Data-Driven Process Optimization of Fused Filament Fabrication based on In Situ Measurements

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Data-Driven Process Optimization of

Fused Filament Fabrication based on

In Situ Measurements ?

Xavier Guidetti ∗,∗∗,Marino K¨uhne ∗∗∗,Yannick Nagel ∗∗∗∗,

Efe C. Balta ∗,Alisa Rupenyan ∗,∗∗,John Lygeros ∗

∗Automatic Control Laboratory, ETH Z¨urich, Z¨urich, Switzerland

∗∗ Inspire AG, Z¨urich, Switzerland

∗∗∗ D-MAVT, ETH Z¨urich, Z¨urich, Switzerland

∗∗∗∗ NematX AG, Z¨urich, Switzerland

Abstract: The tuning of fused ﬁlament fabrication parameters is notoriously challenging. We

propose an autonomous data-driven method to select parameters based on in situ measurements.

We use a laser sensor to evaluate the surface roughness of a printed part. We then correlate the

roughness to the mechanical properties of the part, and show how print quality aﬀects mechanical

performance. Finally, we use Bayesian optimization to search for optimal print parameters.

We demonstrate our method by printing liquid crystal polymer samples, and successfully ﬁnd

parameters that produce high-performance prints and maximize the manufacturing process

eﬃciency.

Keywords: Process control applications, Process optimization, Applications in advanced

materials manufacturing, Bayesian methods, Machine Learning, Sensing

1. INTRODUCTION

In fused ﬁlament fabrication (FFF), the selection of opti-

mal process parameters is a complex task that has been

tackled with diﬀerent methods (Dey and Yodo, 2019). The

properties of a manufactured part are strongly dependent

on a large number of inputs. This is particularly true

for high-performance feedstock materials such as liquid

crystal polymers (LCPs). Under- or over-extrusion, which

are caused by poor parameter selection, have been shown

to strongly inﬂuence the mechanical properties of poly-

mers (Siqueira et al., 2017). As the evaluation of a sample

surface can reveal print quality, we propose to use in

situ measurements of surface roughness to optimize the

FFF process parameters. We do so by utilizing Bayesian

optimization (BO), a sample-eﬃcient approach to the op-

timization of problems that can be evaluated only point-

wise. In Sec. 2 we introduce the literature and concepts

upon which this work is based. Sec. 3 formalizes the

problem we tackle. Finally, Sec. 4 and Sec. 5 present our

approach to FFF parameters optimization based on in situ

data and the corresponding results.

2. BACKGROUND

2.1 FFF Parameters Conﬁguration

FFF has a large number of tunable process parameters

that aﬀect manufactured part properties such as dimen-

?Work supported by the Swiss Innovation Agency (Innosuisse,

grant №102.617) and by the Swiss National Science Foun-

dation under NCCR Automation (grant №180545). E-mails:

{xaguidetti,ebalta,ralisa,lygeros}@control.ee.ethz.ch,

mkuehne@student.ethz.ch,yannick.nagel@nematx.ch

sional accuracy, part strength, and surface roughness,

among others (Turner and Gold, 2015). A number of

process optimization methods have been proposed in the

literature, see (Dey and Yodo, 2019) for a recent survey.

Most of the existing methods rely on a design of experi-

ments study based on e.g. Taguchi analysis (Sood et al.,

2009; Wankhede et al., 2020), Q-optimal based models

of experimental data (Mohamed et al., 2016), response

surface methods, fuzzy inference systems, artiﬁcial neu-

ral networks, genetic algorithms (Peng et al., 2014), and

more. However, these methods tend to be too speciﬁc and

resource-intensive (e.g. using destructive testing) to char-

acterize performance under changing process parameters.

Additionally, the models often do not make use of in situ

measurements for the eﬃcient evaluation of printed part

characteristics. In practice, there is a need for autonomous

optimization methods that can use in situ data to optimize

system parameters in an online fashion, selecting new

parameters based on previous measurements, and subject

to process constraints.

In this study, we focus on some key parameters that jointly

aﬀect the surface roughness of a print. The print speed

and the amount of extruded material are the two main

parameters that inﬂuence surface roughness. The print

speed vpis the speed of the extruder head during the

deposition of a layer. The amount of extruded material is

often characterized by the extrusion multiplier em, which

multiplies the baseline extrusion amount (i.e. the theoret-

ically needed amount of material according to extrusion

modeling (Aksoy et al., 2020)) to produce a ﬁne-tuned

command for the extruder.

arXiv:2210.15239v1 [eess.SY] 27 Oct 2022

2.2 Bayesian Optimization

BO is an iterative strategy for the optimization of black-

box and expensive-to-evaluate functions, often under per-

formance constraints. In a general optimization problem,

the objective function f(x) and constraint function c(x)

are modeled by Gaussian process (GP) regression trained

with data. The GP models can produce predictions of

the functions (with the corresponding uncertainties) away

from the training data points. In BO, the GP model

predictions and uncertainty are used to select the input x∗

at which to conduct the next evaluation. The evaluation

results f(x∗) and c(x∗) are added to the available data set

and the next optimization iteration takes place. The func-

tion returning the most valuable xto test depending on the

already available data and models is called an acquisition

function. Numerous acquisition functions are presented in

the BO literature (Hern´andez-Lobato et al., 2016; Garrido-

Merch´an and Hern´andez-Lobato, 2019; Gardner et al.,

2014). BO has been successfully used in numerous applica-

tions, such as manufacturing (Maier et al., 2020; Guidetti

et al., 2021) or control under safety constraints (Khosravi

et al., 2022). In this work, we use the BO algorithm studied

in (Guidetti et al., 2022), that was speciﬁcally designed

for the conﬁguration of advanced manufacturing processes

such as FFF.

