed. Their effects on
reducing the shrinkage of built objects are investigated using different combinations of
the defining parameters.
The experimental procedure is described as follows. First, a benchmark test part is
fabricated without any exposure mask pattern. The part serves as a control group. Then,
test parts with “treatments” by applying different exposure strategies are built. In addition
to different exposure mask patterns and related defining parameters, the effect of setting
“Boundary Exposure Last” is also investigated. If Boundary Exposure Last is set, the
building of each layer will be decomposed into two exposures, the projections of the
mask with inner regions and the mask with the boundary. Between the two exposures, the
platform will not move in the Z axis. In our study, the boundary thickness is set at
0.45mm (3 pixels).
For the first experiment, the isolated cube structure pattern, with gap size 8 pixels,
Iteration Number 4 and with Boundary Exposure Last is used. For the experiments to
investigate the effects of different mask patterns and parameters, the following patterns
and combinations of parameters are studied:
(1) In the isolated cube structure pattern, experiments with the combinations of
following parameter values are considered: Gap size = 5, 6, 7, or 8 pixels, Iteration
Number = 4, 8, or 12, and with or without Boundary Exposure Last.
42

(2) In the loop structure pattern, experiments are conducted with the combinations
of the following parameter values: size a = b = c = d = 8 pixels, a = 12, b = c = 8, d = 4
pixels, Iteration Number = 4, and with or without Boundary Exposure Last.
(3) In the weave structure pattern, experiments are conducted with the
combinations of the following parameter values: size = 8, Iteration Number = 4, or 8, and
with or without Boundary Exposure Last.
Due to the cost of the experiments, a Design of Experiment (DOE) approach based
on a Full Factorial Design is applied to the parameter combinations in these experiments
to investigate their effects.
2.5 Experiment Results and Discussions
2.5.1 Test Case 1
A simple rectangular bar test part (similar to the one shown in Figure 1.4(c), differs
only in thickness) is selected to verify the effectiveness of the proposed mask pattern
exposure strategy. The physical built test part and its 2D sketch are shown in Figure
2.14(a) and 2.14(b), respectively. The size of test part is 60 mm in length, 5 mm in width
and 2.6 mm in thickness. A support structure of 1.6 mm height is added below the test
part. During building process, the cured layer will shrink; however, the shrinkage
movement is restricted by the underlying layers that have already been cured before.
Consequently, residual stresses will be generated in the built object. After building the
part, the residual stresses will be released when the part is removed from supports, which
lead to the curl distortion (refer to two tips A and B in Figure 2.14(a)).
43

Figure 2.14. Test case 1. (a) Photo of built part; (b) a 2-dimensional sketch of the test part
The test parts with no mask pattern exposure, and the ones with isolated cube
pattern of Gap Size 8 pixels, Iteration Number 4 and with Boundary Exposure Last, are
built in Ultra machine with exposure time 7 s and the layer thickness of 0.05 mm for each
layer. The curl distortions of the built parts are measured using a precision measuring
machine from Micro-Vu Inc. (Windsor, CA) [75]. The resolution of the used measuring
machine is one µm. Figure 2.15 shows the schematic of the measurements, in which the
distance e is denoted as the curl distortion of the part. Ideally, e is zero if no curl
distortion exists. The curl distortion e of all the test parts are measured and compared to
show the effectiveness of the mask-pattern-based exposure strategy.

Figure 2.15. Schematic of the measured curl distortion
Three replicates for both test parts have been built. After finishing the building, the
test parts are removed from the platform. Then the supports are removed and the parts are
cleaned. Note that all the test parts strictly go through the same procedures during and
(a) (b)
44

after the building process in order to avoid any undesirable factors in the results. The
measurement curl distortion is shown in Table 2.1.
Table 2.1. Curl distortion results (e) using no mask pattern and isolate cube pattern exposure
(unit: mm)
Size: 5 x 60 x2.6mm Replicate 1 Replicate 2 Replicate 3 Mean
Baseline(no pattern) 0.345 0.406 0.376 0.38
Isolated cube pattern 0.236 0.285 0.269 0.26

The measurement results show that the average distortion for the baseline part
(without using any mask patterns) is 0.38 mm. In comparison, the test parts using the
proposed isolated cube patterns have average curl distortion of 0.26 mm. This represents
31.6% improvement compared to the baseline parts. The test case shows the effectiveness
of the proposed exposure strategy based on the isolated cube pattern.
2.5.2 Test Case 2
After verifying the effectiveness of the mask-pattern-based exposure strategy,
another test case has been designed to study what kind of exposure strategy and related
parameter combinations can have the largest improvement on distortion. The benchmark
test part designed in the study is similar to “Letter-H” that has been widely used in the
SLA accuracy study [31]. The 3D model of the designed test part is shown in Figure
2.16(a). Its 2D sketch is shown in Figure 2.16(b) with related dimensions. The bottom
base has a length and width of 101.6 mm and 20.32 mm, respectively. The total height of
the test part is 50.8 mm. The thickness of the sidewall is 2.54 mm, and the thickness of
the plate A is 5.08 mm.

Figure 2.16. The benchmark part. (a) Photo of a built object; (b) a 2
Appropriate support structures are added in the test part in order for the MIP
process to build the part. The base is positioned on a
direction is along the Z axis. During the building process, the pla
which will cause the two
such deformation. Dents on each
2.17 as the two sidewalls are pulled inwardly. The l
comparing it with the nominal value of 101.6
building process can be evaluated. One of the discussed mask pattern exposure strategies
can be used in building plate
in the built object is closer to the nominal value.
with different exposure strategies were built in Ultra machine with exposure time 9
each layer. The total number of slic
number of layers to be processed with different mask patterns is 51 (related to the layers
of Plate A).
(a)

. The benchmark part. (a) Photo of a built object; (b) a 2-dimensional sket
part
Appropriate support structures are added in the test part in order for the MIP
process to build the part. The base is positioned on a XY plane and the layer building
axis. During the building process, the plate A will shrink
which will cause the two sidewalls deform. Figure 2.17 shows the defects associated with
such deformation. Dents on each sidewall (refer to Point A and B) can be seen in Figure
walls are pulled inwardly. The length of AB can be measured. By
comparing it with the nominal value of 101.6 mm, the shrinkage of plate
building process can be evaluated. One of the discussed mask pattern exposure strategies
can be used in building plate A. The deformation is reduced if the measured length of
s closer to the nominal value. The benchmark test part and test parts
with different exposure strategies were built in Ultra machine with exposure time 9
each layer. The total number of sliced layers in the benchmark part is 508, while the
number of layers to be processed with different mask patterns is 51 (related to the layers
(b)
45

dimensional sketch of the test
Appropriate support structures are added in the test part in order for the MIP-SL
plane and the layer building
will shrink and bend,
shows the defects associated with
) can be seen in Figure
can be measured. By
mm, the shrinkage of plate A during the
building process can be evaluated. One of the discussed mask pattern exposure strategies
s reduced if the measured length of AB
The benchmark test part and test parts
with different exposure strategies were built in Ultra machine with exposure time 9 s for
ed layers in the benchmark part is 508, while the
number of layers to be processed with different mask patterns is 51 (related to the layers
46

Figure 2.17. Shrinkage comparison between (a) An optimal part, and (b) a benchmark part
2.5.2.1 Experiment Results
After finishing the building of a test part with specified mask patterns, the built
object is taken out from the platform and the post-processing including removing
supports and cleaning the part are performed. Afterwards, the length of AB is measured
using the Micro-Vu precision measuring machine. The measured result is saved and
compared with the nominal length.
Table 2.2 shows the measurement result of the benchmark test part without
applying any exposure mask patterns. Three measurements are performed for each built
part. The Mean value and standard deviation of the measurements are calculated. In the
table, absolute shrinkage (Error) is defined as
min no al mean
Error L L   ; and the shrinkage
rate (Error%) is defined as
min min
% ( ) / *100%
no al mean no al
Error L L L   , where
min no al
L is
the nominal dimension of length AB (i.e. 101.6 mm),
mean
L is its corresponding calculated
mean dimension using the three measurements.
47

Table 2.2. Measurements of length AB in the benchmark test part (unit: mm, M
1,2,3
are
measurements)
Nominal M
1
M
2
M
3
Mean Std Error Error %
101.6 99.261 99.256 99.273 99.263 0.0087 2.337 2.3

All the test parts by applying different exposure patterns have undergone the same
building and post-processing steps. The built objects have also been measured using the
same procedure. Table 2.3 show their shrinkage results compared to the benchmark part.
The shrinkage improvement is calculated by (Error%
benchmark
-Error%
patterns
)/ Error%
benchmark
,
where Error%
benchmark
is the shrinkage rate of benchmark part (i.e. 2.3% as shown in Table
2.2), and Error%
patterns
is the shrinkage rate of a test part using a designed exposure
pattern.
Table 2.3. Results using different exposure strategies
Results Comparisons
Type Data show the shrinkage improvement
Isolated
Cube
Gaps(Pixels)
Using Boundary
Exposure
No Boundary Exposure
Iteration Number Iteration Number
4 8 4 8
7 12.93 16.87 9.33
8.55(Gap size is 5 pixels)
16.05(Gap size is 6 pixels)
17.88
13.02
(Iteration Number is 12)
8 26.28 30.72 22.92 32.32

Loop
Sizes(Pixels) 4 4
a=b=c=d=8 18.88 17.99
A=12 b=c=8
c=4
19.16 15.42

Weave
Gap Sizes(Pixels) 4 8
8 -1.38 -0.13
48

As shown in Table 2.3, the exposure strategy based on the isolated cube pattern
with parameters of Gap Size = 8, Iteration Number = 8 and without Boundary Exposure
Last leads to the best shrinkage improvement (a 32.32% improvement compared to the
benchmark test part without adding any exposure patterns). A picture of the built part
based on such a configuration is shown in Figure 2.17(a); in comparison, a picture of the
benchmark test part is shown in Figure 2.17(b). The differences of the dents generated in
A and B points can easily be observed in the built objects.
2.5.2.2 Results Analysis and Discussions
As shown in Table 2.3, the test parts using the isolated cube exposure patterns
generally have better improvements on reducing shrinkage than the test parts using the
loop structure and the weave structure patterns. In addition, for the test parts based on
the isolated cube patterns, better shrinkage improvement in the test parts is achieved with
a bigger Gap Size.
Figure 2.18 shows the shrinkage improvement of test parts using different Gap
Sizes, however, the same exposure parameters of Iteration Number (set at 8) and with
Boundary Exposure Last. When the Gap Size is 5, the shrinkage improvement compared
to the benchmark part is 8.55%. Such an improvement rises to 32.32% using Gap Size of
8. The rising trend is reasonable because the larger the Gap Size, the smaller the size of
cubes will be cured, which will lead to less shrinkage in the built model.
49

Figure 2.18. Relations between Gap Sizes and shrinkage improvement
Another parameter related to the isolated cube exposure patterns is the Iteration
Number. Figures 2.19 and 2.20 show the effects of Iteration Number on test parts using
Gap Size of 7 and 8 pixels, respectively.

Figure 2.19. The effect of Iteration Number on Gap Size = 7
When Iteration Number increases from 4 to 8, the shrinkage rate decreases in both
test parts using Gap Size of 7 and 8 pixels, irrespective of using Boundary Exposure Last
50

or not. However, in test part using Gap Size of 7 pixels, the shrinkage rate of test part
using Iteration Number of 12 is larger than that using Iteration Number of 8. The
experiments shows that using Iteration Number of 8 can have the best shrinkage
improvement among these three Iteration Numbers in the isolated cube patterns.

Figure 2.20. The effect of Iteration Number on Gap Size = 8
For the loop structure exposure patterns, the test parts using pattern size of
a=b=c=d=8 pixels have better shrinkage improvement than those using pattern size of
a=12, b=c=8, d=4 pixels when Iteration Number is 4 and without applying Boundary
Exposure Last. However, as shown in Figure 2.21, no obvious differences exist when the
Boundary Exposure Last is applied. When the results of the same pattern size using
different Boundary Exposure Last strategies are compared, it is found the test parts using
the Boundary Exposure Last strategy have less shrinkage than the ones without using it.
This result shows that the Boundary Exposure Last strategy can be useful in improving
the accuracy of test parts based on the loop exposure patterns.
51

Figure 2.21. Shrinkage improvement of loop structure patterns
For the weave structure exposure patterns, two test parts using Gap Size = 8,
Iteration Number = 4 and 8, without Boundary Exposure Last have been built. The
results show that no obvious shrinkage improvement is observed. Hence, no further
experiments have been performed using the weave structure exposure patterns with other
parameter settings.
As mentioned before, for different exposure patterns, the connections between
cured regions in each layer are different. In the isolated cube pattern, each cured cube is
isolated. Hence less connection exists between the neighboring cured cubes. Accordingly,
the shrinkage in each cured cube may have little impact on other cubes and the part
boundary. However, in the loop structure and weave structure patterns, cured regions are
more connected to each other, hence the shrinkage on one cured region may affect the
other regions, which leads to bigger shrinkage in the built object.
52

In order to understand which factors are significant in the isolated structure pattern,
the Full Factorial Design method is applied to analyze the measured data. As stated
before, the shrinkage of Plate A can cause the length of AB smaller than the nominal size
(101.6 mm). The shrinkage can be calculated by (101.6 ) /101.6*100%
measured
AB  . Thus,
the physical dimension of AB was chosen as the response in the experiments.
In this exposure strategy, three factors can have effects on the shrinkage including
the Gap Size between squares, pattern Iteration Number, and using Boundary Exposure
Last or not. Thus, the three factors are considered: Gap Size (A), Iteration Number (B),
Boundary Exposure Last (C). Each factor has two levels: Gap Size = 7 or 8 pixels,
Iteration Number = 4 or 8, Boundary Exposure = 0 (no) or 1 (yes). The factors and the
related levels are shown in Table 2.4.
Table 2.4. Factors and levels for the isolated strcutrue pattern
Factor Level
- +
A. Gap Size(pixels) 7 8
B. Iteration Number 4 8
C. Boundary Exposure 0 1

The purpose of this Full Factorial Design experiment is to find the optimal factors
and the levels that can move the response closer to the nominal value with a variation that
is as small as possible. Each treatment is run for three times. The data are shown in Table
2.5, in which y is the average of the response, while
2
ln s is the natural logarithm of
sample variance of the response.
53

Table 2.5. Design matrix and AB dimension data
Run
Factor
AB Dimension (mm)
y
2
ln S
A B C
1 - + - 99.59848 99.62896 99.6315 99.61965 -7.99355
2 + + - 99.89058 99.91598 99.90328 99.90328 -8.73231
3 - - - 99.441 99.41814 99.40544 99.42153 -8.03251
4 + - - 99.74072 99.74326 99.73564 99.73987 -11.1039
5 + + + 99.8347 99.82962 99.83978 99.8347 -10.5649
6 - + + 99.59594 99.6188 99.61372 99.60949 -8.8451
7 + - + 99.73056 99.71532 99.73564 99.72717 -9.09855
8 - - + 99.52482 99.52228 99.51466 99.52059 -10.4848

A statistic software JMP from SAS Institute Inc. (Cary, NC) is used to do the 2
3
Full
Factorial Design analysis. According to JMP, the factorial estimated contrasts are shown
in Table 2.6. Half-normal plots for location effects and dispersion effects are shown in
Figures 2.22 and 2.23, respectively.
Table 2.6. Factorial estimated contrasts
Effect y

2
Ins

A 0.12922 -0.517952
B 0.06974 0.322994
C 0.00095 -0.391391
A*B -0.00201 -0.096684
A*C -0.02127 0.434579
B*C -0.02064 -0.279642
A*B*C 0.00667 -0.679837

54

Figure 2.22. Half-normal plot of location effects

Figure 2.23. Half-normal plot of dispersion effects
According to the half-normal plots, main factors A and B are significant factors in
location model, while factor ABC is significant in dispersion model. By applying
regression analysis to the y data and
2
Ins data given in Table 2.5(let
2
z ln s  ), the
following regression equations are generated.
ˆ 99.672 0.12922 0.06974
A B
y x x   

55

ˆ 9.375 0.6798
A B C
z x x x   

The recommended level for ABC is the +1 to reduce the variance.
In order to move ˆ y close to 101.6, levels 1, 1
A B
x x   are chosen by
approximating the equation: 99.672 0.12922 0.06974 101.6
A B
x x    , and 1
C
x  .That is,
the recommended settings are Gap Size = 8, Iteration Number = 8, and using Boundary
Exposure Last.
The statistical analysis result is consistent with the physical experiment results
except for the last parameter, the setting of Boundary Exposure Last. In the physical
experiments, the part using No Boundary Exposure Last with Gap Size of 8 pixels and
Iteration Number of 8 has better shrinkage improvement than that using Boundary
Exposure Last. In comparison, the statistical analysis suggests to use Boundary Exposure
Last. We think this is because the statistical analysis predicts the trend of final result
using different combinations of parameters with the aim of keeping the final result close
to nominal value while maintaining the smallest variance. The number of physical
experiments performed in our study is not sufficiently large for the specified parameter
combinations. If more physical experiments have been conducted, the physical
experiments results may better support the statistical analysis result.
2.6 Concluding Remarks
Due to the fast building speed and low cost, the mask image projection-based
stereolithography (MIP-SL) process based on digital micromirror devices has been
widely recognized as a promising process for future development of low-cost 3D printers.
56

However, the shrinkage related deformation is one of the major challenges in the MIP-SL
process. To improve the accuracy of a built object, a mask image planning method and
the related algorithms based on applying designed mask patterns to the internal volume of
a built object have been presented. Our method is motivated by the accuracy study of the
SLA process, in which various scanning strategies have been successfully developed for
improving the accuracy of built SLA parts. Similarly, various mask image patterns can be
developed for the MIP-SL process. Based on them, the curing of a large internal volume
may be accomplished by curing multiple small volumes in a single or multiple layers.
Hence the shrinkage of the whole volume and the internal stresses generated during the
curing process can be reduced. Three types of mask image patterns have been
investigated. Among them, the isolated cube pattern generally leads to a smaller
shrinkage compared to the other two types of exposing mask patterns including the loop
structure and weave structure patterns. A Full Factorial Design method has been used in
studying the significant factors and levels among the defining parameters of the isolated
cube pattern. Statistical analysis shows that all the three parameters are significant. Their
combination for achieving the best shrinkage improvement has also been identified.

