Modeling A Scanning-Mask Projection Vat Photopolymerization System For Multiscale Additive Manufacturing

Journal Pre-proof Modeling A Scanning-Mask Projection Vat Photopolymerization System For Multiscale Additive Manufacturing Viswanth Meenakshisundaram, Logan D.Sturm, Christopher B.Williams

PII:

S0924-0136(19)30519-9

DOI:

https://doi.org/10.1016/j.jmatprotec.2019.116546

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PROTEC 116546

To appear in:

Journal of Materials Processing Tech.

Received Date:

26 November 2018

Revised Date:

2 December 2019

Accepted Date:

8 December 2019

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Modeling A Scanning-Mask Projection Vat Photopolymerization System For Multiscale Additive Manufacturing Viswanth Meenakshisundaram, Logan D.Sturm, Christopher B.Williams∗ Design,Research and Education for Additive Manufacturing Systems (DREAMS) Laboratory,Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA-24061.

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Macromolecules Innovation Institute, Virginia Tech, Blacksburg, VA-24061.

Abstract

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Industries such as orthodontics and athletic apparel are adopting vat photopolymerization (VP) to manufacture customized products with performance tailored

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through geometry. However, vat photopolymerization is limited by low manufacturing speeds and the trade-off between manufacturable part size and feature resolution. Current VP platforms and their optical sub-systems allow for simul-

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taneous maximization of only two of three critical manufacturing metrics: layer fabrication time, fabrication area, and printed feature resolution. The Scanning Mask Projection Vat Photopolymerization (S-MPVP1 ) system was developed

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to address this shortcoming. However, models developed to determine S-MPVP process parameters are accurate only for systems with an intensity distribution that can be approximated with a first order Gaussian distribution. Limitations of optical elements and the use of heterogeneous photopolymers result in nonanalytic intensity distributions. Modeling the effect of non-analytic intensity distribution on the resultant cure profile is necessary for accurate manufacturing

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of multiscale products. In this work, a model to predict the shape of cured features using analytic and non-analytic intensity distribution is presented. First, existing modeling techniques developed for laser and mask projection VP pro∗ Corresponding

author Email address: [email protected] (Christopher B.Williams ) 1 S-MPVP: Scanning Mask Projection Vat Photopolymerization

Preprint submitted to Journal of Materials Processing Technology

November 15, 2019

cesses were leveraged to create a numerical model to relate the process parameters (i.e. scan speed, mask pattern irradiance) of the S-MPVP system with the resulting cure profile. Then, by extracting the actual intensity distribution from the resin surface, we demonstrate the model”s ability to use non-analytic intensity distribution for computing the irradiance for any projected pattern. Using a custom S-MPVP system, process parameters required to fabricate test

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specimens were experimentally determined. These parameters were then input

into the S-MPVP model and the resulting cure profiles were simulated. Com-

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parison between the simulated and printed specimens’ dimensions demonstrates

the model”s effectiveness in predicting the dimensions of the cured shape with an error of 2.9%.

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Keywords: Additive Manufacturing, Stereolithography, Cure Modeling,

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Large-Area, Multiscale

1. Introduction

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1.1. Vat Photopolymerization Manufacturing Trade-off Vat photopolymerization (VP), also referred to as stereolithography, has remained a promising additive manufacturing (AM) process due to the superior surface finish (Ippolito et al., 1995), high-feature, resolution and nearly

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isotropic mechanical properties (Hague et al., 2004) of the fabricated parts. The true strength of VP lies in the tunability of material chemistry at two stages of fabrication: (i) photopolymerization in the vat and (ii) reactions outside the vat. For example, by introducing competing reactive groups (i.e., thiols

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and alkenes (Cramer and Bowman, 2001)) in the vat, Sirrine et al. (2018) ex-

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ploited the chain-extension mechanism to transform a densely cross-linked brittle oligomer to a sparsely cross-linked elastic oligomer. Outside the vat, thermal post-processing strategies have been used to convert a photo cross-linked, weak polymer pre-cursor to a fully cross-linked performance polymer. Hegde et al.

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(2017) and Herzberger et al. (2018) used this technique to additively manufacture 3D Kapton using acrylate derivatives of polyamic acid and polyamic

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acid salts respectively. In addition, process enhancements such as the use of oxygen inhibition (Tumbleston et al., 2015) has led to the additive manufacturing of performance polymers, such as polyurethanes, at high manufacturing 20

speeds. Several research groups have exploited this tunability of VP to expand the materials catalogue to include families of high-performance polymers such as polyimides (Hegde et al., 2017), high-strain elastomers (Patel et al., 2017),

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ionic liquids (Schultz et al., 2014), ceramics (Griffith and Halloran, 1996) and metamaterials (Zheng et al., 2016). The development of these high-performance photopolymers has kindled the interests of industrial sectors such as aerospace,

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which require low volume fabrication of meter-scale parts with multiscale architecture, and consumer sectors such as orthodontics and performance sports

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apparel (Adidas, 2018), which require high-volume fabrication of meso-scale parts with multi-scale architecture. For VP, tackling these disparate manufacturing requirements is a challenge because current VP process embodiments

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allow for the simultaneous maximization of only two of the three key manufac-

feature resolution.

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turing metrics (i) layer fabrication time, (ii) fabrication area, and (iii) printed

Based on the functional decomposition of AM processes, VP can be broadly 35

classified by the manner in which it selectively applies UV irradiation as 1D

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(laser-based) and 2D (mask-based) processes (Williams et al., 2011). Laserbased VP (LVP) processes use a laser to raster 2D geometries on the surface of the resin. LVP systems improve printed feature resolution by decreasing the laser spot size. With reduced spot size, the number of passes required to

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scan the geometry increases, therefore significantly increasing the manufacturing time. Further, optical phenomenon such as the keystone effect become apparent

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with increase in part size. This often leads to poor part resolution and surface finish. Solutions to mitigate this inherent process limitation often involve the use of multiple lasers and dynamically-varying laser spot diameters (e.g., the

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Mammoth SLA system by Materialize and 3SP series from EnvisionTec), which make the process uneconomical for some manufacturing sectors. Mask-based VP processes use a mask to selectively project a 2D pattern of 3

UV energy on the surface of the resin. Unlike lithography processes that use a stationary mask, Mask-Projection Vat Photopolymerization (MPVP) employs 50

a dynamic mask for projection of 2D patterns. Digital micro-mirror devices R (DMD) are frequently used because the recent advancements in DLP technol-

ogy have made it economically feasible for MPVP systems to achieve features as small as 5 µm (Raman et al., 2016). In general, the size of the printed

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part and the printed feature resolution depend on the size of the mask and the size of smallest controllable unit (pixel) or micro-mirror in the case of DMD.

