Closed Form Solution Modeling
of Filament Deposition Direct
Digital Manufacturing
Steven Devlin
David Grewell PhD
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Presentation Outline
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Introduction
Benefits of FDM for functional parts
Squeeze Flow of Asperity Peaks
Interfacial Healing
Molecular Diffusion
Extrusion
Coupled Model
Proposed Experiment
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Introduction
•  Patent # 4575330 Apparatus for Production of Three-Dimensional
Objects by StereoLithography issued March 1986
•  Solid Freeform Fabrication / Additive Manufacturing
•  Multiple Technologies and Systems Available SLA, SLS, LOM,
EBM, 3DP, and FDM
•  Design Development Tool, Visualization, Customer Understanding,
Part Interference, Speed of Design
•  Utilization for Production Applications Continues to Lag
•  Engineering need for understanding of material properties associated
with SFF / AM
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
FDM Benefits
•  Thermoplastics Dominate AM Industry – Number of Factors
•  Performance and ease of manufacturing
•  Cost-effectiveness because of: Low energy consumption, Low weight, Low cost of
complex tooling, Fast tooling time
•  Corrosion resistance
•  Styling latitude - creation of parts not possible using traditional methods
•  Commercialized by Stratasys in 1991, FDM is one of the most
important rapid prototyping technologies
•  FDM Material - ABS (acrylonitril butadiene styrene (C8H8·C4H6·C3H3N)n)
•  Strong, durable production-grade thermoplastic
•  Potential for final machining and cutting of parts
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Squeeze Flow
•  Asperity peaks must be displaced to allow polymer interfaces to fully engage
•  During welding, asperity peaks soften and flow to fill interstitial spaces
•  To understand this flow, it is proposed to model asperity deformation as the idealized
squeeze flow of many small identical cylinders of molten material placed between
two rigid plates separated by some distance 2h
•  The derived equation can then be used to predict the gap height as a function of time,
or more importantly, the closing of two faying surfaces as function of time
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Interfacial Healing
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Healing occurs when faying surfaces come into intimate contact
Healing initiates prior to squeeze flow completion
Squeeze flow and healing occur simultaneously
Healing occurs through diffusion of polymer chains across interface
and entanglement with other polymer chains
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Molecular Diffusion
•  Full healing is determined by molecular structure,
molecular weight, chemical structure of the polymer, as
well as time, temperature, and pressure
•  Diffusion of polymer chains can be modeled using the
reptation theory proposed by DeGennes
•  Loos plots of autohesion as a function of time ¼ used to
model temperature-independent activation energy
•  Temperature-dependent closed form
model more closely represents data
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Extrusion
In the FDM process the material is a wire or filament at the cartridge which is entered to the prin7ng head where the ABS, PLA or other material is melted and is pressed through a nozzle to the build plaAorm. The nozzle moves to produce a profile of the part model, then the plaAorm translates down and the next layer is built on top of the previous layer un7l the en7re model is fully built. Typically a support structure is constructed for overhanging features. [5]
Assumptions
• Constant material proper7es
• Homogeneous material
• No phase change
• Constant velocity
• Heat loss only through convec7on • Assume constant coefficient of heat loss • Assume rod is uniform temperature in r-direction
• No internal heat loss/generation
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Coupled Model
Assuming no healing prior to welding, and assuming welding occurs between 7me = 0 and t’ (7me at end of welding process), it is proposed that the degree of welding (DW), which combines squeeze flow and healing, can be defined as:
where A0, ka and Γ can be determined experimentally and represent lumping of both squeeze flow and healing processes.
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory
Proposed Experiment
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Filament strand orientation and test method evaluation
Film analysis of intermolecular healing model
Pre-experimental sample fabrication and analysis
Factorial experimental sample fabrication
PLA Proof of parts and experimental sample fabrication
Proof of variable deposition rates and sample fabrication
Test specimen fabrication and testing
IOWA STATE UNIVERSITY
Department of Agricultural & Biosystems Engineering
Biomass Processing Laboratory