57

Chapter 3 Curing Temperature Study and Exposure Strategies on
Reducing Deformation in MIP-SL Process
In order to understand the deformation in MIP-SL process, the thermal effects during
the curing process need to be studied. Temperature sensors such as thermal couples have
been used to measure the temperature changes at some sample points in a single layer in
previous research (e.g. [33]); however, it is more desired to measure the temperature
distribution of an entire cured layer dynamically, and continuously monitor the
temperature changes in multiple layers.
In this section, a high-resolution Infrared (IR) camera is adopted to in-situ monitor
curing temperature distribution and evolution in the building process of the MIP-SL
process. Designed experiments have been performed to investigate the effects of layer
thickness, curing region sizes and shapes on curing temperature. Besides, the curing
temperatures of built layers have been studied using different exposure strategies
including varying exposure time, grayscale levels and mask image patterns. The curl
distortion of a test case based on various exposure strategies, such as using grayscale
levels and mask image patterns, have been measured and analyzed. It is shown that curl
distortion can be effectively reduced by decreasing the curing temperature of built layers
when using designed exposure strategies. In addition to curl distortion control, the curing
temperature study also provides a basis for the curl distortion simulation in the MIP-SL
process.
58

3.1 Temperature Distribution Study of Cured Parts with Single Layer
In the MIP-SL process, the mask image of a sliced layer is projected onto the liquid
resin surface. Depending on the sliced geometric shapes and the slicing parameters, the
mask images may have various shapes, sizes, and layer thicknesses. All these factors may
affect the temperature distribution during the curing process. A set of experiments have
been conducted to understand their effects.
A high-resolution infrared (IR) camera (ThermoVision SC8000, FLIR System),
shown in Figure 3.1, was used in recording the real-time temperature changes. Similar
thermal sensor has been reported to be used to measure the build surface temperature in
electron beam additive manufacturing (EBAM) process [76, 77].The image resolution of
the camera is 1280×1024. At a lower resolution, the frame rate of the IR camera can be
over 100 fps. It can detect temperature differences that are smaller than 25mK [78].

Figure 3.1. The IR camera used in study –
FLIR SC8000 [79]

Figure 3.2. In-situ temperature monitoring
using IR camera in MIP-SL
The schematics of using the IR camera in the monitoring of the MIP-SL process is
shown in Figure 3.2. The IR camera is fixed beside the MIP-SL system, and its lens is
focused on the curing platform. The temperature evolution within the curing regions can
be recorded and displayed in real-time using the computer that the IR camera is
59

connected to. The recorded data is exported for further processing.
3.1.1 Calibration of IR Camera and Assumptions of Measurement
The IR camera is calibrated before it can be used for measurement. In the process of
calibration, the IR camera takes a number of blackbody measurements at several known
reference temperature (e.g. 20°C, 30°C, etc.), which creates a data table that relates
radiance values to temperature. During measurement, the IR camera detects the radiance
value from the target object, and converts it to temperature using the temperature and
radiance relation table calibrated, based on the emissivity of target object [80]. The
emissivity of acrylate resin used in our experiments is assumed to be 0.94 by looking up
the emissivity table [81]. Besides, the IR camera employs another technique, called
“Built-In NUC” (On-camera Non-Uniformity Corrections), to make the temperature
measurement accurate [82]. All experiments are conducted at room temperature (20°C).
To verify the accuracy of IR camera, the temperature of human hand is chosen as a
reference. The IR camera measurement is about 35.8°C, and a calibrated K-type
thermocouple measures about 35.7°C.
Several assumptions have been made during the temperature measurements:
(1) The effects of radiation of projector on the curing region is neglected.
(2) There is negligible difference of emissivity between cured resin and liquid resin.
Actually, the top surface of cured region is wet due to oxygen inhibition effects.
(3) Ambient environment has equal effects on the cured and uncured region, and
cured region within consecutive layers.
60

3.1.2 Experiment Design and Setup
Five test cases with two types of shapes and different sizes were designed to study the
effects of shapes and sizes on the temperature distribution of a layer. Figure 3.3 shows
the test cases including circular shapes with radius of 3", 2" and 1", and square shapes
with lengths of 2" and 3". The two shapes represent two types of boundary conditions:
curves and corners. During the experiments, the mask images of the five test cases were
projected onto the liquid resin surface using a DMD system.

Figure 3.3. Test cases of different shapes and
sizes

Figure 3.4. The setup of making single
layer of resin
Since only one sliced layer is needed in studying the curing effects of shapes and
sizes, a simple setup of making one layer of liquid resin is used (refer to Figure 3.4). Two
spacers at a set thickness (e.g. 100 μm) are used to build two guide rails on a glass
platform. Based on them, an aluminum roller is used to sweep the liquid resin into a
uniform layer on the platform with the set thickness. In the experiments, the layer
thickness is set to 100 μm, and the exposure time for each test case is 9 seconds.
The workflow of experiments is shown in Figure 3.5. One example of a built layer (a
circular shape with R = 3") is shown in Figure 3.6.
61

Figure 3.5. Workflow of one-layer experiments

Figure 3.6. A built single layer test case (a circle with R = 3")
3.1.3 Temperature Distribution
After finishing the physical experiments, the temperature data recorded by the IR
camera was exported to excel files and then processed by a Matlab program. Figure 3.7
shows the maximum temperatures when building a circle with R = 3". The figure shows
that the temperature distribution within the curing region is non-uniform. The center
portion (shaded as green and yellow regions) has lower temperatures than the other
62

portions (shaded as red regions). The temperature range is between 28.5~34°C.

Figure 3.7. The maximum temperature of a circle with R=3"
Figure 3.8 shows the temperature distribution along the X axis through the circle
center. In the figure, the Y axis denotes the temperature range (in °C), and the X axis is
the distance from the circle center (in inch). The differences between the highest and
lowest temperature regions are around 4°C.

Figure 3.8. Temperature distribution along the X axis in the circle of R=3”
63

3.1.4 The Effect of Layer Thickness
In order to understand the non-uniform temperature distribution within a cured layer,
the thickness of the built layer (refer to an example as shown in Figure 3.9) was measured
using a digital caliper with the resolution of 1 μm. Some random sampling points in the
layer were measured from different regions. Figure 3.9 shows the readings of layer
thickness in some sampling points (in μm).

Figure 3.9 Thickness measurements at some sampling points in a built circle layer (R = 3”)
The measurements show that the thickness of the built layer varies ranging from 50
to 140 μm. Initially, the target layer thickness is set to be 100 μm; however, due to the
surface tension of liquid resin and the limitations of our hardware setup, liquid resin was
not spread out uniformly at exactly 100 μm thickness.
The thickness measurement data was then oriented to be aligned with the
temperature distribution image (refer to Figure 3.7). It shows that the measured thickness
distribution matches well to the maximum temperature distribution. That is, the higher
temperatures occur at the positions where the layer thicknesses are larger. The same
results have been found in the remaining four test cases. In summary, in the regions with
64

larger layer thickness, more resin was cured by the projected light. Consequently, more
heat was generated in the region, which leads to a higher temperature in the regions.
3.1.5 The Effect of Shapes and Sizes
In the experiments, all five test cases were built. Accordingly, the temperature
distributions during the building process were recorded by using IR camera. Curing
temperatures in the same positions on the platform of five test cases were compared with
each other. The temperature differences between different shapes and sizes are shown in
Figure 3.10.

Figure 3.10. The temperature differences between overlapping areas of five test cases. (a) Circles
of R= 2" and 3"; (b) circles of R= 1" and 2"; (c) R= 1" circle and L= 2" square; (d) L= 2" and L=
3" squares
In the figure, the thermal images of these five test cases were compared by
(a) (b)
(c) (d)
65

calculating their temperature differences in the overlapping regions. The temperature
differences at different positions are represented in grayscale images. The smaller the
temperature difference is, the darker the image is. As shown in Figure 3.10, the
overlapping areas of these comparing shapes are nearly black, which means the
temperature difference in such regions is very small even they are cured in different
shapes and sizes.
In summary, experimental results show that the temperature distribution in MIP-SL
is not depended on the particular shape or size of a built layer; instead, the temperature
distribution is mainly related to the layer thickness in the built layer.
3.2 In-Situ Monitoring of Temperature Evolution in MIP-SL Using IR
Camera
After getting basic understandings of the temperature distribution within one layer of
a built part, an immediate question is how temperature evolves in the successive layers
during the building process. To answer the question, we used the IR camera to in-situ
monitor the entire building process.
It is difficult to use an IR camera to measure the temperature changes in the
constrained-surface-based MIP-SL process since the IR camera cannot see through a
glass cover [30]. In our study, we used a setup based on the free-surface-based MIP-SL
process to facilitate the IR camera measurement. That is, instead of using a glass cover to
recoat liquid resin, a blade is used in the system to form thin layers of liquid resin. For
building each layer, the blade sweeps through the platform to remove excessive resin on
the previously built layers.

Figure 3.11 shows our setup of using an IR camera to monitor the free
MIP-SL process. The IR camera is fixed on a tripod that can be adjusted to gain a proper
view of curing regions. The IR camera is connected to a computer using a cable such that
the temperature data can be transferred and recorded. When the building process starts,
real-time temperature readings can be obtained on selected points of the curing region
Figure 3.11. In-
3.2.1 Experimental Design
A set of experiments were designed to investigate how curing temperature evolves in
consecutive layers, and how building parameters like layer dimension and layer thickness
may affect temperature changes in the building process.
Figure 1.4(c) shows a rectangular thin part that has obvious curl distortion. Similar
shapes with different sizes and layer thi
monitored by the IR camera. The schematic dimension of a test part is shown in Figure
3.12 (similar to the one shown in Figure
shows the building parameters of all t
shows our setup of using an IR camera to monitor the free
SL process. The IR camera is fixed on a tripod that can be adjusted to gain a proper
curing regions. The IR camera is connected to a computer using a cable such that
the temperature data can be transferred and recorded. When the building process starts,
time temperature readings can be obtained on selected points of the curing region
-situ monitoring of the free-surface-based MIP-SL process
Design
A set of experiments were designed to investigate how curing temperature evolves in
s, and how building parameters like layer dimension and layer thickness
may affect temperature changes in the building process.
shows a rectangular thin part that has obvious curl distortion. Similar
shapes with different sizes and layer thicknesses were built in our MIP
monitored by the IR camera. The schematic dimension of a test part is shown in Figure
(similar to the one shown in Figure 2.14(b), differs only in thickness)
shows the building parameters of all the test cases based on the rectangular shape.
66
shows our setup of using an IR camera to monitor the free-surface-based
SL process. The IR camera is fixed on a tripod that can be adjusted to gain a proper
curing regions. The IR camera is connected to a computer using a cable such that
the temperature data can be transferred and recorded. When the building process starts,
time temperature readings can be obtained on selected points of the curing regions.

SL process
A set of experiments were designed to investigate how curing temperature evolves in
s, and how building parameters like layer dimension and layer thickness
shows a rectangular thin part that has obvious curl distortion. Similar
cknesses were built in our MIP-SL setup and
monitored by the IR camera. The schematic dimension of a test part is shown in Figure
, differs only in thickness). Table 3.1
he test cases based on the rectangular shape.
67

Figure 3.12. Dimensions of a built part (in mm).
Table 3.1. Dimensions and building parameters of test cases
Test case
#
Width(mm) Length(mm) Thickness(mm) Layer
Thickness(mm)
Exposure
time(s)
1 5 60 1.27 0.127 24
2 8 60 1.27 0.127 24
3 10 60 1.27 0.127 24
4 5 60 1.27 0.254 36

All these test cases were built directly on platform. For each test case, four sample
points were picked inside a curing region to show the temperature variance within the
region. Figure 3.13 shows the four sampling points and their positions related to the
curing region of a sliced rectangle. During the building process, the mean and maximum
temperatures within the curing region were recorded.

Figure 3.13. Schematics of sample points and a curing region
3.2.2 Temperature Evolution in Consecutive Layers
Figure 3.14 shows the temperature plot for cursor 1 in test case #1. It can be
68

observed that the maximum temperature in building the first 10 layers is ~31.5°C, which
is measured at the 10th layer. In comparison, the resin temperature is measured at 24.7°C.
The maximum temperature of each layer is gradually increasing. This may be caused by
the following reasons. The thermal conductivity of cured resin is low. Therefore the heat
generated during the curing process is dissipating slowly; the current layer is cured on the
top of previous layers. They may still have a higher temperature than liquid resin,
especially when the exposure time for each layer is short (e.g. 24 s).

Figure 3.14. Temperature plot at cursor 1 in test case #1
However, it can also be observed that the temperature increase rate is becoming
smaller as more layers are built. For example, the maximum temperature increases 1°C
from the 2nd to the 3rd layer; in comparison, the maximum temperature increases only
0.2°C from the 9th to the 10th layer. It suggests that the maximum temperature is getting
stable as more layers are built.
The temperature plot also shows that the maximum temperature in the first layer is
higher than that in the second layer. This may be due to the overcuring effect that exists
in the MIP-SL process. That is, the light exposure of a layer is designed to cure 2-3 layers
69

below in order to bond neighboring layers well. From our previous experiments base on a
single layer, it is observed that the temperature increase is directly related to the layer
thickness of liquid resin. The larger layer thickness leads to a higher temperature increase.
Due to the overcuring effect, the cured resin in the 1st layer may be thicker than that of
the 2nd layer.
3.2.3 One Building Cycle Analysis
In our MIP-SL system, a building cycle related to building one layer is described as
following. First, the platform moves down below the liquid resin surface. The blade
moves back to its beginning position. The platform then moves up to leave a gap of one
layer thickness. The blade sweeps across the platform to remove excess resin. Finally,
after a uniform thin layer of liquid resin has been prepared, a mask image is projected
using the DMD system to expose the liquid resin for a specified time.

Figure 3.15. Building sequence in MIP-SL process
Figure 3.15 shows the building sequence of one layer. Corresponding to the building
70

sequence, the temperature evolution in one building cycle is shown in Figure 3.16.