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Maximization of the three key manufacturing metrics in MPVP systems can be achieved with the use of very large, high-resolution DMD arrays. It must be noted that the DMD array size must be at least as big as the part to be manu-

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factured and must contain micro-mirrors that are smaller than or equal to the size of the smallest part feature. However, manufacturing large DMD arrays is

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a technical challenge and is not economically feasible for DMD manufacturers. Assuming that the largest available DMD array with the highest resolution is used for fabrication, the achievable feature size in the MPVP process is still

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fundamentally limited by the choice of optical elements. Projection lenses with large magnifications (Q >1) enable the projection of larger areas. However, large projected pixel size limits the manufacturable feature size. Conversely, using de-

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magnification lenses allows for the fabrication of high-resolution features at the cost of build volume. Therefore, MPVP systems are configured around this limitation to maximize the manufacturing metrics for multiscale materials.

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1.2. Multiscale Fabrication via MPVP Manufacturing multiscale parts requires the process to have the ability to

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fabricate micron-scale features over large areas. While MPVP systems cannot achieve this in their native configurations, certain process modifications have shown the promise for enabling multiscale fabrication. Manufacturing high res-

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olution parts using de-magnification optics with moderate to large fabrication areas has been demonstrated by Zheng et al. (2016), Lee et al. (2015) and Emami et al. (2014). Lee et al. (2015) developed a tiling-MPVP system, wherein small 4

high-resolution tiles were sequentially projected across the resin surface. The seams between the projected tiles were stitched by projecting overlapping tiles 80

with gray-scaling at the edges. While the tiling-MPVP system was successful in fabricating large area high-resolution parts, achieving perfect blending of interfaces is computationally expensive as the complexity of the part geometry increases. Further, indexing time increases linearly with increase in part

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footprint and leads to increase in layer fabrication time. Zheng et al. (2016)

circumvented the layer fabrication time problem by tiling 2D patterns across

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the resin surface using a fixed projector and X-Y scanning galvo-mirrors. While the use of flat-field scan lens solves the keystone problems, it cannot be eas-

ily scaled for industrial manufacturing because manufacturing large flat-field

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lenses with projection areas as big as automobile or aerospace components is a manufacturing challenge.

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To enable true multiscale fabrication, the MPVP system would have to satisfy the following criterion: (i) project high-resolution features, (ii) translate the feature fabrication over large continuous areas, and (iii) eliminate the possibil-

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ity of damage to the printed features during fabrication. Looking at all of the modified MPVP platforms, it can be deduced that the tiling MPVP platform satisfies all but one requirement, i.e. it cannot fabricate large continuous ar-

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eas. This shortcoming could be addressed if the projection unit were scanned across the resin surface. This design modification was incorporated by Emami et al. (2014) as shown in Figure 1. Emami”s scanning mask projection vat pho-

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topolymerization (S-MPVP) system eliminated the size restrictions imposed by the X-Y scanning galvo-mirrors by mounting the entire projection unit on a X-Y stage, similar to the tiling-MPVP machine developed by Lee et al. (2015).

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Further, by using a top-down configuration, the size limitations posed by the adhesion forces in bottom-up MPVP system were also eliminated. Finally, the

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inter-tile seams observed in the tiling MPVP system were significantly reduced by scanning a continuous dynamic moving mask across the resin surface. The construction, operation, and fabrication of parts using the S-MPVP strategy have already been demonstrated by Emami et al. (2014) and He et al. (2017). 5

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Figure 1: An illustration outlining the S-MPVP process flow. CAD parts (A) are sliced into

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cross-sectional layers of desired thickness (B). Each slice (C) is converted into a bitmap image (D) which is further split into multiple rows (E). Each row is converted into a movie and fed into the projector. Projector scans over the surface of the resin while playing the movie (F).

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Further, the S-MPVP concept has also been patented and implemented in the industrial manufacturing system developed by Prodways (Allanic, 2015). 1.3. Modeling the S-MPVP system The operational performance of multiscale parts depends on printed feature

accuracy. To achieve high accuracy multiscale fabrication using the S-MPVP

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system, a model is required to understand how process parameters such as

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projector scanning speed and projected intensity distribution affect the printed feature size. The models developed for MPVP systems cannot be directly translated to S-MPVP systems. In MPVP system, curing is achieved by exposing the resin to a static intensity distribution for a predetermined amount of time. In S-MPVP systems, energy is selectively delivered to the resin by simultaneously 6

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scanning and projecting a movie of the layer at a prescribed scan velocity and frame rate, respectively. Emami et al. (2015) presented a model that relates the projector scanning speed and the resultant resin cure depth. The model assumes that the intensity distribution emanating from a micro-mirror is Gaussian. Zhou and Chen (2009) have demonstrated that the intensity distribution

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from a DMD-based mask projection device is not truly Gaussian. This can be

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attributed to factors such as:

(i) the orientations of the DMD discrete micro-mirrors will not be uniform

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during the projection of a 2D pattern;

(ii) the beam of light impinging on the DMD surface is not purely collimated; (iii) the optical elements used to relay light into and away from the DMD are

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not perfect optical elements;

(iv) the intensity distribution emanating from the projection optics will not be

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identical to the intensity distribution observed by the resin due to optical phenomenon such as scattering;

For accurate prediction of printed feature dimensions, it is thus imperative

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for the intensity distribution to be measured experimentally at the resin surface. This is especially critical for heterogeneous photopolymer systems that employ

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fillers for enhancing mechanical properties (Elliott et al., 2013). Further, capturing the optical interaction at the resin surface with an analytic model is

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very challenging. In this paper, the authors address this research gap with a numerical model that can handle non-analytic intensity distributions that are obtained through direct intensity measurements on the resin surface. The SMPVP model, presented in this paper, is developed to achieve the following

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objectives:

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(i) compute the intensity distribution on the resin surface through experimentally obtained values;

(ii) determine the overall intensity distribution for a projected pattern;

(iii) determine the exposure on the resin surface when the projected intensity distribution varies continuously; 7

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(iv) compute the dimensions of the fabricated part for a given set of material and process parameters; In the course of achieving these objectives, the developed S-MPVP model will enable answering the following research questions: (i) How does the scanning process affect the line width of the cured feature? (ii) For a given material, whose depth of penetration (Dp ) and Critical Energy

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(Ec ) are known, what is the projector scan speed required to achieve the

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required layer thickness?

