Abstract

This paper develops a computational framework to optimize the process parameters such that the bond quality between extruded polymer filaments is maximized in fused filament fabrication (FFF). A transient heat transfer analysis providing an estimate of the temperature profile of the filaments is coupled with a sintering neck growth model to assess the bond quality that occurs at the interfaces between adjacent filaments. Predicting the variability in the FFF process is essential for achieving proactive quality control of the manufactured part; however, the models used to predict the variability are affected by assumptions and approximations. This paper systematically quantifies the uncertainty in the bond quality model prediction due to various sources of uncertainty, both aleatory and epistemic, and includes the uncertainty and the model discrepancy in the process parameter optimization. Variance-based sensitivity analysis based on Sobol’ indices is used to quantify the relative contributions of the different uncertainty sources to the uncertainty in the bond quality. A Gaussian process (GP) surrogate model is constructed to compute and include the model discrepancy within the optimization. Physical experiments are conducted for calibration and validation of the physics model and also for validation of the optimum solution. The results show that the proposed formulation for process parameter optimization under uncertainty results in high bond quality between adjoining filaments of the FFF product.

References

References
1.
Aliheidari
,
N.
,
Tripuraneni
,
R.
,
Ameli
,
A.
, and
Nadimpalli
,
S.
,
2017
, “
Fracture Resistance Measurement of Fused Deposition Modeling 3D Printed Polymers
,”
Polym. Test.
,
60
, pp.
94
101
. 10.1016/j.polymertesting.2017.03.016
2.
Sun
,
Q.
,
Rizvi
,
G.
,
Bellehumeur
,
C.
, and
Gu
,
P.
,
2008
, “
Effect of Processing Conditions on the Bonding Quality of Fdm Polymer Filaments
,”
Rapid Prototyping J.
,
14
(
2
), pp.
72
80
. 10.1108/13552540810862028
3.
Yardimci
,
M. A.
,
Guceri
,
S. I.
,
Agarwala
,
M.
, and
Danforth
,
S. C.
,
1996
, “
Part Quality Prediction Tools for Fused Deposition Processing
,”
International Solid Freeform Fabrication Symposium
,
Austin, TX
, pp. 539–548.
4.
Atif Yardimci
,
M.
, and
Güçeri
,
S.
,
1996
, “
Conceptual Framework for the Thermal Process Modelling of Fused Deposition
,”
Rapid Prototyping J.
,
2
(
2
), pp.
26
31
. 10.1108/13552549610128206
5.
Thomas
,
J.
, and
Rodríguez
,
J.
,
2000
, “
Modeling the Fracture Strength Between Fused-deposition Extruded Roads
,”
International Solid Freeform Fabrication Symposium
,
Austin, TX
, pp. 16–23.
6.
Li
,
L.
,
Sun
,
Q.
,
Bellehumeur
,
C.
, and
Gu
,
P.
,
2002
, “
Investigation of Bond Formation in FDM Process
,”
International Solid Freeform Fabrication Symposium
,
Austin, TX
.
7.
Costa
,
S.
,
Duarte
,
F.
, and
Covas
,
J.
,
2015
, “
Thermal Conditions Affecting Heat Transfer in FDM/FFE: A Contribution Towards the Numerical Modelling of the Process: This Paper Investigates Convection, Conduction and Radiation Phenomena in the Filament Deposition Process
,”
Virtual and Physical Prototyping
,
10
(
1
), pp.
35
46
. 10.1080/17452759.2014.984042
8.
Costa
,
S.
,
Duarte
,
F.
, and
Covas
,
J.
,
2017
, “
Estimation of Filament Temperature and Adhesion Development in Fused Deposition Techniques
,”
J. Mater. Process. Technol.
,
245
, pp.
167
179
. 10.1016/j.jmatprotec.2017.02.026
9.
Pokluda
,
O.
,
Bellehumeur
,
C. T.
, and
Vlachopoulos
,
J.
,
1997
, “
Modification of Frenkel’s Model for Sintering
,”
AIChE. J.
,
43
(
12
), pp.
3253
3256
. 10.1002/aic.690431213
10.
Frenkel
,
J.
,
1945
, “
Viscous Flow of Crystalline Bodies Under the Action of Surface Tension
,”
J. Phys.
,
9
, p.
385
.
11.
Bellehumeur
,
C.
,
Li
,
L.
,
Sun
,
Q.
, and
Gu
,
P.
,
2004
, “
Modeling of Bond Formation Between Polymer Filaments in the Fused Deposition Modeling Process
,”
J. Manuf. Proc.
,
6
(
2
), pp.
170
178
. 10.1016/S1526-6125(04)70071-7
12.
Gurrala
,
P. K.
, and
Regalla
,
S. P.
,
2014
, “
Part Strength Evolution With Bonding Between Filaments in Fused Deposition Modelling: This Paper Studies How Coalescence of Filaments Contributes to the Strength of Final Fdm Part
,”
Virtual Phys. Prototyping
,
9
(
3
), pp.
141