Figure 3.16. Temperature plot of a building cycle at cursor 1
Along the X axis of the figure, t1 corresponds to the time when the platform starts
moving down below the liquid surface; t2 is the time when the blade starts sweeping right;
t3 is the time when the blade starts sweeping left; and t4 is the time when the projection
light is turned on. The time as shown in the figure is in seconds. It takes around 10 s for
the blade to sweep from left to the right of the platform. In comparison, the light exposure
time is 24 seconds.
It is shown in the figure that the temperature at the measured point drops quickly
when the platform moves down. The temperature increases slowly in the beginning of
light exposure. This may be because it takes some time to dissolve the oxygen in the
liquid resin which prevents curing. After the curing process starts, the temperature
increases rapidly until it rises to the maximum temperature.
3.2.4 Temperature Variation Study within One Layer
The temperature evolution of the four sample points in the test case #1 is shown in
Figure 3.17.
71

Figure 3.17. Temperature at 4 sample points
Based on the figure, it can be observed that the trends of temperature increase at
these 4 points are similar. Cursor 1 has slightly higher temperatures than the other three
sample points. The reason is that cursor 1 is located at the position that is the closest to
the right boundary of the platform. Notice that the recoating in our setup is done by
sweeping the blade from right side to the left side of the platform. Therefore, cursor 1
will be recoated first. Due to liquid viscosity, it is observed that there will be some
leftover resin on the right boundary portion of a built region. This will make the right
portion in which cursor 1 locates slightly thicker. Consequently, cursor 1 will have a
higher temperature during the curing process. The other three sample points, cursors 2-4,
have very close temperature. Figure 3.18 shows their temperature comparison. The
maximum temperature increases in the building process between these points are less
than 0.2°C.
72

Figure 3.18. Temperature at 3 sample points (cursors 2- 4)
3.2.5 Verification of the Effects of Layer Size and Thickness on Temperature
Test cases 1, 2 and 3 have the same dimensions and building parameters on their
length (60 mm), thickness (1.27 mm), layer thickness (0.127 mm), and exposure time (24
s). Only their widths are different (5 mm, 8 mm and 10 mm). The mean temperatures
within the cured layers of these three test cases are shown in Figure 3.19.

Figure 3.19. Mean temperature plot in test cases 1, 2 and 3
73

It can be observed that the mean temperatures for these three test cases are close,
with the max temperatures different around 1°C. The mean temperature profiles for test
case #1 (5×60×1.27 mm) and #3 (10×60×1.27 mm) almost overlap with each other, with
the maximum temperatures difference less than 0.3°C. This also confirms our previous
experiment result that the temperature increase of a cured layer is not dependent on its
shape or size.
For the test case #2 (8×60×1.27 mm), there is slight temperature deviation from the
other two test cases. However, after careful examination, it can be observed that the
deviation comes from the first two layers. From the 3rd to 10th layer, the temperature
increase rates for the three test cases are close. The reason for the temperature deviation
in the first two layers may be due to the thinner liquid layer that is formed in the
beginning of the building process. This may be due to the inaccurate leveling of liquid
resin in test case #2.
Test case #4 has the same part sizes as test case #1; however, it uses a layer thickness
of 0.254 mm instead of 0.127 mm as used in the other three test cases. Accordingly, the
exposure time for each layer is increased from 24 s to 36 s. A comparison of the mean
temperature in test cases #1 and #4 is shown in Figure 3.20. It is shown that the
maximum temperature in test case #4 is close to 32.7°C while it is around 30.1°C in test
case 1. This is mainly due to a larger layer thickness in the building process. Similar to
the other three test cases, the temperature increase rate for test case #4 is getting smaller
as more layers are built.
74

Figure 3.20. Mean temperature in test cases #1 and #4
Based on the temperature measurement results, the following conclusions can be
drawn for the MIP-SL process.
(1) The temperature increase is not dependent on the shapes and sizes of cured
regions (e.g. the width of the rectangular part is changed between 5-10 mm in test cases
1-3).
(2) The temperature increase is mainly related to the layer thickness of a cured layer.
The larger the layer thickness, the higher the temperature will reach.
(3) For test parts built directly on platform, the temperature in each layer is getting
higher as more layers are built; however, the temperature increase rate is becoming
smaller.
3.3 Curing Temperature by Varying Exposure Time
Exposure time is a critical building parameter in the MIP-SL process. Longer
exposure time can provides more energy for the building layer, and liquid resin will be
75

more fully cured in the building process. Since heat will be generated when liquid resin
solidifies, longer exposure time may result in higher temperature of curing layer. The
relationship between exposure time and the related maximum curing temperature is
studied in the section.
3.3.1 Experiment Design
Ten different levels of exposure time (5 s, 10 s, 15 s, 20 s, 25 s, 30 s, 35 s, 40 s, 45 s
and 50 s) are used in building layers in our study for understanding how curing
temperature is related to the set exposure time. The workflow of experiments is shown in
Figure 3.21. The experiments were conducted by using a free-surface MIP-SL setup as
shown in Figure 3.11. The size of a test layer is 5 mm× 60 mm and the layer thickness is
0.127 mm (0.005 inch). In the experiments, 10 layers are first built on the platform to
form the base for building the test layers on. The base layers can also eliminate the effect
of unevenness of the platform if any. Subsequent test layers are built on the base layers or
previously built test layers. Before a test layer is built, the platform moves down to
submerge the built layers in liquid resin, and remains there for over 3 minutes until the
previously built layers cool down. After the platform moves up, the blade of the system
sweeps across the platform to prepare one thin layer of liquid resin. When projection light
is turned on to expose the curing region for a specified time (e.g. 5 s, 10 s, etc.), the IR
camera starts recording the temperature evolution at the same time. The recording time is
set to be 90 s to capture the whole cycle of temperature evolution. After testing with
specified exposure time, the test layer is then exposed with an additional 2 minutes to
make it fully cured. The IR camera is also used to record this fully curing process for 3
76

minutes. The process is then repeated for building another test layer. The experiment
workflow is designed to eliminate the effects of other factors on the curing temperature of
test layers, e.g. the accumulation of heat from previous test layers, or the variation of
different runs of experiments.

Figure 3.21. Workflow of testing various exposure time on the maximum curing temperature
3.3.2 Exposure Time Effect on Curing Temperature
The curing temperature measurement image using IR camera is shown in Figure 3.13,
in which polygon 2 is the entire curing region of a test layer. Hence the average curing
temperature of the layer can be calculated based on the measured temperatures of all the
pixels within polygon 2. The curing temperatures are recorded and can be viewed in real-
77

time through a control software system.
3.3.2.1 Exposure Time of 5 s
The average temperature of the test layer using the exposure time of 5 s is plotted in
blue curve in Figure 3.22.

Figure 3.22. Curing temperature using exposure time 5 s
The average temperature in the corresponding fully curing process using additional 2
minutes exposure is plotted in red curve in Figure 3.22. It can be observed that the
temperature increase in the blue curve is very small (from 25.3°C to 25.4°C), and the
maximum temperature is measured at the end of light exposure. However, the maximum
temperature increase in the fully curing process (red curve) is large. It takes almost 30 s
for the layer to reach the maximum temperature (around 28.7°C). Then the layer’s
temperature begins to drop even though the layer is still under the light exposure. The
light exposure of the fully curing process ends at the time t = 123 s. After that, the
temperature cools down much faster compared to when the light exposure is on.
3.3.2.2 Exposure Time of 15 s
78

The temperature plot during the curing process using the exposure time of 15 s is
shown as the blue curve in Figure 3.23.

Figure 3.23. Curing temperature using exposure time 15 s
The temperature plot during the fully curing process is shown as the red curve in
Figure 3.23. The exposure starts at time t = 8 s, and the maximum temperature during the
curing process is 27.7°C, which is measured at the end of the light exposure (t = 23 s). It
can also be seen from Figure 3.23 that temperature rises very slowly (from 25.4°C to
25.5°C) for the first 5 seconds (t = 8 s to t = 13 s), and it rises rapidly (from 25.4°C to
27.7°C) in the next 10 s under the light exposure (t = 13 s to t = 23 s). The temperature
cools down when light exposure ends, however, the cool rate drops as time passes. The
maximum temperature during the fully curing process is around 28°C. Similar to the
result as shown in Figure 3.22, the cool rate after the light exposure ends is faster than
when the light exposure is on.
3.3.2.3 Exposure Time of 45 s
The temperature plots during the curing process using the exposure time of 45 s and
79

the related fully curing process are shown as the red and blue curves in Figure 3.24,
respectively. The maximum temperature during the curing process is 28.3°C; and the
maximum temperature during the fully curing process is 26.5°C. The light exposure starts
at t = 7 s and ends at t = 52 s. The maximum temperature is measured at t = 36 s, which is
before the light exposure ends. Based on Figure 3.24, the relationship between the curing
temperature and the exposure time can be drawn as follows. For the first 5 s exposure, the
layer temperature rises slightly, which may be due to the oxygen inhibition effect [83].
For the next 24 s exposure, temperature rises rapidly to reach the maximum; however, the
increasing rate slows down. After reaching the maximum, the temperature drops even
though it is still under the light exposure.

Figure 3.24. Curing temperature using exposure time 45 s
The temperature plots during the curing process based on other exposure time (10 s,
20 s, 25 s, 30 s, 35 s, 40 s and 50 s) and the corresponding fully curing processes have
similar trends as those of using 45 s. The maximum temperatures using these ten
exposure time settings are tabulated in Table 3.2 and plotted in Figure 3.25.
80

Table 3.2. Comparisons of the exposure time effects
Exposure time(s) 5 10 15 20 25 30 35 40 45 50
Max T during
exposure(°C) 25.4 26.6 27.7 28.3 28.4 28.2 28.3 28.3 28.3 28.6
Max T during fully
curing process(°C) 28.7 28.8 28 27.4 27 26.7 26.6 26.5 26.5 26.3

Figure 3.25. Comparisons of the maximum curing temperatures using varying exposure time
As can be seen from Figure 3.25, the curing temperature rises as the exposure time
increases. The curing temperature reaches the maximum when the exposure time is
around 30 s. In the fully curing process, the maximum temperature is decreased as more
exposure time is applied in the previous exposure process. This is because more portion
of the test layer has been cured when the exposure time is increased. Thus, less portion of
resin remains to be cured in the fully curing process.
3.4 Curing Temperature by Varying Grayscale Values
Exposure based on different grayscale values can be an effective way of controlling
the input exposure energy since different grayscale level corresponds to different energy
intensity [27]. The relationship between grayscale levels and related curing temperature is
81

investigated in the section.
Eight levels of grayscale values, specifically, 70, 100, 130, 160, 190, 205, 220, and
255 are studied (the maximum and minimum light intensities are 255 and 0 respectively).
Some examples of grayscale mask images are shown in Figure 3.26. The workflow of the
experiments is similar to the one as shown in Figure 3.21 for testing various exposure
time (refer to Section 3.3). The only difference is that, instead of exposing the test layer
with a specified exposure time, the test layer is exposed using different grayscale levels
with different exposure time. The exposure time is set to ensure the curing temperature
will reach to the maximum. Experiments are designed to explore the maximum
temperature a cured layer can reach using a specific grayscale level. Likewise, the test
layer will be fully cured using grayscale 255 for 2 minutes after the light exposure using a
grayscale level has been projected.

Figure 3.26. Examples of grayscale mask images
3.4.1 Grayscale Level Exposure Study
3.4.1.1 Grayscale Level of 130
The curing temperature during the grayscale exposure process and its corresponding
fully curing process are plotted in blue and red curve, respectively, in Figure 3.27.
82

Figure 3.27. Curing temperature using grayscale 130
The exposure time of using grayscale 130 is chosen to be 45 s. It can be seen from
Figure 3.27, the temperature almost stays the same during the exposing process using
grayscale 130, while the maximum temperature during the fully curing process reaches
29°C. The temperature plot shows grayscale 130 cannot provide enough energy (less than
the critical energy) to cure liquid resin. The temperature plot of fully curing process is
very similar to the one in Section 3.3 of testing the exposure time effect.
3.4.1.2 Other Grayscale Levels
The curing temperature plots during the exposure process using the grayscale levels
of 160, 190 and 220 are shown in Figures 3.28, 3.29 and 3.30, respectively.
In Figure 3.28, the maximum temperature is around 26.7°C when using grayscale
160 with a total exposure time of 150 s. The temperature evolution is similar to the ones
in Section 3.3; however, temperature evolution rate is much slower. The light exposure
starts at t = 8 s, and ends at t = 158 s. The temperature rises little from t = 8 s to t = 33 s.
This period is denoted as the oxygen inhibition period in the paper. The temperature
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reaches the maximum at t = 117 s. That is, it takes 109 s of exposure using grayscale 160
to reach the maximum temperature.

Figure 3.28. Curing temperature using grayscale 160
Figure 3.29 shows the temperature evolution during the exposure process of using
grayscale 190 with the exposure time of 90 s. The maximum temperature reaches 27.3°C
at t = 65 s. The light exposure starts at t = 5 s, and the oxygen inhibition period lasts 16 s.

Figure 3.29. Curing temperature using grayscale 190
In Figure 3.30, the maximum temperature of using grayscale 220 reaches 28.1°C at t
= 45 s. Total light exposure time is 90 s, which starts at t = 9 s. The oxygen inhibition
period lasts 6 s, which is shorter than the ones using lower grayscale levels.
84

Figure 3.30. Curing temperature using grayscale 220
The maximum curing temperatures based on different grayscale levels are shown in
Table 3.3 and plotted in Figure 3.31.
Table 3.3. Comparisons of the grayscale exposure effects
Grayscale(0-255) 70 100 130 160 190 205 220 255
Max T during exposure(°C) 25.3 25.5 25.6 26.7 27.3 27.6 28.1 28.6
Max T during fully curing
process(°C) 29 28.7 29 27.4 26.9 26.7 26.7 26.4

As can be seen from the plot in Figure 3.31, the maximum temperature increases as
the grayscale level increases, since a higher level of grayscale level corresponds to higher
energy. Thus the curing process will be faster. A lower grayscale level can slow down the
curing process, which leads to a lower maximum temperature. Besides, the maximum
temperature drops in the fully curing process when the layer uses a higher grayscale level
in the curing process.
85

Figure 3.31. Grayscale effects on curing temperature
The time it takes to reach the maximum temperature, as well as the oxygen inhibition
period, is shown in Table 3.4 and plotted in Figure 3.32. It shows that as the grayscale
level becomes higher, the oxygen inhibition period and the time to reach the maximum
temperature decrease. This is because a higher grayscale level provides higher energy for
curing liquid resin.
Table 3.4. Grayscale effects on curing time
Grayscale level 160 190 205 220 255
Oxygen inhibition period(s) 25 16 13 6 5
Time to reach maximum T(s) 109 60 58 36 30

Figure 3.32. Grayscale effects on curing time
86

3.5 Curing Temperatures by Varying Mask Patterns
Instead of being exposed at the same time, the whole region of a test layer can be
divided into several small discrete regions, each of which can be exposed at different time.
These kind of small regions are denoted as mask patterns, as described in Chapter 2. The
temperature of a small region during the curing process is almost the same as the one
when the whole region is exposed, since the temperature is mainly related to the layer
thickness. However, the thermal cooling and polymerization shrinkage only affect the
local discrete regions. The final accuracy of the built layer may not be affected by the
temperature increase and related shrinkage of these small regions since they are not
connected with each other.
In this section, the curing temperatures of layers using varying mask patterns are
investigated. The sliced images with mask patterns studied in our experiments are shown
in Figures 3.33 and 3.34. In comparison, Figure 3.35 shows the mask image of the entire
layer without applying any patterns.