(iii) What is the speed at which the dynamic mask must be changed (i.e. the frame rate of the dynamic mask) to maximize geometric accuracy?

In Section 2, the authors present an overview of the S-MPVP system and the

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process flow. A functional decomposition of the S-MPVP process is presented

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and the process parameters are identified. In Section 3, the process model is introduced and the models for the sub-systems are detailed. In Section 4, the methods used to experimentally validate the S-MPVP model are outlined. In Section 5, the verification and validation of the S-MPVP model via fabrication

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of test specimens is presented. The conclusion and future work are outlined in

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Section 6.

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2. Scanning Mask-Projection Vat Photopolymerization System

Figure 2: Schematic of a top-down scanning-mask projection vat photopolymerization system.

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The projection device is mounted on a X-Y scanning linear stage, while the other components such as the light source and build platform have the same configuration as traditional MPVP

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systems.

As shown in Figure 1, the bitmap image corresponding to a layer is bigger 170

than the projection area for large-scale parts, even after considerable optical

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magnification. In the S-MPVP system, a custom image processing tool splits the bitmap image of the layer into multiple scan rows. Each row is then converted into a movie and projected on the resin surface with the continuously scanning DMD that is mounted on an X-Y gantry. A simplified schematic of the S-MPVP

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system is shown in Figure 2.

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2.1. S-MPVP Functional Decomposition and Process Parameters To assist with the comparison between S-MPVP and traditional MPVP sys-

tems, the functional decomposition (Williams et al., 2011) of both systems are shown in Figure 3. It can be observed that the S-MPVP and MPVP systems

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are mostly identical, except in the pattern motion sub-function: the MPVP pattern is held stationary on the resin surface whereas the S-MPVP pattern

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Figure 3: Functional decomposition of the S-MPVP system.

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is scanned across the resin surface. The scanning sub-function introduces two new process parameters to MPVP: (i) scanning velocity and (ii) pattern frame

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rate. In addition to the scanning velocity and the pattern frame rate, the other process and material parameters that affect the magnitude and the distribution

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of energy delivered to the resin are highlighted in Table 1.

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Table 1: List of process parameters in the S-MPVP process

Process Parameters

Symbol Definition

UV intensity

I

The power per unit area of the incident UV light on the resin surface (mW/cm2 )

Scan speed

Sresin

Speed with which the projected pat-

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tern traverses across the resin surface (mm/s) F

The frequency at which the DMD

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Pattern frame rate

projects the bitmap frames on the resin surface (f rames/s) Symbol Definition

Critical exposure

Ec

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Material Parameters

The exposure at which the resin

Depth of penetration

Dp

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starts to solidify (mJ/cm2 ) Depth of penetration of the UV pattern inside the resin until reduction

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3. Process Model

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in irradiance is 1/e (µm).

In this section, an overview of the strategy used to model the S-MPVP sys-

tem is provided. As shown in Figure 4, the process of fabricating a single layer in

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S-MPVP comprises three fundamental steps: (i) projection of a 2D pattern, (ii) scanning the projected pattern onto the resin surface, and (iii) curing the liquid photopolymer into a solid layer. To determine the cure profile for a specific set

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of process parameters, the single-pixel intensity distribution (process parameter), DMD pitch (machine parameter), and the bitmap pattern (part specific

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parameter) are fed as inputs to the irradiance model. The output of the irradiance model is the intensity distribution that accounts for all the interactions arising from the interference of the projections from individual micro-mirror in the DMD array. The energy model is then used to couple the scan speed, 11

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Figure 4: Overview of the S-MPVP model.

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pattern frame rate (process parameters), and the intensity distribution to determine the exposure on the resin surface. The output of the energy model is not only the magnitude of the exposure during scanning, but also the distribution

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of exposure across the surface of the resin. Finally, the cure model is used to integrate critical exposure and depth of penetration (intrinsic material parameters) with the computed exposure distribution to predict the profile of the cured layer. Sub-sections 3.1-3.3 discuss the development of irradiance, energy, and

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cure models in detail.

3.1. Irradiance model

In the current system, the irradiance on the resin surface is equal to the

intensity (the power per unit area) because the projected light is normal to the resin surface. However, the intensity on the resin surface is not constant and

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varies in the projection (XY) plane. Determining this intensity distribution is critical for computing the shape of the cured photopolymer. In this subsection, the model to determine the intensity distribution during the projection of a 2D pattern is presented. Consider the DMD projecting a single pixel on the resin

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surface as shown in Figure 5. Only the intensity distribution arising from the 12

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Figure 5: Illustration showing the discretization scheme of the projection area. Intensity

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distribution is computed across the entire projection area.

micro-mirror in the ”ON” state (or white pixel in the corresponding bitmap image) will contribute to photopolymerization.