2.3 Material

The feedstock material we use in this work is LCP,

which has been presented in (Gantenbein et al., 2018)

and is currently used for high-end applications by Ne-

matX AG 1. LCPs are composed of aromatic thermotropic

polyesters. When heated above their melting temperature,

these polyesters self-assemble into nematic domains (i.e.

the molecules have their long axes arranged in parallel).

In this spontaneous conﬁguration, however, each coherent

domain is oriented in a diﬀerent and random direction,

and no global molecular arrangement in the material is

present. Extruding the material through a heated nozzle –

the typical deposition method in FFF – has been shown to

produce global alignment: the deformations and forces cre-

ated by the extrusion process reorient the nematic domains

in the extrusion direction. Upon exit from the nozzle,

the aligned nematic domains are frozen in place by the

rapid cooling caused by exposure to ambient temperature.

After printing, the monomers are thus aligned in the axial

direction of the deposited ﬁlament.

3. PROBLEM STATEMENT

The monomer alignment achieved in LCP FFF produces

extraordinary mechanical properties, comparable to tradi-

tional but more complex ﬁber-reinforced materials. How-

ever, LCP is very sensitive to the parameters of the FFF

deposition process. Studying similar polymers, it has been

shown that, during the deposition of adjacent material

lines, contact between an existing line and the nozzle

printing the next line causes drag and subsequent mis-

alignment in the previously deposited monomers (Siqueira

et al., 2017). Clearly, reducing the fraction of aligned

1https://nematx.ch

monomers lowers the mechanical performance of manu-

factured components. This eﬀect has been shown exper-

imentally to exist in LCP printing. For example, in the

case of over-extrusion, the excess of deposited material is

unable to achieve proper monomer alignment and disturbs

the alignment of existing lines in a similar fashion to nozzle

contact. Conversely, in the event of under-extrusion, the

monomer alignment is not impacted, but the amount of

deposited material is lower than what would be necessary

to solidly ﬁll the part, making the mechanical properties

sub-optimal.

Thus, the print quality – which can be quantiﬁed by layer

inspection to detect over- or under-extrusion – aﬀects

the performance of printed components. In this work,

we propose to optimize the FFF of LCPs while using

surface roughness as an easy-to-measure in situ proxy for

mechanical performance. The contributions of this work

are

(1) the validation of an in situ method for surface quality

evaluation using a laser distance sensor,

(2) a study on the correlation between in situ measured

print quality and mechanical properties assessed via

destructive testing, and

(3) the successful application of a sample-eﬃcient opti-

mization algorithm to the FFF of LCPs.

4. METHODS

4.1 Surface Quality Evaluation

To evaluate the quality of the material deposition pro-

cess, we propose to analyze the surface of each deposited

layer while printing. We have modiﬁed a printer head to

accommodate a compact laser triangulation sensor. The

sensor returns the distance between the printer head and

the point directly below it. When moving the printer head

horizontally (i.e. in a plane parallel to the print bed), the

sensor readings can be used to reconstruct the entire proﬁle

of the scanned surface (see e.g. Balta et al. (2021)). In Alg.

1 we detail the steps required to produce an in situ layer-

by-layer scan of a part made of Nlayers.

Algorithm 1: In Situ Layers Surface Scanning

for k←1to Ndo

Deposit layer k;

Lift the printer head;

Begin recording laser sensor measurements;

Move the printer head horizontally and

perpendicularly to the print lines, to pass over

one complete section of layer kat constant

traveling speed;

End recording and save data from layer k;

end

For each layer, we obtain a sequence of distance measure-

ments associated with the position of the printer head.

This data can be processed to draw an elevation proﬁle of

the layer section (cf. Sec. 5.1) or to compute a quantitative

evaluation of the layer surface roughness.

We use the ISO 4287 proﬁle parameter Ra to quantify the

roughness of a proﬁle. This is a commonly used texture

parameter (Townsend et al., 2016) and is calculated as

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Data-DrivenProcessOptimizationofFusedFilamentFabricationbasedonInSituMeasurements?XavierGuidetti;,MarinoKuhne,YannickNagel,EfeC.Balta,AlisaRupenyan;,JohnLygerosAutomaticControlLaboratory,ETHZurich,Zurich,SwitzerlandInspireAG,Zurich,SwitzerlandD-MAVT,ETHZurich,Zurich,Switze...

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Data-Driven Process Optimization of Fused Filament Fabrication based on In Situ Measurements

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