Figure 3.33. Mask pattern 1

Figure 3.34. Mask pattern 2
87

Figure 3.35. Mask image for entire region
In these mask images, the white areas denote the regions to be cured under the light
exposure, while the black regions receive no light exposure. In mask pattern 1, a gap size
of 3 pixels is designed to separate the large curing region into small regions. Mask pattern
2 exposes the gap region which is left non-cured after applying mask pattern 1. These two
mask patterns will be applied sequentially with specified exposure time. The whole
region will be cured after applying the two mask patterns (similar to using a single mask
exposure for the entire region as shown in Figure 3.35). A difference between the one by
applying two or more mask patterns and the one without using any pattern lies in the
curing temperature of built layers. After using mask patterns, the curing temperature of
the built layers may be lower than that of using no pattern exposure.
3.5.1 Curing Temperature Study
Mask pattern 1 and 2, as shown in Figure 3.33 and 3.34, are used in the experiments
to investigate the related maximum curing temperatures in building layers. The workflow
of experiments is similar to Figure 3.21. Instead of exposing the whole region of a test
layer, different small regions will be exposed by using these two patterns, each with a
specified exposure time. Eight different levels of exposure time (i.e. 10 s, 15 s, 20 s, 25 s,
30 s, 35 s, 40 s and 45 s) are tested. The average temperature within the whole region of a
built layer is measured and plotted.
Some examples of the curing temperatures are shown in Figures 3.36, 3.37 and 3.38.
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In each figure, the temperatures of the curing process using the two mask patterns as well
as the fully curing process are plotted, as demonstrated by the three crests on the red
curves over time.
In Figure 3.36, each of the two mask patterns are applied to expose 10 s, and the
layer is then fully cured using the mask image of the entire region for a long time. The
average temperatures of the whole test layer increase 0.3°C and 0.9°C after applying
mask pattern 1 and 2, respectively. During the fully cured process, the maximum
temperature reaches 28.2°C, which suggests the layer is only slightly cured after applying
these two mask patterns.

Figure 3.36. Curing temperature of exposure time 10 s
When the exposure time of the mask pattern is 25 s, the average temperature of the
test layer during the two patterns exposure and the fully cured process is around 26°C
(refer to Figure 3.37). The maximum temperature rises to 26.6°C when applying the first
mask pattern with the exposure time of 40 s (shown in Figure 3.38), and it drops to
26.2°C and 25.9°C during the second mask pattern exposure and the fully curing process,
respectively.
89

Figure 3.37. Curing temperature of exposure time 25 s

Figure 3.38. Curing temperature of exposure time 40 s
The maximum temperature during the fully curing process after using mask patterns
for different exposure time is shown in Table 3.5. It can be observed from the table that,
when the mask pattern exposure increases, the maximum temperature during the fully
curing process decreases. This is because small regions within the test layer have been
partially cured during the mask pattern exposure, and the ratio of curing regions increases
as the exposure time becomes longer. Thus less liquid resin will need to be cured during
the fully curing process.
90

Table 3.5. The maximum temperature in the fully curing process after applying mask patterns
Exposure time of mask pattern 10 15 20 25 30 35 40 45
Maximum temperature(°C) 28.2 27.7 27.1 26.1 25.8 26 25.9 25.9

3.6 MIP-SL Curing Strategies for Curl Distortion Control
It is desired to have a lower maximum curing temperature during the curing process
since the curl distortion is related to the curing temperature of each layer. Based on
previous studies on varying exposure time, grayscale levels, and mask patterns, two
exposure strategies have been developed with the aim of reducing the maximum curing
temperature and related curl distortion of parts. Note that a disadvantage of using these
strategies is, compared to the single exposure of a layer, a longer building time is
generally required. How to balance the curl distortion and the fabrication speed needs to
be further investigated in the future.
3.6.1 Curing Strategy Using Grayscale Exposure
As shown in Figure 3.29, the grayscale level 190 can make the maximum curing
temperature during the grayscale exposure process and the fully curing process close to
each other, which stays around 27°C. Thus, the exposure strategies based on grayscale
190 may be able to reduce the curing temperature of sliced layers and, accordingly, the
curl distortion of related built parts.
One of such exposure strategies based on grayscale 190 is exposing a mask image
using grayscale 190 for 80 s, and then using grayscale 255 to expose the layer for 30 s.
The curing temperature during building a test part can be recorded using the IR camera.
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The resulting temperature plot of a test part with 22 layers is shown in Figure 3.39, in
which the red curve records the liquid resin temperature while the blue curve represents
the temperature of built layers. The first 4 layers are the base layers and the following 8
layers are supports. The remaining 10 layers are the built layers related to the given part,
which will be applied with the exposure strategy. Hence the curing temperature of the last
10 layers is what we are interested in. It can be seen from the temperature plot (blue
curve) that, the maximum temperatures of the last 10 layers are rather close to each other,
which is about 2.8°C higher than the temperature of liquid resin (red curve).

Figure 3.39. Curing temperature of using grayscale 190
In comparison, the curing temperature plot for the same test part using grayscale 255
to expose the whole layer for 40 s is shown in Figure 3.40. The maximum temperature of
the last 10 layer is about 4.3°C higher than the temperature of liquid resin. It is also
higher than that of using the grayscale exposure as shown in Figure 3.39.
92

Figure 3.40. Curing temperature of grayscale 255 for 40 s
3.6.2 Curing Strategy Using Mask Pattern Exposure
As shown in the mask patterns exposure study (refer to Section 3.5), the curing
temperature of test layers can be reduced by applying mask patterns, since a certain
portion of liquid resin of a layer is cured at a time during the mask pattern exposure. Thus
the mask pattern exposure may be effective in reducing the curl distortion of built parts.
The temperature plot of using a mask pattern exposure strategy is shown in Figure
3.41. In each of the last 10 layers, mask pattern 1 as shown in Figure 3.33 is first applied
for 18 s; mask pattern 2 as shown in Figure 3.34 is then applied for 12 s; finally the whole
region is exposed using the mask image as shown in Figure 3.35 for 20 s. The
temperature plot as shown in Figure 3.41 shows the maximum temperature of the last 10
layers is ~3.4°C higher than the temperature of liquid resin.
93

Figure 3.41. Curing temperature of mask pattern exposure
3.7 Physical Experiments and Results
A rectangular thin part was built using different exposure strategies in the MIP-SL
setup as shown in Figure 3.11 and monitored by the IR camera. The schematic dimension
of the test part is shown in Figure 3.12. The layer thickness is 127 um (0.005") and the
test part has a total of 10 layers. Before building the part, anchor supports with a height of
1mm were added on the bottom of the part for the easy removal of the part after the
building process. Accordingly, the test part was built on 8 layers of the supports, which
fixed the part on the platform.
3.7.1 Physical Experiments
Two designed exposure strategies were applied to investigate their effects on the curl
distortion in the built parts.
(1) The first exposure strategy is based on grayscale exposure, in which (i) each
layer is first exposed using grayscale 255 for 5 s; (ii) the layer is then exposed using
grayscale 190 for 60 s; and (iii) finally the layer is exposed using grayscale 255 for 10 s.
94

(2) The second exposure strategy is based on mask pattern exposure, in which (i)
each layer is first exposed using grayscale 255 for 5 s; (ii) the layer is then exposed using
mask patterns similar to those shown in Figure 3.33 and 3.34. A small modification is the
boundary of the layer is exposed separately from the inner regions (refer to a layer
example as shown in Figure 3.42). Each of the three patterns will be exposed for 25 s; (iii)
finally the layer is exposed using grayscale 255 for 10 s.

Figure 3.42. Exposure strategy using mask patterns
To study the effect of these two exposure strategies on curl distortion, a baseline part
has also been built using a single exposure (i.e. exposing the whole region of a layer
using grayscale 255 for 40 s).
To reduce the effect of boundary layers, the first and the last layers of all the test
parts are built with the single exposure strategy. The remaining layers of the test parts are
built using the aforementioned grayscale exposure strategy, the mask pattern exposure
strategy, and the single exposure strategy respectively.
3.7.2 Experimental Results
After the building process, the built parts were removed and cleaned. The
measurement of the build parts was taken based on the schematic measurement as shown
95

in Figure 2.15. The curl distortion of the parts is denoted by the size of e. Micro-Vu
precision measurement machine is used in measuring each built part. The measurement
procedure is described in more details in section 2.5.
The experimental results of measured e values are shown in Table 3.6. Each test case
was repeated four times and the average curl distortion was calculated. As shown in the
table, the average curl distortion for the baseline parts is 0.431 mm; in comparison, the
curl distortions for the test parts using the grayscale and mask pattern exposure strategies
are 0.232 mm and 0.26 mm, respectively. The physical experiment results show that the
two exposure strategies using grayscale values and mask patterns are effective in
reducing the curl distortions in the MIP-SL process (~40% reduction).
Table 3.6. Curl distortion of test parts
Test parts
Curl distortion(mm)
replicate 1 replicate 2 replicate 3 replicate 4 average
Baseline 0.408 0.442 0.434 0.44 0.431
Grayscale exposure 0.201 0.279 0.215 0.232 0.232
Mask pattern
exposure 0.251 0.234 0.243 0.312 0.260

3.8 Concluding Remarks
The curing temperature during the MIP-SL process has been studied using a high-
resolution IR camera in this section. The curing temperature distribution within a single
layer with different sizes and shapes, as well as temperature evolution during the building
process with multiple consecutive layers, have been investigated. The results show the
curing temperature is mainly related to layer thickness, larger layer thickness leads to
96

higher curing temperature. Layer sizes or shapes have little effect on it. Curing
temperature of built layers is getting stable as more layers are built in the MIP-SL process.
The effects of varying exposure time, grayscale levels and mask patterns on the
maximum curing temperature have been studied. The results show the curing temperature
rises very little in the beginning of light exposure due to the oxygen inhibition effect. It
rises rapidly to the maximum with a decreasing rate when reaching the maximum
temperature. The curing temperature can drop even though it is still under light exposure.
Two exposure strategies have been designed based on grayscale and mask pattern
exposures to reduce the curing temperature of test layers. Test parts using the developed
exposure strategies have been built with the curl distortion measured. The physical
experiments show the exposure strategies can effectively reduce the curl distortion
although the building time is significantly longer.
97

Chapter 4 Curl Distortion Simulation and Reverse Compensation
in MIP-SL
As manifested in MIP-SL process, the built parts have deformation, which leads to
deviation from their nominal shape/size. An idea to reduce the deformation is to reverse
compensate the input shape such that the final shape would be close to the nominal model.
This approach requires the measurement of deformation, which can be either done by
using FEA simulation, or by using physical measurement tools such as CMM machines
or 3D scanner. This chapter presents the FEA method to simulate the curl distortion in
MIP-SL process.
Finite Element Analysis (FEA) has been proven to be a useful tool to simulate a wide
range of processes, including manufacturing processes, such as casting, injection molding,
metal forming, etc. Some researchers also apply it in simulating additive manufacturing
processes [44-62]. In this section, a FEA software package COMSOL Multiphysics is
adopted to simulate the MIP-SL process. A simple rectangular bar test case has been
selected to go through the simulation process. Reverse compensation based on the
simulated deformation has been conducted. The final deformation after reverse
compensation is much smaller than the one without compensation.
4.1 Finite Element Model
Thermal cooling and volumetric shrinkage are two of the major sources lead to
deformation of built parts in MIP-SL process. In order to simulate the deformation, these
98

two major factors need to be incorporated into the FEA model. In the FEA simulation,
each built layer is assumed to be elastic. The elastic domain and boundary condition for
general linear elastic model is shown in Figure 4.1.

Figure 4.1. Elastic domain and boundary conditions
The object is subjected to external press P on the surface A, and the body force load
G is applied on the whole domain. The bottom of the part is fixed.
The total potential energy is [84]:
i e
W W   
where W
i
is internal virtual energy:
1
2
T
i
V
W dV   


W
e
is the external virtual work due to body force and surface force:
T T
V A
e
W u GdV u PdA  
 

For equilibrium, internal virtual work equals to external virtual work:
(1)
(2)
(3)
99

T T T
0
V V A
dV u GdV u PdA           
  

The constitutive relation between stress and strain for elastic model:
e e
D   
where
e
 is elastic stress matrix,
e
 is elastic strain matrix and D is elasticity matrix.
For 3D case:
1 0 0 0
1 0 0 0
1 0 0 0
1 2
0 0 0 0 0
2
(1 )(1 2 )
1 2
0 0 0 0 0
2
1 2
0 0 0 0 0
2
E
D
  
  
  

 


  
 

 
  
 

 

 
 
 

 
 
 

 
 

The total deformation strain of resin comes from several aspects [28]:
0 e t v p 
            
where
e
 is elastic strain,
t
 is thermal strain,

 is the strain of cure shrinkage,
v
 is
viscous strain,
p
 is plastic strain, and
0
 is initial strain. In SLA process, the viscous
strain and plastic strain can be neglected, therefore the deformation strain can be
rewritten as:
0 e t v
        
Total stress is:
0 e
    
(4)
(5)
(6)
(7)
(8)
(9)
100

Plug equations (8) and (9) into equation (5), we can get:
0 0
( )
t v
D           
Displacement matrix is:
u Nd 
where N is shape function, d is nodal displacement vector.
Strain and displacement relation is:
Lu  
where L is first order differential operator, for 3D problem:
0 0
0 0
0 0
0
0
0
x
y
z
L
y x
z y
z x






 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 

Plug equation (11) into (12), we get:
Bd  
where
B LN 
In SLA process, the external force P and G are neglected, plug equations (10) and
(14) into (4), we can get:
(10)
(11)
(12)
(13)
(14)
(15)
101

T
0 0
0 0
[ ) ]
0
(
T T
V V
T T T T T T T T T T
V V V V
t
V
t
dV d B dV
d B dV d B dV d B
D
D D dV d B dV d B dV D D


    
 
    
       
     
    


 
    

which can be rewritten as:
Kd f 
where K is stiffness matrix and written as:
T
V
DB K B dV 


f is force vector and written as:
0 0
T T T T
V V
t
V V
f B D D D dV B dV B dV B dV

        
   

The first term in the right side is the equivalent nodal force due to initial stress, the
second term is equivalent nodal force due to thermal strain; the third term is equivalent
nodal force due to volumetric shrinkage; and the fourth term is equivalent nodal force due
to initial strain.
4.2 Geometric Model
In stereoligthography process, parts are built layer by layer. Each layer is an
independent geometry. In order to simulate deformation of part, the first step is to create
the geometry of part consists of required number of layers, determined by the part height
and layer thickness. It would be inefficient or impractical to create geometry of each
layer manually, especially for parts with complex features and large number of layers.
COMSOL Multiphysics has been selected to simulate the SLA building process.
Several attempts have been tried to create the geometry of parts in COMSOL. One trial is
to load STL directly into COMSOL. COMSOL provides interface to input external STL
(16)
(17)
(18)
(19)
102

model. However, the resulting geometry is not accurate when the STL is loaded into
COMSOL, especially for complex shape model. Besides, COMOSL does not provide
function to slice the STL part. Even it does, it would be difficult to record the indices of
domains, boundaries and points, etc. Another trial is to find 3D CAD software to slice the
STL into an assembly of layers, and then load the assembly into COMSOL, it is difficult,
however, to track the indices of domains, boundaries, etc. It is found that COMSOL
enables users to create geometry based on sketch, so an approach is to extract the
boundary contour of each sliced layer and create the layer geometry on a specified work
plane based on these data. The workflow of creating geometry of layers in COMSOL is
shown in Figure 4.2.

Figure 4.2. Workflow of creating geometry of layers in COMSOL
103

The input STL model is first sliced into layers, and the contours of each layer is
extracted and recorded. The topology of contours in the layer needs to be created so as to
facilitate the extrusion operation later. The contours are recreated in COMSOL based on
the data extracted from contours during slicing. Since COMSOL requires user to
explicitly specify Boolean operation of curves to create geometry, the topology data of
the contours is applied before these contours can be extruded to layer geometry.
Repeating the procedure until the final layer is created.
A test case (shown in Figure 4.3) has been designed to test the feasibility of creating
geometry model in COMSOL automatically. The test case has 4 hollow regions inside it.
These regions are designed specifically to increase the complexity.

Figure 4.3. Input STL of test case
The sliced image of each layer is the same in this case. One sliced image is shown in
Figure 4.4.

The extracted boundar
There are 8 loops in Figure
follows:
(1) First create the tree data stru
represent an isolated contour, the loops inside the root loop will become its leaf or non
root node.
(2) Scan the sliced image to find loops based on their
the loop with the lowest y
Figure 4.4. Sliced image of one layer
The extracted boundary contours are shown in Figure 4.5.
Figure 4.5. Boundary contours of one layer
There are 8 loops in Figure 4.5. The idea of creating topology of these loops is as
(1) First create the tree data structure, the tree can have multiple roots, each root
represent an isolated contour, the loops inside the root loop will become its leaf or non
(2) Scan the sliced image to find loops based on their y coordinates (
y coordinates will be found first.
104

. The idea of creating topology of these loops is as
cture, the tree can have multiple roots, each root
represent an isolated contour, the loops inside the root loop will become its leaf or non-
coordinates (row in image),
105

(3) Compare the newly found loop (denoted as A) with the root loops of tree. If there
is no root node, then the newly found loop will be a root. If there exists root loops, and A
does not fall inside any of the root loops, then A will become a new root. If A is inside a
root loop B, then iteratively compare A with the non-root node of B to find its correct
position in the tree rooted at B.
(4) Go through step (2) and (3) to insert all loops into the loop tree.
The final topology tree of loops in Figure 4.5 follows aforementioned steps is shown
in Figure 4.6.