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The projected area, L × W , is discretized into small elements ∆x. The discretization is selected such that ∆x << Q × 2w, where Q and 2w are the

linear magnification and micro-mirror pitch, respectively. Any point in the projected area can be represented as P (X, Y ) = P (u∆x, v∆x). If the intensity distribution on the resin surface produced by micro-mirror Mi,j at the location (i,j) is represented by Ii,j (X, Y ), then its transformation into the discretized

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projection area can be represented as shown in Eq.1     0≤i≤m    Ii,j (X, Y ) ≡ Ii,j (u∆x, v∆x), when      0 ≤ j ≤ n

0≤u≤

L ∆x (1)

0≤v≤

W ∆x

To compute the overall intensity distribution, arising from the projection of 13

a bitmap image, the intensity contributions of all active micro-mirrors have to 220

to be considered. Zhou et al. (2009) have shown that the intensity distribution emanating from a micro-mirror is dependent on the state of the adjacent micromirrors and the constructive interference occurring between the micro-mirrors can be computed using superposition principle. Using Zhou”s strategy, the overall intensity distribution is modeled as a function of the bitmap pattern, i.e. the projected frame. The overall intensity distribution for any projected

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frame, If (X, Y ), is computed using Eq.2, where Bi,j (f ) is a discrete function

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for a particular projection pattern f. When a pixel is turned on at location i,j in the frame f, Bi,j (f ) = 1 else Bi,j (f ) = 0. i=m X X j=n i=1 j=1

(2)

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3.2. Energy model

Bi,j (f ) × Ii,j (u∆x, v∆x)

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If (X, Y ) ≡ If (u∆x, v∆x) =

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Figure 6: In the standard MPVP process, the desired pattern (A) is converted to a bitmap image (B) and transferred to the DMD (C). The projected pattern and the associated intensity distribution are invariant with respect to time (for a single layer). Consequently, exposure distribution is a product of the intensity distribution and the exposure time.

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Modeling the exposure distribution is important because it controls the cure

profile and the layer thickness (F. Jacobs, 1992). In traditional MPVP systems,

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shown in Figure 6, the exposure distribution on the resin is equal to the product of intensity distribution and exposure time. Since the intensity profile is dependent on the projected bitmap pattern, the energy distribution and the resulting

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cure profile are functions of the bitmap pattern and the exposure time. In the S-MPVP system, a dynamic intensity distribution is scanned over the resin surface to deliver energy. Therefore, exposure distribution cannot be estimated 14

using strategies developed for MPVP systems. This section models the effect of scanning on the exposure distribution on the resin surface. 3.2.1. Exposure on the resin surface during the scanning of a projected frame

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Figure 7: Discretization scheme for estimating the exposure distribution during the scanning

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of a single frame.

Consider the case where a single pixel has to be fabricated, as shown in

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Figure 6(A). First the bitmap representation of the feature is created as shown in Figure 6(B). Consider frame F1 is projected and scanned on the resin surface for a distance r∆x, as shown in Figure 7. The scan parameter ‘r’ is an integer value that represents the additional number of discretized units that will be exposed

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to UV light during scanning. If the scanning speed of the projector is Sproj , then the velocity of the scanned pattern on the resin surface is Sresin = Q × Sproj because each projected pixel is magnified by a linear magnification factor of Q.

The exposure time for each discretized unit, ∆x, is given by t = ∆x/Sresin . The exposure at any point on the resin(u∆x, v∆x), is directly proportional

to the intensity distribution of the projected frame If (X, Y ) and exposure time

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t. The exposure distribution on the resin surface arising from the scanning of a

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single frame Ef s (X, Y ) is given by Eq.3.

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Ef s (X, Y ) ≡ Ef s (u∆x, v∆x) =  P  t × uk=0 If ((u − k)∆x, v∆x) when u ≤ r    (3) Pr t × I ((u − k)∆x, v∆x) when r < u < U + r k=0 f      if (u − k) > U, then If ((u − k), v) = 0 It must be noted that the intensity distribution is limited to a projection area

of (U × V )∆x, whereas, the exposure distribution is across an area defined by

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((U + r) × V )∆x due to the scanning of the projected pattern for a distance of

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r∆x, as shown in figure 7.

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3.2.2. Change in exposure distribution due to pixel cycling

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Figure 8: Schematic illustrating the creation and projection of frames in the S-MPVP process. Intensity distribution changes as the frame projected on the resin surface changes with time.

Consider the case where frame F1 , shown in Figure 8(C), is scanned across

the resin surface from left to right. A long rectangular pattern will be cured instead of the desired square feature. However, if the bitmap pattern is updated from frame F1 to F2 after the projector scans the projected pixel width 16

(Q × 2w), then the projected pattern will irradiate the same region as frame F1 as illustrated in Figure 8(D,E). This phenomenon of projecting new bitmap patterns is referred to as pixel cycling. Pixel cycling forces a ‘Zero Relative Velocity’ condition between the projected frame and the scanning projector, allowing for the accurate fabrication of required features. Pixel cycling is analogous to projecting a movie with multiple frames (F1 − Fm ), with each frame

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updating every T seconds. Since the distance scanned between every pixel cycle

is Q × 2w, the scan parameter r is calculated to be r = (Q × 2w)/∆x. Further,

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since the exposure time for each discretized unit is t, the time elapsed between consecutive pixel cycles T is given by Eq.4. Pattern frame rate (F) is the rate at

which the bitmap frames are updated for projection and is computed as shown Q × 2w ∆x × ∆x Sresin

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T =r×t=

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in Eq.5.

F =

1 T

(4)

(5)

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As observed in Figure 8(C), the number of frames created for projecting a single bitmap pattern is directly dependent on the size of the DMD array, i.e. if the scanning is occurring along the length of DMD, then there is a maximum

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of ‘M’ number of columns available for pixel cycling (number of micro-mirrors along the length of the DMD). Further, if the part size is greater than the projection area, the number of frames required for projecting the layer also

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increases significantly.