149
. 10.1080/17452759.2014.913400
13.
Kobryn
,
P.
, and
Semiatin
,
S.
,
2001
, “
The Laser Additive Manufacture of Ti-6Al-4V
,”
JOM
,
53
(
9
), pp.
40
42
. 10.1007/s11837-001-0068-x
14.
Rodriguez
,
J. F.
,
Thomas
,
J. P.
, and
Renaud
,
J. E.
,
2000
, “
Characterization of the Mesostructure of Fused-Deposition Acrylonitrile-Butadiene-Styrene Materials
,”
Rapid Prototyping J.
,
6
(
3
), pp.
175
186
. 10.1108/13552540010337056
15.
Pierson
,
H. A.
, and
Chivukula
,
B.
,
2018
, “
Process–property Relationships for Fused Filament Fabrication on Preexisting Polymer Substrates
,”
ASME J. Manuf. Sci. Eng.
,
140
(
8
), p.
084501
. 10.1115/1.4039766
16.
Gutmann
,
H.-M.
,
2001
, “
A Radial Basis Function Method for Global Optimization
,”
J. Global Optimiz.
,
19
(
3
), pp.
201
227
. 10.1023/A:1011255519438
17.
Costa
,
S.
,
Duarte
,
F.
, and
Covas
,
J.
,
2008
, “
Towards Modelling of Free Form Extrusion: Analytical Solution of Transient Heat Transfer
,”
Int. J. Material Forming
,
1
(
1
), pp.
703
706
. 10.1007/s12289-008-0312-9
18.
Palais
,
R. S.
, and
Palais
,
R. A.
,
2009
,
Differential Equations, Mechanics, and Computation
, Vol.
51
,
American Mathematical Society
,
Providence, RI
.
19.
Kennedy
,
M. C.
, and
O’Hagan
,
A.
,
2001
, “
Bayesian Calibration of Computer Models
,”
J. R. Stat. Soc.: Ser. B (Statistical Methodology)
,
63
(
3
), pp.
425
464
. 10.1111/1467-9868.00294
20.
Arendt
,
P. D.
,
Apley
,
D. W.
, and
Chen
,
W.
,
2012
, “
Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability
,”
ASME J. Mech. Des.
,
134
(
10
), p.
100908
. 10.1115/1.4007390
21.
Ling
,
Y.
,
Mullins
,
J.
, and
Mahadevan
,
S.
,
2014
, “
Selection of Model Discrepancy Priors in Bayesian Calibration
,”
J. Comput. Phys.
,
276
, pp.
665
680
. 10.1016/j.jcp.2014.08.005
22.
Hastings
,
W. K.
,
1970
, “
Monte Carlo Sampling Methods Using Markov Chains and Their Applications
,”
Biometrika
,
57
(
1
), pp.
97
109
. 10.1093/biomet/57.1.97
23.
Casella
,
G.
, and
George
,
E. I.
,
1992
, “
Explaining the Gibbs Sampler
,”
The American Statistician
,
46
(
3
), pp.
167
174
. 10.1080/00031305.1992.10475878
24.
Neal
,
R. M.
,
2003
, “
Slice Sampling
,”
Ann. Stat.
,
31
(
3
), pp.
705
767
. 10.1214/aos/1056562461
25.
Novak
,
E.
, and
Woźniakowski
,
H.
,
2009
, “
Approximation of Infinitely Differentiable Multivariate Functions is Intractable
,”
J. Compl.
,
25
(
4
), pp.
398
404
. 10.1016/j.jco.2008.11.002
26.
Sobol
,
I. M.
,
2001
, “
Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates
,”
Math. Comput. Simulat.
,
55
(
1–3
), pp.
271
280
. 10.1016/S0378-4754(00)00270-6
27.
Saltelli
,
A.
, and
Tarantola
,
S.
,
2002
, “
On the Relative Importance of Input Factors in Mathematical Models: Safety Assessment for Nuclear Waste Disposal
,”
J. Am. Stat. Assoc.
,
97
(
459
), pp.
702
709
. 10.1198/016214502388618447
28.
Li
,
C.
, and
Mahadevan
,
S.
,
2016
, “
An Efficient Modularized Sample-based Method to Estimate the First-order Sobol’ Index
,”
Reliab. Eng. Syst. Safety
,
153
, pp.
110
121
. 10.1016/j.ress.2016.04.012
29.
Iooss
,
B.
, and
Ribatet
,
M.
,
2009
, “
Global Sensitivity Analysis of Computer Models with Functional Inputs
,”
Reliab. Eng. Syst. Safety
,
94
(
7
), pp.
1194
1204
. 10.1016/j.ress.2008.09.010
30.
DeCarlo
,
E. C.
,
Mahadevan
,
S.
, and
Smarslok
,
B. P.
,
2018
, “
Efficient Global Sensitivity Analysis with Correlated Variables
,”
Struct. Multidisc. Optim.
,
58
(
6
), pp.
2325
2340
. 10.1007/s00158-018-2077-1
31.
Du
,
X.
, and
Chen
,
W.
,
2004
, “
Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design
,”
ASME J. Mech. Des.
,
126
(
2
), pp.
225
233
. 10.1115/1.1649968
32.
Zaman
,
K.
,
McDonald
,
M.
,
Mahadevan
,
S.
, and
Green
,
L.
,
2011
, “
Robustness-based Design Optimization Under Data Uncertainty
,”
Struct. Multidisc. Optim.
,
44
(
2
), pp.
183
197
. 10.1007/s00158-011-0622-2
33.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K.-L.
, and
Mistree
,
F.
,
1996
, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
ASME J. Mech. Des.
,
118
(
4
), pp.
478
485
. 10.1115/1.2826915
34.
Schneider
,
C. A.
,
Rasband
,
W. S.
, and
Eliceiri
,
K. W.
,
2012
, “
Nih Image to Imagej: 25 Years of Image Analysis
,”
Nat. Methods.
,
9
(
7
), p.
671
. 10.1038/nmeth.2089
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