Figure 4.6. Topology of loops
After creating topology structure of all loops in one layer, the topology data, as well
as the coordinates, are saved into data files, which will be retrieved by Matlab program.
COMSOL provides interface for Matlab to manipulate it. The creation of one layer
geometry in COMOSL base on the contour data is shown in Figure 4.7.
Figure 4.7 shows the extrusion of all contours in one layer, geometry after Boolean
operations is shown in Figure 4.8.

106

Figure 4.7. Creation of one layer in COMSOL

Figure 4.8. Final geometry of one layer
Following the same steps, all ten layers have been created in COMSOL, shown in
Figure 4.9.

Figure 4.9. Geometry of 10 layers in COMSOL
The above steps for creating geometry in COMSOL is generic, which means any
complex STL model can be modeled in COMSOL.
4.3 Physics Settings
4.3.1 Modeling of Layer by Layer Dynamic Building Process
In SLA, the dynamic layer by layer building process is simulated by using the birth
and death technique [85, 86]. In this method, each layer is modeled as a single
deactivated domain, which will be activated when the layer is built. For example, in the
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first step, only the first layer is activated, while all other layers are deactivated. While in
the second step, both the first and second layers are activated, with all layers above them
being deactivated. For the newly activated layer, thermal load, as well as other materials
parameters will be set. The deactivation of layer is implemented by setting its Young's
modulus to a negligible value ( e.g. 1e-12 Pa), while the activation is accomplished by
switching the Young's modulus to normal value. An illustration of setting parameters in
different layers is shown in Figure 4.10.

Figure 4.10. An illustration of dynamic building process (a) First layer is activated in step 1 (b)
the second layer is activated in step 2
The example consists of 3 layers, which will be finished building in 3 steps. Only the
activation of the first and second steps is illustrated. In the first step, only the first layer is
activated, material properties and thermal load is set on this layer; while layers 2 and 3
are deactivated, as demonstrated in dash line. In the second step, both layers 1 and 2 are
activated, while layer 3 is deactivated. The second layer is set to have normal material
properties. Thermal load or other shrinkage factors will also be set to the newly activated
layer. The stress generated from the first step is inserted as initial stress for the layer 1 in
the second step. Layer 1 is also set to have normal material properties; however, no
shrinkage effect is set to it. The settings for the newly and existing activated layers, and
deactivated layers in the following steps are similar to that in the second step.
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4.3.2 Initial Conditions Settings
The layer undergoes thermal and volumetric shrinkage when it solidifies; the
structure mechanics module in COMSOL is selected to simulate the shrinkage effects.
The thermal and volumetric shrinkage can be modeled as equivalent nodal force, as
shown in Equation (19).
It is assumed that curing temperature is uniform within each layer, and it cools to
room temperature when the layer is built. The curing temperature used in simulation is
calibrated from IR camera, which is 30.1 Celsius degree, while the room temperature is
24 Celsius degree.
For a specified step, the current layer is sitting on the layers that have been solidified
in previous steps, thus the result of simulation from last step serves as initial condition for
the newly activated layer. Specifically, in current step simulation, previous layers have
initial stress, while current layer has material activation settings and initial condition to
incorporate the fact that it sits on the previous deformed layers.
The simulation process consists of N+1 steps if the part has N layers to be built, in
which the first N steps modeling the building of N layers, while the last step is used to
simulate the process of removing part from supports.
4.4 Entities Selection
After the geometry of given STL is modeled in COMSOL, another critical issue is
how to automatically select specified domains, boundaries or points. Different steps
require different selections of domains, and boundaries. COMSOL has its own rule to
index domains, boundaries and points of the created geometry. It is possible to calculate

the indices for simple part, such as the rectangular bar part, based
it is not feasible when the part has varied cross
has complex features, or large number of layers.
The extrusion of geometries on a specified workplane can be grouped as one
selection. That means the geometries in an entire layer can be selected as a whole.
domains in one layer are created at the same time
physics settings will be
layer is shown in Figure 4.11
it, with indices 10, 20, 30 and 40, shown
Figure
In some cases, the selection of multiple layers are necessary, for example,
second step, only the first and second layers are activated, while all other 8 layers are
deactivated. Two groups of domains selection need to be made, since diffe
settings will be made on them. For the first group, which consists of the first and second
layers, normal Young's modulus will be set. While the other grou
the indices for simple part, such as the rectangular bar part, based on the rules. However,
it is not feasible when the part has varied cross-sections on different z height, or the part
has complex features, or large number of layers.
extrusion of geometries on a specified workplane can be grouped as one
t means the geometries in an entire layer can be selected as a whole.
domains in one layer are created at the same time in the building process
physics settings will be applied on them. The example of selecting all domains in one
4.11. The test part has 10 layers. The 10th layer has 4 domains in
it, with indices 10, 20, 30 and 40, shown as highlighted in Figure 4.11.
Figure 4.11. Selection of all domains on the 10th layer
In some cases, the selection of multiple layers are necessary, for example,
second step, only the first and second layers are activated, while all other 8 layers are
deactivated. Two groups of domains selection need to be made, since diffe
settings will be made on them. For the first group, which consists of the first and second
layers, normal Young's modulus will be set. While the other group, with the remaining 8
109
on the rules. However,
height, or the part
extrusion of geometries on a specified workplane can be grouped as one
t means the geometries in an entire layer can be selected as a whole. All
in the building process, therefore same
on them. The example of selecting all domains in one
The test part has 10 layers. The 10th layer has 4 domains in

In some cases, the selection of multiple layers are necessary, for example, in the
second step, only the first and second layers are activated, while all other 8 layers are
deactivated. Two groups of domains selection need to be made, since different physical
settings will be made on them. For the first group, which consists of the first and second
p, with the remaining 8
110

layers, will be set with extremely small Young's modulus to represent their deactivated
status. For these cases, the unions of selections of layers need to be created. The selection
of all domains in two layers is shown in Figure 4.12.

Figure 4.12. Selection of all domains in two layers
4.5 Boundary Conditions
During MIP-SL building process, there is no curl distortion if the part is constrained,
the deformation happens only after the part is removed from constraints. Parts are built
on supports, which consist of many tiny rods. It is assumed that these support constraints
only hold bending force, while holding no net force in the in-plane direction (as shown in
Figure 4.13). Stress builds up during the building process, since the shrinkage of newly
built layer is restrained either by its underlying layers or constraints. From stress analysis,
it is expected the top layer has tensile stress while its underlying layer has compressive
stress. After the constraints are removed, the residual stress leads to deformation. The
support constraints are removed in the final step of simulation, in order to model the
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process of separating part from supports. The residual stress is incorporated as equivalent
nodal force and applied on the part to simulate final curl distortion.

Figure 4.13. Mechanical boundary conditions
4.6 Material Properties
Linear elastic models with constant material properties, such as Young's modulus,
Poisson's ratio and coefficient of thermal expansion, were assumed in the simulation. The
material used in the experiment is SI500 resin from EnvisionTec.Inc. The values of
material properties are based on previous research [32, 48] and open sources [87-94],
shown in Table 4.1.
Table 4.1. Material properties in simulation
Property Value Unit
Young’s Modulus (1.8~3.8)*e9 Pa
Poisson’s ratio 0.3
Density 1100 kg/m
3

Coefficient of thermal expansion (0.4 ~ 1.2)*e-4 1/K

4.7 Mesh
In the simulation, free tetrahedron mesh is generated on the test part since it is easy
to approximate complex part. All layers can be meshed using the same meshing size
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criterion, or they can be meshed separately using different mesh size. The meshing result
of test part in Figure 4.9 is shown in Figure 4.14.

Figure 4.14. Meshing using tetrahedron
4.8 Simulation of Part Removal from Constraint Process
Stress builds up during the SLA building process, since the shrinkage of newly built
layer is restrained by its underlying layers. From stress analysis, it is expected the top
layer has tensile stress while its underlying layer has compressive stress. After the
constraints are removed, the residual stress leads to deformation. Previous research has
been conducted on modeling the process of removing part from constraints in Shape
Deposition Manufacturing process [56]. For an illustration, the stress in X and Y
directions only varies in Z direction before the constraints are removed. It can be assumed
that elastic unloading happens when the part is separated from supports, thus the bending
moment can be calculated based on the residual stress. The schematics of warping after
removing constraints is shown in Figure 4.15, in which (a) shows no warping while the
stress builds up due to the bottom constraint, (b) shows the resulted bending moment is
applied to the edge after the constraint is removed.
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Figure 4.15. Warping after removing constraint[56]
The bending moment per unit length can be calculated by:
x xx
M zdz   


y yy
M zdz   


The final curvatures in x and y direction are calculated by:
x y
x
M M
k
EI
 

y x
y
M M
k
EI
 

Where  is Poisson ratio, E is Young’s modulus, and I is cross sectional moment of
inertial per unit width.
As illustrated in previous section, the thermal and volumetric shrinkage in SLA
building process are modeled as equivalent nodal force and applied on the part. The
residual stress calculated from building process serves as initial stress for the final step,
thus can be modeled as equivalent nodal force to simulation curl distortion.
(20)
(21)
(22)
(23)
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4.9 Deformation Alignment to Find the Optimal (Actual) Deformation
In SLA process, curing layers are subjected to thermal and volumetric shrinkage.
The resin material is assumed to be isotropic. The built layer has the tendency to shrink
toward the center. Thus symmetric curl distortion can be found for built parts with
symmetric features. Take the curl distortion of a simple rectangular bar in Figure 1.4(c)
for example. Its dimension is 5 mm (width) by 60 mm (length) by 1.27 mm (thickness),
and it has a total of 10 layers, with layer thickness of 0.127 mm. After built, the part has
deformation, with two sides (denoted as A and B) curl up.
In the FEA simulation, part with symmetric features can be simulated with only one
feature modeled, which can reduce the computational cost. Take the simple bar test case
as an example, the part is symmetric along X and Y axes, only 1/4 of original model is
simulated. As shown in Figure 4.16, the highlighted boundaries are symmetric surfaces,
where the symmetric boundary conditions will be applied during simulation. The bottom
corner point where the highlighted surfaces intersect is fixed during the simulation.

Figure 4.16. Symmetric boundary conditions settings (1/4 of original part)
In the simulation, the Young's modulus is set to 3.2e9 Pa, coefficient of thermal
expansion is 1.2e-4 1/k, other material properties and parameters are set according to
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values specified in the settings section. The simulation result is illustrated in Figure 4.17,
from which it can be found the right side curls up, which shows the same distortion trend
with the physical built part.

Figure 4.17. Simulation of curl distortion for simple bar
However, the simulation results depends largely on the constraints it applies,
specifically the fixed point constraint during the building and part removal process. For
symmetry test part, the simulation result is reasonable since the fixed point constraint is
applied to the symmetric point. For non-symmetry part, however, it is difficult to find and
apply fixed point constraint on the symmetric point. Thus the deformation result does not
reflect the actual deformation. Consider the simple bar test case again, if the test part is
not modeled as symmetric part, but rather modeled as a non-symmetry part (which is
accomplished by fixing a point or small region on the left side of bottom surface instead
of the center point, as shown in highlighted in Figure 4.18). Then the deformation result
is biased, with only the right side curls up, as shown in Figure 4.19, which is similar to
that shown in Figure 4.17. Obviously, the deformation result is not reasonable, since it
will not happen in the physical built part, as shown in Figure 1.4(c).
116

Figure 4.18. An illustration of non-symmetry constraint

Figure 4.19. Simulation result applying non-symmetry constraint
A rigid transformation (rotation and translation) needs to be applied on the simulated
result to align with original model to find the minimum deformation. The ideal
deformation is expected to be symmetric along X axis (with both sides curl up).
4.9.1 Rigid Transformation
Many researches have been conducted on finding optimal rigid transformation to
align two datasets with minimum errors [95-97]. The method can be applied in aligning
the deformed and original parts. Consider two point sets A and B in 2D plane, as
illustrated in Figure 4.20.
Fixed constraint
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Figure 4.20. Two point sets: A and B
Point set A has 4 points P1, P2, P3 and P4, while point set B has 4 corresponding
points P1', P2', P3' and P4'. The 4 points in point set A can be considered as deformation
from the 4 points in point set B. The procedures to find optimal rigid transformation
matrix are shown as follows:
1. Find the centroids of both point sets.
2.Translate both point sets to the origin of coordinate system, and then find the
optimal rotation matrix R.
3. Find the translation matrix t.
The illustration of moving centroids of two point sets to origin is shown in Figure
4.21.

Figure 4.21. Illustration of rigid rotation
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The optimal rotation matrix R to align two point sets can be found through Singular
Value Decomposition (SVD) method (suppose each point has X, Y and Z coordinates):
1. Compute centroids of both point sets:
1 1
1 1
,
N N
c i c i
i i
A A B B
N N
 
 
 

2. Compute matrix:
1
(A )( )
N
T
i c i c
i
E A B B

  


3. Apply SVD on the matrix E:
[U,S,V] SVD( ) E 
4. Calculate rotation matrix:
1
R V 1
det(VU )
T
T
U
 
 

 
 
 

The translation matrix is calculated by:
c c
t R A B    
After rigid transformation, point set A becomes A':
' A R A t   
which is aligned with point set B with minimum error.
For the simple bar test case with non-symmetric constraint, the deformed part can be
rigid transformed to align with original part to reflect actual deformation. The vertices of
both deformed and original STL model can be obtained. The alignment of deformed STL
model with original STL model is shown in Figure 4.22. The comparison of two parts is
(24)
(25)
(26)
(27)
(28)
(29)

conducted by using Meshlab
range shows difference between deformed part an
biggest difference of 0.92
part shows symmetric distortion
Figure
4.10 Reverse Compensation
In order to reduce curl distortion of built part, one straightforward method is to
modify original part geometry model,
such that the modified geometry has less curl distortion after fabricated.
Some researches have
critical issue is to explore the relationship between
compensation. It could be linear or nonlinear.
add same amount of deformation reversely on the original part geometry
deformation using modified geometry and
simulated deformation is bigger than tolerance. Iterate these procedures until the
deformation is within the desired tolerance. Take a single iteration
Meshlab, a software tool to view and operate meshes
range shows difference between deformed part and original part, with the blue shows the
biggest difference of 0.92 mm, as compared to 3.55 mm in Figure 4.19
part shows symmetric distortion after rotation.
Figure 4.22. Curl distortion after rigid transformation
Compensation
In order to reduce curl distortion of built part, one straightforward method is to
modify original part geometry model, similar to reverse compensate the geometry shape,
such that the modified geometry has less curl distortion after fabricated.
researches have been conducted on these reverse problems
critical issue is to explore the relationship between deformation and reverse
compensation. It could be linear or nonlinear. An intuitive compensation approach is to
add same amount of deformation reversely on the original part geometry
deformation using modified geometry and update the input geometry again if the newly
simulated deformation is bigger than tolerance. Iterate these procedures until the
deformation is within the desired tolerance. Take a single iteration for example, consider
119
o view and operate meshes [98]. The color
d original part, with the blue shows the
4.19. The deformed

In order to reduce curl distortion of built part, one straightforward method is to
similar to reverse compensate the geometry shape,

been conducted on these reverse problems [72, 73]. The
deformation and reverse
An intuitive compensation approach is to
add same amount of deformation reversely on the original part geometry. Simulate the
eometry again if the newly
simulated deformation is bigger than tolerance. Iterate these procedures until the
for example, consider
120

the curl distortion in Figure 4.22, the maximum curl distortion is 0.92 mm, which occurs
on the left and right side edges. The reverse compensated model with same amount of
distortion is shown in Figure 4.23, in which the geometry curls down, with left and right
side edge distort 0.92 mm from its original position.

Figure 4.23. Reverse compensated model
Using the reverse compensated model as input geometry, and go through the same
simulation process. The simulation result can then be compared with original model
without any compensation to show the improvement of curl distortion using reverse
compensation. The created geometry in COMSOL, based on the reverse compensated
model in Figure 4.23, is shown in Figure 4.24.