Consider the case where the part size is Lp × W and the corresponding layer

bitmap size is Mp × N . Assume that the width of the part is equal to the width

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of the projected area and the length of the part is greater than the projected length, i.e. Lp > L. It is desirable to use the maximum number of micromirrors, M , to deliver energy to the resin because low UV intensities can be used. Low UV intensities increase DMD life and allow for increased chain mobility during photopolymerization. However, fewer micro-mirrors can be employed to vary the energy distribution across a layer to facilitate in the fabrication of

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geometries with graded mechanical properties. Assuming all the micro-mirrors along the scan direction are used for delivering energy, the total number of frames required for scanning a single layer is Mp + M . Since the projected frames change during pixel cycling, the intensity and exposure distribution on the resin surface also change with time. The final exposure distribution on the resin surface can be expressed as a summation of the Ef s of each frame, i.e.

m X

Ef ((m − (f − 1)), n)

f =1

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E(X, Y ) =

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E = EF1 s + EF2 s + · · · + EF(Mp +M ) s .

if m − f > M

 for 1 ≤ n ≤ N

1 ≤ m ≤ M + Mp

  for (m − 1)r < u ≤ m × r

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Ef (m, n) = Ef s (u∆x, v∆x)

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  Ef ((m − (f − 1)), n) = 0

(6)

(7)

 and (n − 1)r < v ≤ n × r

The exposure distribution on the resin, shown in Eq.6, accounts for the ex-

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posure contributions arising from pixel cycling and scanning occurring between the transition of projected frames. Ef (m, n) is the exposure distribution for a particular frame f at pixel location (m, n) on the resin surface. Ef (m, n) is mapped to the global co-ordinates as shown in Eq.7.

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3.3. Cure model

Assuming normal incidence with no reflection, the exposure distribution

within the resin E(X, Y, Z), where Z = 0 at the resin surface, is obtained

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using Beer-Lambert Law (F. Jacobs, 1992). E(X, Y, Z) = E(X, Y ) × e−Z/Dp

(8)

The depth of penetration (Dp ), is an inherent material property that deter-

mines the cure depth and the layer thickness of the cured part. If the pattern is scanned with a velocity Sresin and the exposure reaches the resin’s critical

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exposure (Ec ), the resin will polymerize, forming a gel. The locus of the points 18

inside the resin where exposure E(X, Y, Z) = Ec represent the cure profile. Rearranging the terms, the cure depth (Cd ) at a point (X, Y ) can be determined using Eq.9. Further, the cured line-width, at any height Z can be extracted by measuring the distance between points where E(X, 0, Z) = Ec . It must 280

be noted that, unlike the model developed for laser based systems (F. Jacobs, 1992), where the maximum cure depth occurs at the center of the laser beam,

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the 2D irradiated pattern can exhibit multiple peaks, based on the pattern that

Cd (X, Y ) = Dp ln

 E(X, Y, 0)  Ec

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is projected.

(9)

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Equations 8 and 9 are valid only when the photopolymer obeys the BeerLambert Law, i.e. when the photopolymer is homogeneous. For heterogeneous systems, advanced Mie and Rayleigh scattering models can be employed to de-

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4. Experimental Methods

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velop an equivalent cure model (Griffith and Halloran, 1996).

The primary aim of this work is to demonstrate that the developed S-MPVP 290

process model provides an accurate representation of the S-MPVP process. To

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this end, the authors fabricate a characterization specimen with empirically determined process parameters and compare the dimensions of the fabricated specimens with simulations (forward problem). First, the intensity distribution of two test patterns is captured by a camera that is integrated in the S-MPVP

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machine. Using a custom computer-vision algorithm, the intensity distribution of a single-projected pixel is computed. Then, the intensity distribution for the

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projected frames are computed using the developed Irradiance model. Specimens are then fabricated in the MPVP mode and the dimensions of the printed parts are compared with the simulations to determine the accuracy of the Irra-

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diance Model. The computed intensity distribution is then used to compute the exposure distribution and the cure profile for the S-MPVP process. The results of this simulation are then compared to the dimensions of specimens fabricated 19

with a S-MPVP machine using a set of known process parameters. Sections 4.1-4.6 describe the methods used to determine the single pixel intensity distri305

bution, fabricate and measure the specimens. 4.1. Materials A commercial photopolymer, G+ with red pigment, was procured from Mak-

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erJuice Labs. 1-Propanol, solvent for cleaning fabricated specimens, was procured from Fischer Scientific.

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4.2. S-MPVP System

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Figure 9: The S-MPVP system constructed for fabrication of multiscale parts.

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The projection unit for the S-MPVP system was procured from DLi innovations. The projection unit comprises of a Texas Instruments DLP controller and DMD with a resolution of 1920x1080 and a 0.65” diagonal micro-mirror array. Using an optical magnification (Q) of 4.2, the projected area was set

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to 61x34 mm, with a projected pixel size of 31.7 µm. A broad-spectrum (300500 nm) UV light source (Dymax – Bluewave 75 Spot Curing) with light guide

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(Dymax: 5721) was used to illuminate the DMD. The projector was fixed on two cross-mounted high-load, high-precision linear stages (Zaber: A-LST0500AE01) to enable scanning in the X-Y plane. A high precision linear stage (Zaber:

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A-LST0250A-E01) was used to translate the build platform in the Z direction. The build platform was additively manufactured using Ultem-9085 and mounted

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on the Z-stage. A custom glass vat (150x150 mm) contained the photopolymer during fabrication.

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4.3. Estimating intensity distribution of a single projected pixel

Figure 10: The bitmap images projected on the resin surface for extraction of intensity distri-

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bution of a single projected pixel. I1 and I2 correspond to the test patterns whose intensity distributions are captured by the camera embedded in the S-MPVP machine.

Two 1-pixel wide patterns, shown in Figure 10, are projected on the resin sur-

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face. The images of these patterns, when projected on the resin surface, are captured by the camera. The values of intensity in the captured images vary in the

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range of 0-255. The non-normalized intensity distribution for a single projected † pixel (Ii,j (u∆x, v∆x)) is obtained by subtracting (I2 ) from (I1 ). Intensity levels

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† 0-255 in Ii,j (u∆x, v∆x) are converted to actual intensity values through the fol-

lowing iterative normalization process. First a circular pattern, (Φ = radiometer sensor diameter (10 mm), is projected on the radiometer sensor, and the mean intensity is recorded (Isensor ). Then, an arbitrary normalization factor (K)

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† is introduced such that Ii,j (u∆x, v∆x) = K × (Ii,j (u∆x, v∆x). Starting with

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an assumption that K = 0.001, the actual projected pixel intensity distribution

(Ii,j (u∆x, v∆x)) is computed. Then, the intensity distribution for the projected

circular pattern (If (u∆x, v∆x)) is computed by substituting Ii,j (u∆x, v∆x) in Eq. 2 of the Irradiance model (Section 3.1). K is then iteratively varied until the following criterion is achieved: I f (u∆x, v∆x) − Isensor < 10−6 , where 21

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I f (u∆x, v∆x) is the mean of If (u∆x, v∆x). The normalization factor K determined through this iterative routine is then used for computing the single-pixel intensity distribution for all subsequent projection patterns. The intensity distribution was captured three times for one resin formulation. The pixel configuration and camera location was not altered to ensure that the

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optical path lengths and camera focus remained consistent between MPVP and

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S-MPVP fabrication modes.

