1,201 research outputs found
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Quantifying Dimensional Accuracy of a Mask Projection Micro Stereolithography System
Mask Projection Microstereolithography is capable for fabricating true three-dimensional
microparts and hence, holds promise as a potential micro-fabrication process for micro-machine
components. In this paper, the Mask Projection Micro-Stereolithography (MPµSLA) system
developed at the Rapid Prototyping and Manufacturing Institute at Georgia Institute of
Technology is presented. The dimensional accuracy of the system is improved by reducing its
process planning errors. To this effect, the MPµSLA process is mathematically modeled. In this
paper, the irradiance received by the resin surface is modeled as a function of the imaging system
parameters and the pattern displayed on the dynamic mask. The resin used in the system is
characterized to experimentally determine its working curve. This work enables us to compute
the dimensions of a single layer cured using our system. The analytical model is validated by
curing test layers on the system. The model computes layer dimensions within 5% error.Mechanical Engineerin
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Process Planning to Build Mask Projection Stereolithography Parts with Accurate Vertical Dimensions
Mask Projection Stereolithography (MPSLA) is a high resolution manufacturing process
that builds parts layer by layer in a photopolymer. In this paper, we formulate a process planning
method to cure MPSLA parts with accurate vertical dimensions. To this effect, we have
formulated and validated the “Layer cure” model that models the thickness of a cured layer as a
transient phenomenon, in which, the thickness of the layer being cured increases continuously
throughout the duration of exposure. We have shown that for longer durations of exposures, such
as those common with MPSLA systems, cure depth varies linearly with exposure. We have also
quantified the effect of diffusion of radicals on the cure depth when discrete exposure doses, as
opposed to a single continuous exposure dose, are used to cure layers.
Using this work, we have formulated and validated the “Print through” model that
computes the extra curing that would occur when multiple layers are cured over each other.
We have implemented the Print through model to simulate the profile of a down facing surface
of a test part and validated the simulation result by building the test part on our MPSLA system.Mechanical Engineerin
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Compensation Zone Approach to Avoid Z Errors in Mask Projection Stereolithography Builds
Print-through results in unwanted polymerization occurring beneath a part cured using
Mask Projection Stereolithography (MPSLA) and thus creates error in its Z dimension. In this
paper, the "Compensation zone approach" is proposed to avoid this error. This approach entails
modifying the geometry of the part to be cured. A volume (Compensation zone) is subtracted
from underneath the CAD model in order to compensate for the increase in the Z dimension that
would occur due to Print-through. Three process variables have been identified: Thickness of
Compensation zone, Thickness of every layer and Exposure distribution across every image used
to cure a layer. Analytical relations have been formulated between these process variables in
order to obtain dimensionally accurate parts. The Compensation zone approach is demonstrated
on an example problem.Mechanical Engineerin
Irreducibility Criteria for Local and Global Representations
It is proved that certain types of modular cusp forms generate irreducible
automorphic representation of the underlying algebraic group. Analogous
archimedean and non-archimedean local statements are also given.Comment: 9 page
Representations of SL_2(R) and nearly holomorphic modular forms
In this semi-expository note, we give a new proof of a structure theorem due
to Shimura for nearly holomorphic modular forms on the complex upper half
plane. Roughly speaking, the theorem says that the space of all nearly
holomorphic modular forms is the direct sum of the subspaces obtained by
applying appropriate weight-raising operators on the spaces of holomorphic
modular forms and on the one-dimensional space spanned by the weight 2 nearly
holomorphic Eisenstein series.
While Shimura's proof was classical, ours is representation-theoretic. We
deduce the structure theorem from a decomposition for the space of n-finite
automorphic forms on SL_2(R). To prove this decomposition, we use the mechanism
of category O and a careful analysis of the various possible indecomposable
submodules. It is possible to achieve the same end by more direct methods, but
we prefer this approach as it generalizes to other groups.
This note may be viewed as the toy case of our paper ["Lowest weight modules
of Sp_4(R) and nearly holomorphic Siegel modular forms"], where we prove an
analogous structure theorem for vector-valued nearly holomorphic Siegel modular
forms of degree two.Comment: 13 page
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