Figure 4.24. Reversed geometry created in COMSOL
There are totally 17 layers, instead of 10, created with each layer thickness of 0.127
mm, since the geometry input is reversely deformed. The simulation consists of 18 steps.
The first 17 steps are used to simulate the building of 17 individual layers, while the last
121

step is to model the part removal from constraint process. Birth and death technique is
used to model the layer by layer dynamic building process. Material properties (shown in
Table 4.1) with Young's modulus of 3.2e9 Pa and coefficient of thermal expansion of
1.2e-4 1/k, thermal shrinkage (cooling from curing temperature to room temperature),
and initial values are set to newly activated layer. The bottom surfaces of activated layers
are restrained from curling during building; however, they support no net force in in-
plane directions (X and Y axes directions). The fixed point constraint is the same as the
original geometry simulation, shown in Figure 4.18. The meshing result using tetrahedron
mesh is shown in Figure 4.25.

Figure 4.25. Meshing of reverse compensated geometry
The simulation is conducted step by step, the simulation result after part is removed
from constraint is shown in Figure 4.26.

Figure 4.26. Simulated deformation of reverse compensated geometry

The simulation result does not show the actual curl distortion, it depends on the
position of the fixed point constraint
needs to be rigid rotated to
compared with original geometry to show the
shown in Figure 4.27.
Figure 4.27
From the figure, it can be seen that the maximum cur distortion is 0.2
to the original flat geometry
distortion before reverse compensation, there is obvious improvement on reducing
distortion.
4.11 Materials Properties Effects
As mentioned in material setting section, the material used in our experiment is
acrylate resin. The Young's
of thermal expansion ranges from 0.4 x10
The simulation result does not show the actual curl distortion, it depends on the
fixed point constraint selected in the simulation. The deformed shape
rigid rotated to find its minimum bounding box in terms of z
compared with original geometry to show the actual curl distortion. The comparison is
27. Actual curl distortion after reverse compensation
From the figure, it can be seen that the maximum cur distortion is 0.2
to the original flat geometry, as shown in blue color. In comparison with the curl
distortion before reverse compensation, there is obvious improvement on reducing
Properties Effects on Curl Distortion
As mentioned in material setting section, the material used in our experiment is
acrylate resin. The Young's modulus typically ranges from 1.8 to 3.8 GPa, and coefficient
of thermal expansion ranges from 0.4 x10
-4
to 1.2 x10
-4
1/k. Suppose other parameters or
122
The simulation result does not show the actual curl distortion, it depends on the
The deformed shape
z height, and then
curl distortion. The comparison is

curl distortion after reverse compensation
From the figure, it can be seen that the maximum cur distortion is 0.2 mm compared
In comparison with the curl
distortion before reverse compensation, there is obvious improvement on reducing
As mentioned in material setting section, the material used in our experiment is
a, and coefficient
Suppose other parameters or
123

settings are the same, different combinations of Young's modulus and coefficient of
thermal expansion are set in the simulation to investigate their effects on curl distortion.
4.11.1 Simple Bar Test Case
The process and settings for simulation of the simple bar test part is the same as
described before, Figure 4.17 shows the simulation result using the combination of
Young's modulus 3.2e9 Pa and coefficient of thermal expansion 1.2e-4 1/k. Three sample
values of Young's modulus, 1.8e9, 3.2e9 and 3.8e9, together with three sample values of
coefficient of thermal expansion, 0.4e-4, 0.7e-4 and 1.2e-4, are selected and combined to
test their effects on curl distortion. The curl distortion using these parameters
combinations has same trend with that shown in Figure 4.17, differs only in the
magnitude. The simulation results using all combinations of parameters are tabulated in
Table 4.2.
Table 4.2. Simulation results of simple bar test case: curl distortion(unit: mm)
Simple rectangular bar Young's modulus
Coefficient of thermal expansion(CTE) E = 1.8e9 E = 3.2e9 E = 3.8e9
CTE = 0.4e-4 0.394 0.295 0.282
CTE = 0.7e-4 0.69 0.516 0.494
CTE = 1.2e-4 1.183 0.884 0.846

The 2D surface plot using two parameters, Young's modulus and coefficient of
thermal expansion, as two variables, and curl distortion as response, is shown in Figure
4.28.

Figure 4.28. Curl distortion
From the 2D surface plot, it can be found that the curl distorti
with coefficient of thermal expansion, larger coefficient of thermal expansion leads to
larger curl distortion. While the curl distortion has a reverse relations with Young's
modulus, larger Young's modulus leads to
4.11.2 Test Part with Holes
In order to verify the capability of current simulation process,
geometry than simple bar test part has been designed and simulated. The geometry model
in COMSOL is shown in Figure
Figure
. Curl distortion of simple bar test case using different Young's modulus and
coefficient of thermal expansion
From the 2D surface plot, it can be found that the curl distortion has a linear relation
coefficient of thermal expansion, larger coefficient of thermal expansion leads to
larger curl distortion. While the curl distortion has a reverse relations with Young's
larger Young's modulus leads to smaller curl distortion.
Part with Holes
In order to verify the capability of current simulation process, a more complex
geometry than simple bar test part has been designed and simulated. The geometry model
in COMSOL is shown in Figure 4.29.
Figure 4.29. Rectangular test part with holes
124

using different Young's modulus and
on has a linear relation
coefficient of thermal expansion, larger coefficient of thermal expansion leads to
larger curl distortion. While the curl distortion has a reverse relations with Young's
a more complex
geometry than simple bar test part has been designed and simulated. The geometry model

125

Three holes with varied sizes are created on the rectangular plane. The part size is 50
mm (length) by 20 mm (width) by 1.27 mm (height), with layer thickness of 0.127 mm.
The simulation procedures and settings are similar to that in the simple bar test part
simulation process. The simulation result with Young's modulus 3.2e9 Pa, coefficient of
thermal expansion 0.7e-4 1/k is shown in Figure 4.30.

Figure 4.30. Curl distortion for test part with holes
From the simulation result, it can be seen that the test part also has left and right
sides curl up, which is agreed with distortion of the physical built part. Similar to that in
simple bar test case, effects of Young's modulus and coefficient of thermal expansion
have been investigated on running the simulations. The curl distortion results are shown
in Table 4.3.
Table 4.3. Simulation results of test part with holes: curl distortion(unit: mm)
Test case with holes Young's modulus
Coefficient of thermal expansion(CTE) E = 1.8e9 E = 3.2e9 E = 3.8e9
CTE = 0.4e-4 0.322 0.242 0.232
CTE = 0.7e-4 0.564 0.424 0.405
CTE = 1.2e-4 0.967 0.727 0.695

The 2D surface plot using curl distortion of response, Young's modulus and
coefficient of thermal expansion as variables are shown in Figure
Figure 4.31. Curl distortion
Similar to the simulation results in the simple bar test case, it can be found from the
2D surface plot that the curl distortion has a linear relation with coefficient of thermal
expansion, with larger coefficient of thermal expansion leads to larger curl distortion.
While the curl distortion has a reverse relationship with Young's modulus, larger Young's
modulus leads to smaller curl distortion.
4.12 Concluding Remarks
Deformation is one of the biggest and most critical issues in MIP
other AM processes. To reduce deformation of built part, this chapter presents a pre
modified geometry approach by using FEA simulation to predict the deformation of built
part and calculate the reverse compensation based on it. The final deformation using the
reverse compensated model has less deformation when compared to the original model
without any compensation.
The 2D surface plot using curl distortion of response, Young's modulus and
coefficient of thermal expansion as variables are shown in Figure 4.31.
. Curl distortion of test part with holes using different Young's modulus and
coefficient of thermal expansion
Similar to the simulation results in the simple bar test case, it can be found from the
2D surface plot that the curl distortion has a linear relation with coefficient of thermal
sion, with larger coefficient of thermal expansion leads to larger curl distortion.
While the curl distortion has a reverse relationship with Young's modulus, larger Young's
modulus leads to smaller curl distortion.
ding Remarks
one of the biggest and most critical issues in MIP
other AM processes. To reduce deformation of built part, this chapter presents a pre
modified geometry approach by using FEA simulation to predict the deformation of built
the reverse compensation based on it. The final deformation using the
reverse compensated model has less deformation when compared to the original model
without any compensation.
126
The 2D surface plot using curl distortion of response, Young's modulus and

using different Young's modulus and
Similar to the simulation results in the simple bar test case, it can be found from the
2D surface plot that the curl distortion has a linear relation with coefficient of thermal
sion, with larger coefficient of thermal expansion leads to larger curl distortion.
While the curl distortion has a reverse relationship with Young's modulus, larger Young's
one of the biggest and most critical issues in MIP-SL process and
other AM processes. To reduce deformation of built part, this chapter presents a pre-
modified geometry approach by using FEA simulation to predict the deformation of built
the reverse compensation based on it. The final deformation using the
reverse compensated model has less deformation when compared to the original model
127

COMSOL Multiphysics, a FEA software package, has been adopted to simulate the
MIP-SL process. The deformation of built part in MIP-SL process can be modeled as a
structural mechanics problem, where the shrinkage during building can be considered as
the body or thermal load. Linear elastic material model has been applied on each layer,
assuming the build layer has linear elastic material behavior. The curing temperature
calibrated in the previous chapter is incorporated as thermal load. To simulate the
dynamic layer-by-layer building process for the whole part, birth and death technique has
been applied to activate the building layers in a sequence that is similar to the real
building process.
A simple rectangular bar test case has been selected to go through the simulation
process. Reverse compensation based on the simulated deformation has also been
conducted. The result shows the final deformation of the test case after reverse
compensation is much smaller than the one without compensation.

128

Chapter 5 A Reverse Compensation Framework for Shape
Deformation in Additive Manufacturing
Shape deformation is one of the most important issues in additive manufacturing
such as the mask image projection based stereolithography process. V olumetric shrinkage
combined with thermal cooling during the photopolymerization and other factors such as
support-constrained layer building process, lead to complex part deformation that is hard
to predict and control. In this chapter, a general computation framework based on a
reverse compensation approach is presented to reduce the shape deformation of
fabricated parts. During the reverse compensation process, the shape deformation is first
calculated by physical measurements. A novel method is presented with added markers
for identifying the optimal correspondence between the deformed shape and the given
nominal CAD model. Accordingly, a new CAD model based on the determined
compensation can be constructed. The intelligently modified CAD model, when used in
fabrication, can significantly reduce the part deformation when compared to the nominal
CAD model. Two test cases have been designed to demonstrate the effectiveness of the
presented computation framework.
5.1 Related Work of Reverse Compensation in Additive Manufacturing
Deformation of part built in AM processes is very complex issue since many factors
contribute to it. The majority of research work conducted are focused on the following
three aspects: (1) Path planning methods to reduce shrinkage or internal stresses; (2)
optimization of process parameters during the building process; (3) simulation methods
129

using FEA or analytical modeling to predict deformation based on select deformation
sources. These research efforts targeted on the building process and tried to study the
effects of building parameters. However, it is very challenging to investigate all building
parameters. Besides, the deformation sources such as shrinkage will not be eliminated by
optimizing the building parameters. Therefore, some researches have been conducted to
study compensation instead to reduce deformation. Specifically, Huang and Lan [63, 64]
used FEA simulation to predict the distortion of part, and calculated the static reverse
compensation by adding distortion reversely on original model, and dynamic reverse
compensation by considering the distortion of added compensation. Tong et al. [99]
presented a method to transfer all errors sources in AM process into parametric error
functions of axes of AM machines. Errors were predicted by the parametric error
functions, and original CAD model was compensated by applying negative values of
errors. Later, Tong et al. [66] presented another slice file compensation method to
compensate X and Y axes errors for each vertex in the sliced layer. Zha and Anand [65]
presented a geometric approach to improve errors of part by modifying input STL model
in AM process. Huang et al. [69] conducted research using statistical approaches to
model and predict in-plane shrinkage of cylindrical part, and derive optimal shrinkage
compensation to improve accuracy of built part in mask image projection based
stereolithography process. Later, they presented a novel statistical predictive modeling
and compensation approach to predict and improve the quality of more complex shapes,
such as prismatic parts [70]. In addition to the modeling of in-plane deformation, they
recently conducted research on reducing out-of-plane deformation of built parts. A
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theoretical foundation of three-dimensional geometric error compensation for AM
processes has been established [71].
All these research have effects on improving errors of part built in AM processes,
however, there are some limitations: using FEA simulation is difficult to incorporate all
deformation sources, thus the error prediction is not accurate. Modifying the original STL
model by directly adding the predicted error reversely on the vertices is inaccurate since
the added compensation also has deformation. It is difficult to predict complex shape
using statistical model, which may need more experimental data.
Due to the fact that the shape deformation of a fabricated part comes from many
different and complex factors, it is difficult to predict and compensate the factors one-by-
one. This chapter proposes a reverse compensation to combine all the factors to a
geometric design problem based on physical experiments by assuming the parts are
fabricated by the same manufacturing process. Specifically, the relationship between the
shape and its deformation is studied, and input geometry is modified accordingly such
that fabricating the modified shape with the same building process will result in a built
part that is close to the original nominal model. In this way, the “law” of shrinkage and
stress in the photopolymerization process and other deformation sources is preserved.
5.2 Overview of Compensation Framework
The computational framework to reduce deformation in the MIP-SL process is
shown in Figure 5.1.
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Figure 5.1. Computational framework to reduce deformation
Any built part has deformation exceeding required tolerance can use the
computational framework to reduce the deformation due to the fabrication process. In
order to reduce the deformation, the first step is to calculate it. As deformation is difficult
to predict accurately by analytical models or FEA simulation, we adopt the approach of
measuring deformation based on physical measurement, by using tools such as CMM or
3D scanners. Since the measured deformed shape and nominal model are represented as
two data sets with respective local coordinate systems, alignment of these two data sets
needs to be conducted for comparison, which can be done using Iterative Closest Point
(ICP) method [100]. After these two models have been aligned, correspondence between
points on the nominal model and measured data needs to be established.
There are different methods/principles to find correspondence, e.g., find the closest
point. In this research, we use feature points or added artificial markers to find the
correspondence between two models. The deformation can be easily calculated by
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subtracting the coordinates of corresponding points on two models. After the deformation
is calculated, reverse compensation method can be applied to compensate the nominal
model such that the built part is closer to the designed CAD model. The schematics of the
simple bar test case is provided as an illustration to go through each step for the reverse
compensation based on physical measurement in the computation framework. As shown
in Figure 5.1, the original flat simple bar has deformation after built, such that the two
tips curl up. We can use CMM or microscope to measure its deformed profile (shown in
blue solid line in Figure 5.1). Alignment between the measured deformed profile and
original nominal profile (shown in red solid line) is conducted. For each point on the
nominal model, a corresponding point can be found on the deformed profile, as denoted
by red and blue dash line. The nominal STL model can be modified by using the reverse
compensated profile, and the final built part would be much closer to the desired shape.
Specifically, the compensation for each point can be calculated based on the
deformation of offset models. Pick a random point P on the original nominal model as an
illustration. Let the added compensation to be X, and the deformation of the compensated
point (P+X) in MIP-SL process is denoted as f(P+X), which is a function of added
compensation X. The objective of compensation is to find X such that:
P + X + f(P+X) = P
It can be rewritten as:
X + f(P+X) = 0
To solve this equation, there are two main issues that have to be tackled.
(1)
(2)
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First, given the nominal and the deformed models, how to capture the true
deformation for every point on the models, such that f can be computed for a particular P?
Second, for an AM process, the relation f(P+X) is unknown and may be a non-linear
equation. How to find the value of X that can satisfy or approximate the equation?
These two questions will be answered in the following two sections. Before that, we
define the following notions that will be used in the paper:
N: The nominal model, which is the CAD model needs to be fabricated.
M:The measured data of the fabricated physical model, which has undergone
deformation.
C: The compensated CAD model.
N+/-:The subscript + or – denotes the offset version of the model, outwardly or
inwardly, respectively.
This study is mainly based on the MIP-SL process. However, note that the presented
computation framework is general, which can also be used to reduce part deformation in
all other additive manufacturing processes.
5.3 Correspondence and Deformation
To capture the deformation for each point on the nominal model (N), such that the
deformation function f can be computed, we need to find its corresponding point in the
physical deformed model (M). One way to find the corresponding points is using the
closest points like in the ICP method. Unfortunately, using closest points may lead to a
many-to-one or one-to-many mapping that will result in degenerated shapes, which
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violates the deformation in nature. Instead, these correspondences can be established by
cross-parameterization, which will be described in this section.
5.3.1 Establish Correspondence between Models
In this research, the correspondence between nominal model (N) and deformed
model (measured model, M) or between nominal model (N) and offset models (N+, N-)
were established by using feature points that are known to have correspondence on two
models, which can be either done by manual specification, or by some intelligent feature
recognition algorithms [101]. If there were no salient feature point on the models,
artificial markers would be added on the surface of models to serve as the feature points.
This is important especially for freeform shapes. An illustration of added markers is
shown in Figure 5.2.