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4.4. Specimen fabrication

First, the working curve for the photopolymer was generated using an intensity of 20 mW/cm2 and exposure times of 5, 6, 7, and 10 seconds to determine the resin’s intrinsic photocuring properties (Ec and Dp ) (F. Jacobs, 1992). A

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solid model of a characterization sample, consisting of four supporting layers

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and one comb-patterned layer, was designed in a commercial CAD package. Netfabb, a commercial pre-processing AM software, was then used to (i) slice the model into 250 µm layers and (ii) generate the layer’s corresponding bitmap images. The MPVP characterization sample was printed on the S-MPVP sys-

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tem in a static MPVP configuration with an exposure time of 8 seconds. The bitmap pattern created for the MPVP fabrication was converted into a movie

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using a custom movie-rendering algorithm, where each frame of the movie was created by performing a linear transformation operation on the original bitmap

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image and rendered at a frame rate of 135 frames/second using OpenCV python modules. The S-MPVP specimen was fabricated on the S-MPVP system in its scanning mode with a scan speed of 4.28 mm/s. Fabricated parts were thoroughly washed with 1-Propanol and wiped dry with KimwipesTM before

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measurement. Three characterization samples, each containing 19 ribs, were

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fabricated for repeatability. 4.5. Optical measurement of printed specimens An optical table-top microscope, Dinolight (AM4815ZTL), was used to measure the dimensions of the printed features using a fixed magnification of 30x.

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4.6. Process and simulation parameters 370

The process and simulation parameters used for fabrication and simulation are listed in Table 2. These parameters were input into the S-MPVP model for the simulation of cure profile and cure width. Table 2: List of process and simulation parameters

Simulation Parameters

Pixel pitch (2w)= 7.56 µm

MPVP Exposure time = 8 s

Pixel Cycling factor (M )= 1080

Exposure time/pixelcycle(T)= 7.4 ms

Projection length (L) = 61 mm

∆x = ∆y= 3.1 µm

Projection width (W )= 34 mm

Scanning parameter (r) = 10

Magnification (Q)= 4.2

Mean UV Intensity (Isensor )= 20

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Machine Specifications

mW/cm2

Exposure time for ∆x (t) = 0.74 ms

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Process Parameters Scan velocity (Sresin )= 4.28 mm/s Pattern frame rate (F ) = 135 fps

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Material Properties

Depth of penetration (Dp )= 124 µm

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Critical Exposure (Ec )= 35 J/m2

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5. Results and Discussion

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Figure 11: Specimen fabrication. (A) The designed bitmap pattern (B) The specimen printed using the stationary MPVP system (C) The specimen printed using the Scanning MPVP system (D) Cross-section of the designed rib (E) Cross-section of MPVP printed rib (F) Cross-section of the S-MPVP printed rib.

The characterization specimens were successfully fabricated using the MPVP

and S-MPVP techniques as shown in Figure 11(B,C) respectively and the spec-

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imen dimension are listed in Table 3. The CAD design dimension of the rib was 300 µm. However, the conversion from STL to bitmap format resulted in the

generation of 10-pixel wide ribs. This resulted in the true design dimension of 317 µm (projected pixel size = 31.7 µm). Ribs, 10-pixel wide, printed in the

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MPVP mode were measured to be 300±4 µm. Ribs, 10-pixel wide, printed in

24

the S-MPVP mode were measured to be 344±5 µm. Cross-section of the ribs printed with the MPVP and S-MPVP methods, shown in Figure 11(E) and (F) respectively, highlight the resultant cure profile. The error between the line widths of printed specimens and the design dimension are -5.36% and 8.5% for 385

the MPVP and S-MPVP methods respectively. The cross-section view of the MPVP printed rib in Figure 11(E) shows line width increasing with cure depth.

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This is characteristic of resins demonstrating a high degree of oxygen inhibition.

The effect of oxygen inhibition is so enhanced in this resin that features smaller

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than 125 µm cannot even be fabricated. Therefore, the error in MPVP printed

dimension can be primarily attributed to oxygen inhibition. Further, it can be observed that MPVP parts show greater taper than the S-MPVP counterparts.

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Oxygen inhibition is more pronounced in smaller areas, and since the exposure for MPVP ribs is lower in magnitude and size when compared to the S-MPVP

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process (as discussed on Section 5.2), it is expected that the MPVP ribs will exhibit tapering to a greater extent when compared to the S-MPVP specimen. Methods to improve the dimensional accuracy and mitigate oxygen inhibition

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are beyond the scope of this work and will be discussed in future publications. Table 3: Comparison between dimensions predicted by the S-MPVP model and the specimens printed in MPVP mode

True design

%

Error

width

dimension

MPVP printed specimen

MPVP printed specimen

10 pix

317 µm

-5.36

8.5

Design

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Rib

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vs.

% Error Design vs.

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5.1. Verification of the Irradiance model

Figure 12: Experimentally determined intensity distribution of a single projected pixel varies

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significantly when compared to an equivalent theoretical Gaussian distribution (A) Intensity distribution is nearly uniform in the projected pixel area, with mean intensity of 20 mW/cm2 (B) Theoretical intensity distribution of an equivalent Gaussian beam with peak

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intensity of 20 mW/cm2

The intensity distribution of a single projected pixel on the resin surface is determined using the method described in Section 4.3. The mean intensity,

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arising from the projection of a circular pattern in the radiometer sensor, was measured to be 20 mW/cm2 (Isensor ). Using Isensor , the arbitrary normalization factor was determined to be 0.337. The reconstructed single-pixel intensity

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distribution (Ii,j (X, Y )) is shown in Figure 12(A). The mean intensity in the

projected pixel was computed to be 11.34 mW/cm2 . Assuming beam radius = DMD pitch and peak intensity = 11.34 mW/cm2 , an equivalent Gaussian intensity distribution was constructed as shown in Figure 12(B). Visual inspection reveals that the intensity distributions of the projected pixel and the theoreti-

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cal Gaussian distribution are significantly different. Quantitatively, the actual

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single-pixel intensity distribution bleeds into adjacent micro-mirrors for a distance of 15.8 µm, whereas the theoretical Gaussian distribution extends into adjacent micro-mirrors only for a distance of 3.2 µm.

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Figure 13: Intensity and exposure distribution in the MPVP mode.(A) The projected bitmap pattern. (B) Plot of the intensity distribution for a sub-section of the rib - using actual single-pixel intensity distribution (C) Contour plot of the exposure distribution on the resin

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surface for the rib - using actual single-pixel intensity distribution. (D) Plot of the intensity distribution for a sub-section of the rib - assuming Gaussian intensity distribution for every pixel (E) Contour plot of the exposure distribution on the resin surface - assuming Gaussian intensity distribution.

In the MPVP method, the exposure distribution within the resin for a pro-

jected pattern is computed by E(X, Y, Z) = t × I(X, Y )e(Z/Dp ) , where t is the exposure time. Since there is no scanning involved in the MPVP process, the

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dimension of the fabricated rib is directly dependent on the intensity distribution. Thus, if the Irradiance Model is accurate, then the dimensions predicted through simulation will match the dimensions of the fabricated specimen. Using the computed single-pixel intensity distribution, the Irradiance Model is used

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to simulate intensity distribution for the bitmap image show in Figure 13(A). 27

The computed intensity distribution and exposure distribution are shown in Figure 13(B) and Figure 13(C), respectively. A mean intensity of 20 mW/cm2 was recorded when the rib was projected on the radiometer sensor. The mean intensity observed in the intensity distribution simulation matches the mean 425

intensity recorded by the radiometer. Similarly, the intensity distribution and exposure for the bitmap image, assuming a Gaussian intensity distribution,

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were simulated, and the results are shown in Figure 13(D) and Figure 13(E), respectively. Inspection of Figures 13(B) and (D) reveals that the distribution

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computed with actual single-pixel intensity distributions is more uniform when compared to the Gaussian equivalent. This difference is further exacerbated

in Figures 13(C) and (E). The exposure for the Gaussian distribution (Figure

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13(E)) shows hot spots in the center of each projected pixel, whereas the exposure calculated with actual intensity distribution (Figure 13(C)) shows an

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averaged, even exposure distribution.

For the simulations created by assuming actual single-pixel intensity distribution, the line width estimated by measuring the distance between iso-lines

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where E = Ec was calculated to be 327 µm. Similarly, for simulations created by assuming a Gaussian intensity distribution, the line width was calculated to be 271 µm. The error in the line width estimation with respect to the fabricated specimen was 9% and -9.6% for the simulations performed with actual single-

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pixel intensity distribution and Gaussian distribution, respectively. While the magnitude of error are comparable for the Gaussian distribution assumption and actual intensity distribution, the simulation with the Gaussian intensity distribution predicts the occurrence of distinct low and high spots in the printed

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ribs. These surface irregularities were not observed in any of the printed ribs

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(n=57), thus proving that the Gaussian assumption is not representative of the projection device. Further, it must be noted that if effects of oxygen inhibition are ignored,

it is expected that the simulation using the actual single-pixel intensity will be

450

able to provide a more accurate prediction of line width. In theory, the intensity distribution of a single projected pixel can be directly captured; however, the 28

limited aperture on the camera prevents the capture of the intensity distribution of a single projected pixel. Increasing the exposure leads to an increase in sensor noise and unreliable data. Projecting a line increases the brightness in the area 455

and allows capturing of low-noise images. The authors recognize these steps can be eliminated, and the intensity distribution can be captured with greater accuracy if the intensity of a single projected pixel can be directly captured

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using beam profilometers. However, the capability of the model to accurately

represent the process is agnostic to these measurement techniques. Therefore,

the authors anticipate the accuracy of the prediction technique to improve with improvement in instrumentation in the future.

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5.2. Validation of the S-MPVP model

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Figure 14: Intensity and exposure distribution in the S-MPVP mode.(A) Intensity distribution on the resin surface for projected frame F1 and FM (B) Exposure distribution on the resin

surface after completion of part fabrication using the S-MPVP process.

The intensity distribution during the start of the scanning process is shown

in Figure 14(A). As observed in the MPVP mode, there is significant amount of light bleeding into the adjacent pixels. However, when the DMD is scanned

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across the resin surface, the bitmap pattern is updated and the intensity distribution also changes. The exposure distribution arising from the S-MPVP process is more uniform compared to the MPVP method, as shown in Figure 14(B). The 10-pixel line widens to a 11-pixel wide line during the scanning. The

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line width calculated from the simulation was found to be 354 µm. The error 29

Table 4: Comparison between dimensions predicted by the S-MPVP model and the printed specimens

MPVP Mode Simulated

dimension

dimension

300±4 µm

327 µm

%Error

9

Printed

Simulated

dimension

dimension

344±5 µm

354 µm

%Error

2.9

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Printed

S-MPVP Mode

between the rib line width predicted by the simulation and the printed feature,

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estimated across 19 ribs and 3 specimens, was 2.9%. The simulation of the

S-MPVP process was also conducted with Gaussian intensity distributions and the resultant line width prediction was 312 µm (error = -9.3%), thus proving that using the actual single-pixel intensity distribution provides a more accurate

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representation of the printing process. Peterson et al. (2016) have demonstrated

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that intensity can affect the mechanical performance of printed parts, thus uniform distribution of energy in the S-MPVP process facilitates the fabrication of more-isotropic parts when compared to the parts manufactured via the MPVP process. The comparison between the predicted dimensions and the printed

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specimen dimensions, using actual intensity distribution, is shown in Table 4. The error in prediction of line width for the MPVP specimen is primarily

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attributed to oxygen inhibition. The ribs fabricated in the MPVP mode show signs of oxygen inhibition. This reduction in line width leads to exaggerated

485

error values. However, a portion of the errors (both in MPVP and S-MPVP parts) can be attributed to incorrect estimation of single-pixel intensity distribution. These errors can be attributed to two main factors: (i) the setup used to capture the actual projected intensity distribution and (ii) low resolution and

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sensitivity of the image capturing device. The setup used for the work outlined

490

in this paper did not perfectly capture images in the plane parallel to the resin surface. While image processing tools were used to correct the camera viewing angles, intensity distributions in the blind spots of the camera could not be captured. Further, the resolution of the camera was only two times greater that the projection device. This limited the discretization scheme and increased the 30

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error in the prediction of intensity distribution.

6. Conclusions In this work, the authors use computer-vision to extract the intensity distribution from the resin surface to predict the feature dimension. A new Irradiance

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Model was developed to handle non-analytic intensity distributions. Energy and Cure models were developed to understand the relationship between the energy

distribution and the process parameters such as scan speed and pattern frame

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rate. The solution to the forward problem of determining the cure profile using experimental process parameters was presented. Through experimental valida-

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tion, the authors demonstrate that the S-MPVP model can predict the feature dimensions with an error of 2.9%. In conclusion, the developed process model is able to accurately model the S-MPVP process and illustrate the relationship

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between the cure shape and the printing parameters such as scan speed and projection frame rate. Further, the model serves as a general framework for

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merization systems.

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cure width and cure profile estimation for all mask projection vat photopoly-

The authors note that the experiments presented in this paper validate the accuracy of the S-MPVP model only for the forward problem in a homogeneous

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photopolymer; i.e., the model was used to predict the profile of the cured geometry using the process and material parameters determined from the experiment.

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For complete validation of the S-MPVP model, the backward problem has to be solved; i.e., for a required energy distribution, identify the combination of scan speed, intensity, and bitmap pattern that will lead to the fabrication of a

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feature with maximum accuracy. Finally, the salient feature of the developed S-MPVP model is the ability to directly integrate it in a closed loop process

520

monitoring system, allowing for accurate fabrication of multi-scale parts. This work will be addressed by the authors in future publications.

31

7. Acknowledgements The authors would like to thank Dr. Timothy E. Long (Virginia Tech) for providing the UV radiometer to measure the intensity of the DLP projector. 525

The authors would like to thank Lance Yelton (Virginia Tech) for handling the purchase and procurement of components for the S-MPVP machine. The

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authors acknowledge Nicholas A. Chartrain (Virginia Tech), Dr. Maruti Hegde (University of North Carolina, Chapel Hill), Philip J. Scott (Virginia Tech) and Camden A. Chatham (Virginia Tech) for the helpful discussion regarding the

effects of intensity distribution and its effects on photopolymerization. Finally,

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the authors acknowledge Dr. Susheel Sekhar and Lindsey Bezek (Virginia Tech)

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for proof-reading and suggesting edits to the manuscript.

8. Declaration of Interest None

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9. Image Captions Figure 1: An illustration outlining the S-MPVP process flow. CAD parts (A) are sliced into cross-sectional layers of desired thickness (B). Each

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slice (C) is converted into a bitmap image (D) which is further split into multiple rows (E). Each row is converted into a movie and fed

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into the projector. Projector scans over the surface of the resin while playing the movie (F). 635

Figure 2: Schematic of a top-down scanning-mask projection vat photopolymer-

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ization system. The projection device is mounted on a X-Y scanning linear stage, while the other components such as the light source and

tems. 640

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build platform have the same configuration as traditional MPVP sys-

Figure 3: Functional decomposition of the S-MPVP system.

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Figure 4: Overview of the S-MPVP model.

Figure 5: Illustration showing the discretization scheme of the projection area.

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Intensity distribution is computed across the entire projection area. Figure 6: In the standard MPVP process, the desired pattern (A) is converted to a bitmap image (B) and transferred to the DMD (C). The pro-

645

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jected pattern and the associated intensity distribution are invariant with respect to time (for a single layer). Consequently, exposure distribution is a product of the intensity distribution and the exposure time.

650

Figure 7: Discretization scheme for estimating the exposure distribution during the scanning of a single frame.

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Figure 8: Schematic illustrating the creation and projection of frames in the S-

655

MPVP process.Intensity distribution changes as the frame projected on the resin surface changes with time.

Figure 9: The S-MPVP system constructed for fabrication of multiscale parts.

Figure 10: The bitmap images projected on the resin surface for extraction of intensity distribution of a single projected pixel. I1 and I2 correspond 36

to the test patterns whose intensity distributions are captured by the camera embedded in the S-MPVP machine. 660

Figure 11: Specimen fabrication. (A) The designed bitmap pattern (B) The specimen printed using the stationary MPVP system (C) The specimen printed using the Scanning MPVP system (D) Cross-section of the designed rib (E) Cross-section of MPVP printed rib (F) Cross-section

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of the S-MPVP printed rib.

Figure 12: Experimentally determined intensity distribution of a single projected

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pixel varies significantly when compared to an equivalent theoretical

Gaussian distribution (A) Intensity distribution is nearly uniform in the projected pixel area, with mean intensity of 20 mW/cm2 (B) The-

peak intensity of 20 mW/cm2

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oretical intensity distribution of an equivalent Gaussian beam with

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Figure 13: Intensity and exposure distribution in the MPVP mode.(A) The projected bitmap pattern. (B) Plot of the intensity distribution for a sub-section of the rib - using actual single-pixel intensity distribution

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(C) Contour plot of the exposure distribution on the resin surface for the rib - using actual single-pixel intensity distribution. (D) Plot

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of the intensity distribution for a sub-section of the rib - assuming

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Gaussian intensity distribution for every pixel (E) Contour plot of the exposure distribution on the resin surface - assuming Gaussian intensity distribution.

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Figure 14: Intensity and exposure distribution in the S-MPVP mode.(A) Intensity distribution on the resin surface for projected frame F1 and FM

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(B) Exposure distribution on the resin surface after completion of part fabrication using the S-MPVP process.

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