Figure 5.2. Models with no salient feature points (a) Nominal CAD model (b) physical model
Note that the designed markers on the nominal model as shown in Figure 5.2(a) need
to have a suitable size in order to be successfully built and measured, as shown in Figure
Markers
Markers
(a) (b)
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5.2(b). After multiple testing, we design the markers as a set of cylinders with a diameter
of 0.6 mm and a height of 0.5 mm in this study.
The specified feature points define a sparse and discrete correspondence between
different models. To establish a continuous mapping from the sparse one, we apply the
cross-parameterization method [102, 103]. Specifically, the method partitions both of the
models to a set of corresponding patches by linking the input feature points in a
consistent way. Then, the cross-parameterization between the models is found by
computing the mapping between all the corresponding patches. The mapping computed is
bijective and optimized to have low distortion.
An example of cross-parameterization result is shown in Figure 5.3, in which 35
artificial markers have been added respectively on two models.

Figure 5.3. Cross-parameterization of two models with 35 artificial markers
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5.3.2 Capture the Deformation of Physical Model
Once the correspondence between the nominal model (N) and the deformed physical
model (M) is established, the two models are firstly aligned, and the deformation for each
point on the nominal profile can be easily calculated by subtracting its coordinate from
that of its corresponding point on the measured profile.
For an illustration, the modified letter H model used for the accuracy study in
Chapter 2 is selected. The schematic of the model used in this study are shown in Figure
2.16(b) (unit in mm). The part has length of 101.6 mm, width of 20.32 mm and height of
50.8 mm. The model was built using a commercial MIP-SL machine (Ultra by
EnvisionTec Inc. [24]). The built object is shown in Figure 2.16(a). It can be observed
that plate A is curved, and points A and B have dents on the vertical surfaces.
As the modified letter H part is a 2.5D model, we can measure its 2D profile using a
vision-based measurement tool. In this research, a high-precision microscope
measurement machine – Micro-Vu [75] was used to measure the deformation of the built
object. As can be seen from Figure 2.16(b), the 2D profile of letter H part is a regular
shape consists of several rectangles. It would be intuitively to measure the corner points
of these rectangles and their edges, and use these corner points to establish
correspondence between nominal model (N) and measured deformed model (M).
The sample points in the nominal model (N), and their correspondences from the
measurement of the physical model (M) are plotted in Figure 5.4, in which 10 points are
sampled from each boundary curve, and more points are sampled around corner or
position where large deformation gradients exist. User can control the number of sample
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points. The “*” points in blue denote nominal data, while “+” points in red denote
measured data. From the magnified views of section (1) and (2), which are picked from
the top horizontal plate and side surface, respectively, it is found that the measured data
shows the top horizontal plate is curved, while the sidewalls have dents after built, which
agrees with the deformation found on the physical built part. The deformation for each
point on the nominal model can be easily calculated.

Figure 5.4. Sample points of the nominal model and the corresponding points on the physical
model
5.4 Compensation Calibration
The relations between the added compensation and the final deformation are non-
linear, which makes it difficult to predict and compensate. Therefore, we investigated the
relations of added compensation and deformation based on physical experiments in this
research. In addition, we studied adding small compensation (or offsets) on the original
nominal model in order to establish the relations between these small offsets and their
related deformation using modified models, and to calculate the compensation based on
them. The method is based on the following assumptions and observations:
Unit: mm
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(1) Parts with the homogeneous shape will have the homogeneous deformation, i.e.,
deform in a similar trend and vary only in the amount. For example, bars with different
thicknesses will all have curl distortion, although they may differ in the magnitudes.
(2) Models with small offsets will have the homogeneous shape as that of the
original model.
(3) As the deformation of each point with or without compensation is in the same
trend, it is assumed that there is no or very little compounded deformation caused by
neighbors. Therefore, the deformation can be considered individually point-by-point.
It must be noted that the cross-parameterization presented in Section 3 is used to
compute the correspondences among all the nominal model (N), measured physical
model (M), offset CAD models (N+, N-) and their measured physical models (M+, M-).
Therefore, for each point on any offset model or scan model, it would be straightforward
to find its corresponding point on all the other models, and thus the deformation can be
easily calculated and the comparisons of deformation using offset models can also be
conducted.
5.4.1 Using Offset Models for Calibration
The method used in this study is explained as follows:
(1) First, building the original nominal model N, and for each point ( , [1,n]
i
P i  , n is
total number of vertices or sample points) on N, find the corresponding point
i
Q on the
measured model M, and calculate its deformation
i
D :
i i i
D Q P  
(3)
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(2) Modifying N according to the deformation calculated in step (1) to generate
offset models N+ and N-. For each point , [1,n]
i
P i  , modify it by offsetting along its
normal direction outwardly and inwardly of distance X
1
and X
2
, respectively, such that X
1

< -D
i
< X
2
. A corresponding point can be found on N+ and N-, denoted as
i
P

and
i
P

,
respectively. Similarly, the corresponding point on measured models M+, M- can be
found and denoted as
i
Q

and
i
Q

, respectively. The deformation for each point on the
offset models can also be calculated as:
i i i
D Q P
  
 
i i i
D Q P
  
 
(3) The physical experiments are to use several sets of compensation X (e.g. X
1
, X
2
,
etc.) and their corresponding deformation (e.g. f(P+X
1
), f(P+X
2
), etc.) to approximate the
deformation function f, and find approximation to the root of Equation (2).
As an illustration, two additional offset models for modified Letter H model are
designed by offsetting every point along its normal direction outwardly and inwardly 0.5
mm since the physical part has deformation around 0.5 mm. The offset models (N+, N-)
and physical built parts (M+, M-) of the modified Letter H model are shown in Figure 5.5.
The red dotted lines show the offset profiles (N+, N-), while the solid blue lines represent
original nominal profile (N).
(4)
(5)

Figure
The offset models are built, measured and analyzed following the same procedures
as the original nominal baseline model (
sampling points is picked on the offset profiles (
with no offset (N). Deformation for each point on the offset models (
by using point in the deformed profiles (
nominal profiles (N+, N-
outwardly model (N+) is
deformation for a point
calculated by Equation (5). The comparisons of measured deformed profiles (
M-) and original nominal baseline (
Figure 5.5. Offset models and physical built parts
The offset models are built, measured and analyzed following the same procedures
as the original nominal baseline model (N). After measurements, the same number of
sampling points is picked on the offset profiles (N+, N-) corresponding to that of profi
). Deformation for each point on the offset models (N+, N
by using point in the deformed profiles (M+, M-) minus its corresponding point on the
-). As illustrated earlier, the deformation for a po
) is
i
D

, which is calculated by Equation (4). Similarly, the
deformation for a point
i
P

on the offset inward model (N-) is represented as
quation (5). The comparisons of measured deformed profiles (
) and original nominal baseline (N) are shown in Figure 5.6.
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The offset models are built, measured and analyzed following the same procedures
). After measurements, the same number of
) corresponding to that of profile
N+, N-) is calculated
) minus its corresponding point on the
). As illustrated earlier, the deformation for a point
i
P

on offset
quation (4). Similarly, the
) is represented as
i
D

and
quation (5). The comparisons of measured deformed profiles (M, M+ and
141

Figure 5.6. Comparisons of deformation of models with no offset and offsets
In Figure 5.6, the blue “*” dots show the nominal baseline profile with no offset (N),
while the red “+” dots show the deformed profile with no offset (M), the gray “x” dots
show the deformed profile with offset inwardly 0.5mm (M-), and the pink “.” dots show
the deformed profile with offset outwardly 0.5mm (M+). From the magnified view of
sections (1) and (2), it is found that nominal baseline profile (N) is within the range of
deformed profiles with offsets (M+ and M-).
5.4.2 Compensated Profile
Compensation for each point is calculated by using three pairs of offset and
deformation. There are many ways to calculate the compensation based on these data, e.g.
use polynomial functions with different orders to fit the data, and find the target
compensation, etc. In our study, we used second-order polynomial to fit these data. The
compensated profile is shown in Figure 5.7. The nominal baseline profile (N) and the
original deformation profile with no offset (M) are also plotted in the figure for
Unit: mm
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comparisons. The compensated profile shows in red dots, while blue dots show the
nominal profile (N), and pink dots represent deformed profile (M). Magnified views of a
point on the top surface of central plate, as well as a section on the region where dent
occurs, denoted as (1) and (2), are drawn to better demonstrate the compensation result.
From Figure 5.7, it can be seen that the compensated profile is in the reverse direction of
deformed profile with respect to nominal profile, and every point has different values of
compensation.

Figure 5.7. Compensated profile
5.5 Test Case 1 – 2.5D Freeform Shape
The modified Letter H part has been selected as test case 1 for compensation study.
The schematic of the model is shown in Figure 2.16(a). The correspondence between
nominal models (N) and the measured physical models (M), as well as the calculation of
compensated profile are explained in previous sections. Based on the compensation
calculated, a modified nominal model is generated accordingly (denoted as C). The
compensated STL model to be fabricated is shown in Figure 5.8.
Unit: mm
143

Figure 5.8. Compensated STL model
5.5.1 Comparisons of Deformation Before and After Compensation
The compensated STL is built and measured following the same procedure as other
models. The measured deformed profile is aligned with nominal baseline profile, and the
same number of sampling points are picked from the same positions of baseline nominal
model and measured profile of compensated part. The comparisons of deformation using
compensated STL model (C) and original model without compensation (N) are shown in
Figure 5.9.

Figure 5.9. Comparisons of deformation before and after compensation
Unit: mm
144

Similar to previous analysis, magnified views of a section on the top surface of
central plate and sidewalls where dents occur are drawn to better illustration. The
compensated profile shows in red “.” dots, while the original deformed profile shows in
pink “x” dots, and the blue “*” dots represent original nominal profile. From the plot, it
can be found that the pink profile using compensated STL model (C) is more conformal
to the blue nominal baseline profile (N), which suggests the deformation using
compensated model (C) is much smaller than original model without compensation (N).
The comparisons of physical built part using compensation and original part are
shown in Figure 5.10. To quantitatively characterize the deformation for parts built with
and without compensation, we calculate the L
∞
-norm (max distance) and L
2
-norm (root
mean squared distance) of points in nominal profile to corresponding closest points in the
deformed profile, and the results are shown in Table 5.1.

Figure 5.10. Comparison of physical built parts. (a) Original part; (b) part with compensation
Table 5.1. Deformation comparisons before and after compensation for test case 1(unit: mm)
Before
compensation
After
compensation
Improvement
L
∞
-norm 0.768 0.270 65%
L
2
-norm 0.276 0.090 67%
(a) (b)
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From the table, it is found that using the compensated model (C) can effectively
reduce deformation when compare to using original model without any compensation (N),
specifically, the deformation improvement is 65% and 67% in terms of L
∞
-norm and L
2
-
norm, respectively.
5.6 Test Case 2 – 3D Freeform Shape
In order to further verify the effectiveness of our reverse compensation strategy,
another test case, which is a freeform 3D shape as shown in Figure 5.11, has been
selected to apply the presented computational framework.

Figure 5.11. Testcase 2 – 3D freeform shape: (a) Isometric view; (b) front view
The test case was built vertically, as shown in Figure 5.11(b). The physical built part
has deformation with two legs spreading out. The deformation is mainly caused by the
shrinkage of the top arch. The nominal dimension between the leftmost point and
rightmost point is 51.92 mm. However, in this test case, the surface of the test part is
smooth with no sharp edge. Therefore, it would be difficult to use microscope to measure
(a) (b)
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the deformed profile. Instead, a 3D scanner is required to measure the built physical
object. Similar measuring approach can be used for other 3D test parts.
In our study, a DA VID-SLS2 3D scanner [104] has been employed to measure the
deformation of test case 2. The 3D scanner is calibrated before it is used for scanning. As
it shows in Figure 5.11, test case 2 does not have many salient feature points which can
be used for parameterizing the given model. Small artificial markers are added on
selected positions to assist the parameterization by establishing correspondence between
points on nominal model and deformed model.
5.6.1 Measurement Error of 3D Scanner
Although the 3D scanner is carefully calibrated before use, and the measurement
error needs to be studied. A standard square block test part has been designed to study the
measurement error, shown in Figure 5.12.

Figure 5.12. Standard test part for accuracy study
The dimension of top surface on the test part is 30 mm by 30 mm. The test part has
some added features such as chamfer and cylinder hole cut to assist scan data alignment.
Three types of markers, e.g. cylinder, cone and block, with different dimensions, ranging
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from 0.2 mm to 1.3 mm in terms of diameter or length, have been designed on the surface
test part. There are two purposes for the designed markers, the first one is to help scan
data alignment during the fusion process, while the other is to investigate the suitable size
of markers that can be built in MIP-SL process as well as recognized by 3D scanner, and
provide a basis for artificial markers design study.
The designed test part was built in MIP-SL machine, and was measured using
DA VID SLS-2 scanner. The scan and fusion result is shown in Figure 5.13, in which the
dimension of top surface is shown in Figure 5.13(b)). As it can be seen, the scan result
has a dimension of 30.199 mm by 30.253 mm. For comparison, the physical built part
was measured by using caliper, and the readings for the dimension of corresponding
length are around 29.95 mm by 30 mm, therefore the measurement error for 3D scanner
is around 0.2 ~ 0.3 mm.

Figure 5.13. Scan result of test part for accuracy study. (a) Scan fusion result; (b) dimensions of
top surface
5.6.2 Artificial Markers Design
From the measurement error study of 3D scanner, it is found that using markers with
cylinder shape and diameter of larger than 0.6 mm can be built and scanned; therefore,
(a) (b)
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we used cylinder marker with diameter 0.6 mm and height of 0.5 mm in our study. The
purpose is to pick the smallest markers that can be built and measured using 3D scanner,
and have least effect on test part deformation study. In our study, 35 markers have been
used to consistently parameterize two homogeneous models, an example is shown in
Figure 5.3, in which the green dots with indices show the positions where artificial
markers are placed.
Two sets of markers have been applied in this research. The first set of markers is to
establish correspondence between baseline nominal model and its offset models. The
other set of markers is to find correspondence between nominal model and scan model.
Ultimately, all models can share the same number of mesh and vertices as the baseline
nominal model. For each point on any offset model or scan model, it would be very easy
to find its unique corresponding point on all other models, therefore the deformation can
be easily calculated and comparisons of deformation using offset models can also be
easily conducted.
5.6.3 Deformation Calculations
The baseline nominal model with 35 artificial markers was built in Ultra machine.
The nominal STL model (N) and physical built are shown in Figure 5.2. The physical
built part was scanned using a 3D scanner followed the same procedures as those in test
case 1. It should be noted that the top surface was scanned while the bottom is hollow,
and the hole was filled during fusion process. The fusion result is shown in Figure 5.14(a),
from which it can be seen that there are artificial markers on front and side surfaces.
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Figure 5.14. Scan model of baseline part. (a) Scan model with markers; (b) scan model with
markers removed
The artificial markers on the scan model are correspondent to that on the nominal
STL model. The positions of these markers on respective mesh model were recorded. To
calculate the deformation of built part, these markers were smoothed and removed from
both scan model and STL model since they are only designed to establish the
correspondence of these two models and to assist mesh parameterization. The smoothed
scan model with no marker is shown in Figure 5.14(b). Consistent mesh parameterization
of smoothed scan model (M) and nominal STL model (N) with no marker can be
calculated based on the positions of these 35 corresponding markers, similar to that as
shown in Figure 5.3. Every vertex in the scan model (with no marker) has a bijective
mapping to a vertex in nominal STL model after parameterization.
The scan model is then transformed to align with nominal STL model, and plotted in
Figure 5.15(a). Magnified views of two sections selected from top and bottom are created
for better illustration, shown in Figure 5.15(b).
(a)
(b)
150

Figure 5.15. Comparison of baseline nominal model and scan model compensation (a)
Comparison of entire model; (b) magnified views of two sections
The blue dots represent the nominal STL model (N), while the red dots show the
scan model (M). From which it can be clearly seen that the scan model has deformation
with two legs splayed outwardly, and the part has shrinkage. Besides, by carefully
examine the plot, it can be found that the deformation of left leg and right leg is not
symmetric, which agrees with deformation of physical built part. This slightly non-
symmetric deformation, which may be generated by hardware such as non-uniform light
projection, demonstrates the effectiveness of using artificial markers and
parameterization to find correspondence between scan model and nominal model.
5.6.4 Deformation of Offset Models and Analysis
In order to investigate the relations of compensation and related deformation, two
additional models (N+, N-) have been designed with offset outwardly 0.5 mm and
inwardly 0.5 mm, respectively. The nominal offset models are shown in Figure 5.16.
(a) (b)
Unit: mm
151

Figure 5.16. Nominal offset models of test case 2
These two test parts are built and scanned with same parameter settings as the
original baseline part. The physical built parts for offset models are shown in Figure 5.17.
The physical built parts manifest deformation with two legs splayed outwardly, which
can be found by closely examine and compare Figure 5.16 and 5.17.

Figure 5.17. Physical built parts of offset models
Similar to the parameterization process in baseline model and its scan model, the
nominal offset models (N+, N-) and scan models (M+, M-) are parameterized using the
(a) (b)
(a)
(b)
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positions of 35 artificial markers on them. The comparisons of deformation using offset
models with outwardly 0.5 mm and inwardly 0.5 mm are plotted in Figure 5.18(a) and
5.18(b), respectively. In both figures, the blue dots show the nominal model, while the
red dots represent the deformed model (scan data).

Figure 5.18. Deformation using offset models: (a) Offset outwardly; (b) Offset inwardly
As can be seen from Figure 5.15 and 5.18, all these three test parts (M, M+ and M-)
follow the same deformation trend; with two legs splayed outwardly, and have dents in
the center portion of legs. The parts are built on support structures. During the building
process, two legs are built first. It can be found that the legs are built with a small angle
upwards. The solidification of current building layer is restricted by the underlying layer,
causing tensile stress on current layer and compressive stress on the underlying layer.
Besides, the slightly mismatch of curing region between current layer and the layers
below it will generate a bending moment, which has the tendency of bending the legs
outwardly. The arch is built on top of two legs. Similarly, the shrinkage of arch layers are
Unit: mm
(a)
(b)
Unit: mm
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constrained by the two legs and the support structures, which leads to internal stress built
up. The residual stress is released when the building process is finished and the part is
removed from the support structures. The related bending moment will cause the legs
splayed outwardly.
5.6.5 Reverse Compensation
After mesh parameterization using artificial markers, all six models (nominal models
N, N+, N- and scan models M, M+ and M-) have well-defined correspondence. Each
vertex in one model has a unique bijective mapping to a vertex in another model.
Therefore, the relations between deformation and offset for each vertex can be
approximated by using the physical parts we built. Based on which the compensation can
be calculated for each vertex (refer to Equation (2) in Section 5.1). The calculated
compensation and compensated STL model is shown in Figure 5.19(a) and 5.19(b),
respectively.

Figure 5.19. Compensation. (a) Compare with nominal model; (b) compensated STL model
Unit: mm
(a)
(b)
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In Figure 5.19(a), the compensation profile is shown in red dots while the nominal
model is shown in blue dots from which it can be found that the compensation is in the
reverse direction as original deformation shown in Figure 5.15 and 5.18. Using the
compensation profile, the nominal model can be easily modified with compensation
added on it and exported as compensated STL model.
5.6.6 Deformation Comparisons
The compensated STL model is built with 35 artificial markers added on it, and then
measured using 3D scanner and compared with nominal model following the same
procedure as before. The comparisons of physical part with and without compensation are
shown in Figure 5.20.

Figure 5.20. Physical parts comparisons. (a) Without compensation; (b) with compensation
The deformation of physical part with compensation is calculated by comparing
nominal STL model and scan model, and shown in Figure 5.21.
(a) (b)
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Figure 5.21. Deformation of built part with compensation. (a) Comparison of entire model; (b)
magnified views of two sections
Magnified views of two select sections on the top and bottom are created for better
illustration. When compared with Figure 5.15, it can be found that the part built with
compensation has much less deformation than original designed shape.
Similar to test case 1, the deformation of physically built objects with and without
compensation are quantitatively compared. L
∞
-norm (max distance) and L
2
-norm (root
mean squared distance) of points in nominal model to corresponding closest points in
deformed model (x-z plane) is calculated for both parts, and shown in Table 5.2.
Table 5.2. Deformation comparisons before and after compensation for test case 2(unit: mm)
Before
compensation
After compensation Improvement
L
∞
-norm 2.240 1.300 42%
L
2
-norm 0.692 0.3111 55%

(a)
(b)
Unit: mm
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The L
∞
-norm of deformation before and after using compensation is 2.24 mm and
1.3 mm, respectively, with deformation improvement around 42%. The L
2
-norm of
deformation without compensation is 0.692 mm, while the L
2
-norm of deformation with
compensation is 0.311 mm, which shows that using compensation can have around 55%
improvement on deformation.
5.7 Concluding Remarks
In this chapter, we present a general computation framework based on reverse
compensation to reduce the complex deformation that may happen in additive
manufacturing processes. Corresponding points between nominal and deformed shapes
are found by applying cross-parameterization using feature points. Such features points
could be the existing salient features on the model, or any artificial markers added on 3D
freeform shapes. By studying relations of offsets and deformation for each point, the
reverse compensated models can be calculated. Two test cases have been selected to
demonstrate the capability of the developed computation framework. The final
compensated STL models are built and compared with original models. It is found that
the compensated models can greatly reduced the shape deformation for both test cases.
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Chapter 6 Conclusions and Recommendations for Future
Research
Part accuracy is one of the most important issues in mask image projection based
stereolithography process and other additive manufacturing processes. The primary goal
of this research is to reduce deformation of built part in mask image projection based
stereolithography process. The research scope and procedure is oriented around this goal.
In this chapter, hypotheses are tested and verified in the first section. Following that, the
contributions and intellectual merit of this research are summarized. The limitations of
current research and future research work are discussed in the last section.
6. 1 Answering the Research Questions/Testing Hypotheses
As stated in Chapter 1, the primary research question is:

Q1. How to reduce part deformation in the mask image projection based
stereolithography process?

To answer this question, the following hypotheses are investigated:

H1. Less deformation can be achieved by using process planning methods
(exposure strategies).
H2. Deformation can be reduced by using pre-modified part geometry approach.

Hypothesis 1 can be further divided into two sub-hypotheses:

158

H1.1. Part deformation can be reduced by reducing shrinkage effect by using
exposure strategies.
H1.2. Part deformation can be reduced by lowering down curing temperature of
built layer.

To test Hypothesis 1.1, mask image planning method for the MIP-SL process is
developed in Chapter 2 to reduce the shrinkage and related deformation in the built parts.
Three different exposure strategies have been investigated, with their defining parameters
characterized. Physical experiments with two test cases have verified that the proposed
mask patterns exposure strategies can effectively reduce deformation.
Hypothesis 1.2 is tested in Chapter 3, in which a high-resolution IR camera is
adopted to systematically study curing temperature distribution and evolution in the
building process of the MIP-SL process. Effects of building parameters, such as layer
thickness, grayscale levels (light intensity) and mask patterns exposures, etc. on curing
temperature have been investigated. Exposure strategies based on the study results have
been designed to lower curing temperature of building layers. Physical experiments
demonstrated the effectiveness of the designed exposure strategies.
Similar to Hypothesis 1, Hypothesis 2 can also be divided into two sub-hypotheses:

H2.1. Reverse compensation based on Finite Element Analysis simulation can be
adopted to improve the part accuracy.
H2.2. Reverse compensation based on physical measurement can be used to
modify original part geometry, and improve the part accuracy.

159

To test Hypothesis 2.1, a Finite Element Analysis model has been developed in
Chapter 4 to simulate the deformation of build part in MIP-SL process. A test case has
been selected to go through the simulation process, which shows similar deformation
trend as physical built part. Reverse compensation based on the simulated deformation
has been conducted, which shows the final deformation after reverse compensation is
much smaller than the original deformation.
Hypothesis 2.2 is tested in chapter 5, where a reverse computation framework based
on physical experiments is presented to reduce the shape deformation of fabricated parts.
A novel method is developed to establish the optimal correspondence between the
deformed shape and the nominal CAD model. Compensation is calculated by studying
the relations of offsets and related deformation. Physical experiments with two test cases
have verified the effectiveness of the presented computation framework.
6. 2 Contributions and Intellectual Merit
The contributions of this research are as follows:
1. Propose mask patterns exposure strategies in MIP-SL process, and a method to
generate mask patterns flexibly.
2. Insight into the effects of mask pattern parameters on shrinkage related
deformation, including mask pattern types and structures, gap size, iteration number and
with or without using boundary exposure.
3. Systematically study the curing temperature distribution within building layer, as
well as temperature evolution during the MIP-SL building process, by using high-
resolution IR camera.
160

4. Insight on effects of building parameters on curing temperature of built layer,
including layer thickness, curing region sizes and shapes, and grayscale levels exposures.
5. Develop a Finite Element (FE) model and related procedure to simulate curl (out-
of-plane) distortion in MIP-SL process.
6. Establish a reverse compensation procedure based on FE model to reduce out-of-
plane distortion error in MIP-SL process.
7. Develop a general reverse compensation computational framework based on
physical measurements to deal with deformation comes from complex sources.
8. Develop a novel method to capture the deformation for each point on the freeform
models based on cross-parameterization.
9. Develop a compensation calibration method to study the relationship of shape and
deformation, and predict the compensation intelligently.
This research is mainly focused on improving accuracy of parts built in MIP-SL
process; however, MIP-SL process and other AM processes have a lot in common in
terms of deformation sources. The exposure strategies developed in this research, and the
reverse compensation computational framework based on FEA simulation or physical
experiments, can also be applied to other AM processes. Therefore, this research work
would be very significant.
6. 3 Limitations and Future Work
Deformation is one of the most challenging problems in MIP-SL process and all
other AM processes due to its various complex deformation sources. This research
developed several effective methods to control deformation. However, there are lots of
161

limitations need to be improved. The limitations and future research work are including
but not limited to:
(1) Inappropriate designed mask patterns exposure strategies may increase building
time or have weaker mechanic properties than original exposure without mask patterns.
(2) Exposure strategies using grayscale levels can effectively reduce deformation;
however, they can significantly increase the exposure time and building time of each
layer.
(3) FEA simulation model assume the material model is linear elastic, however, the
real material behavior is rather complex since the state of materials evolves from liquid to
solid. Besides, the simulation ignores the heat transfer to the environment, and assumes
uniform temperature within the building layer.
(4) FEA framework can only simulate small object with limited number of layers, it
would be very computational costly and time-consuming to simulate deformation of
bigger objects.
(5) To study the relations of offsets and their related deformation, the computational
framework based on physical experiments assume uniform offsets of nominal model,
however, the deformation of each point on the model is different, adaptive offset for each
point should be calculated instead.
The future research work would include:
(1) Conducting more physical experiments for the isolated cube pattern to better
understand the effects of related parameters, and investigating more effective mask
patterns.
162

(2) Developing optimized mask patterns based on the study of effects of building
parameters.
(3) In FEA simulation of deformation, actual material behavior needs to be studied
and modeled. More deformations sources (e.g. volumetric shrinkage, etc.) need to be
incorporated into FEA model. Besides, FEA simulation framework needs to be optimized
to efficiently simulate complex part with bigger size.
(4) Effective and efficient methods need to be developed to add smart artificial
markers on more general 3D shape model to assist finding correspondence between
deformed shape and nominal model.
(5) More intelligent offsetting strategies for compensation calibration need to be
investigated.
163

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Abstract (if available)

Abstract Based on a Digital Micromirror Device (DMD), Mask Image Projection based Stereolithography (MIP-SL) uses an area-processing approach by dynamically projecting mask images onto a resin surface to selectively cure liquid resin into layers of an object. Consequently, the related additive manufacturing process can be much faster with a lower cost than the laser-based Stereolithography Apparatus (SLA) process. However, the part built in MIP-SL process has deformation after building, which may be attributed to several reasons. First, the volumetric shrinkage takes place during the phase change process when liquid monomers are converted to solid polymer. Second, heat will be generated since the photopolymerization is an exothermic process, and thermal shrinkage is resulted when the curing layer cools down. Third, SLA is a layer-by-layer dynamic building process, in which current curing layer is restricted by the layers solidified below, therefore residual stress builds up. Moreover, the material used in MIP-SL process is acrylate resin, which has much larger shrinkage when it is solidified than the epoxy resin widely used in SLA process. As a result, the deformation of built part in MIP-SL is more obvious than that built in traditional SLA process. ❧ In this research, we address the deformation problems in MIP-SL process from two approaches. The first approach is based on using different exposure strategies. The shrinkage related deformation control method has been studied and verified using physical experiments, besides, the curing temperature during the photopolymerization process has been investigated, and exposure strategies have been designed to reduce part deformation. The second approach tries to reduce deformation through reverse compensation of input geometry based on the deformation calculation, which can either be done by using simulation or physical measurement. Finite Element Analysis(FEA) has been adopted to model and simulate the MIP-SL building process based on the curing temperature calibrated, and reverse compensation computational framework based on physical measurements has been investigated and applied to reduce deformation of fabricated part in MIP-SL process. ❧ For the shrinkage related deformation control method, an exposure strategy is investigated based on mask patterns by decomposing the exposure of a large area in one layer into several exposures of smaller areas in several layers, instead of curing the whole layer in one exposure. A mask image planning method and related algorithms have been developed for the MIP-SL process. The planned mask images have been tested by using a commercial MIP-SL machine. The experimental results illustrate that our method can effectively reduce the deformation. ❧ In the curing temperature studies, test cases of curing layers with different shapes, sizes and layer thicknesses have been designed and tested. The experimental results show that the temperature increase of a cured layer is mainly related to the layer thickness, while the layer shapes and sizes have little effect. The curing temperatures of built layers using different exposure strategies including varying exposure time, grayscale levels and mask image patterns have been studied. The curl distortion of a test case based on various exposure strategies have been measured and analyzed. It is shown that, by decreasing the curing temperature of built layers, the exposure strategies using grayscale levels and mask image patterns can effectively reduce the curl distortion. ❧ COMSOL Multiphysics software has been used to simulate the curl distortion of part built in MIP-SL. The dynamic layer-by-layer building process of MIP-SL has been simulated using birth and death technique. The curing temperature calibrated for each layer has been incorporated as thermal load into the FEA model. The curl distortion simulation result has the same trend with that of the physical built part. Based on the simulation result, a reverse compensation method has been applied on a simple test case to show the effectiveness of reducing curl distortion. ❧ A general reverse compensation computation framework based on physical measurements is presented to reduce the complex deformation in additive manufacturing process. A novel method is presented for identifying the optimal correspondence between the deformed shape and the given nominal CAD model. By studying relations of offsets and deformation for each point, the reverse compensated CAD models can be calculated. The intelligently modified CAD model, when used in fabrication, can significantly reduce the part deformation when compared to the nominal CAD model. Two test cases have been designed to demonstrate the effectiveness of the presented computation framework.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Xu, Kai (author)

Core Title Deformation control for mask image projection based stereolithography process

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Industrial and Systems Engineering

Publication Date 02/23/2016

Defense Date 01/19/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag additive manufacturing,deformation,mask image planning,OAI-PMH Harvest,photocuring temperature,reverse compensation,simulation,stereolithography

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Chen, Yong (committee chair), Huang, Qiang (committee member), Wu, Wei (committee member)

Creator Email ericxukai@gmail.com,kaixu@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-214352

Unique identifier UC11277503

Identifier etd-XuKai-4151.pdf (filename),usctheses-c40-214352 (legacy record id)

Legacy Identifier etd-XuKai-4151.pdf

Dmrecord 214352

Document Type Dissertation

Format application/pdf (imt)

Rights Xu, Kai

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA