00207540210146099
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This article was downloaded by: [UNAM Ciudad Universitaria]On: 13 October 2014, At: 14:17Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office: Mortimer House, 37-41 Mortimer Street,London W1T 3JH, UK
International Journal of
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Analysis of the surfaceroughness and dimensional
accuracy capability of
fused deposition modelling
processesC. J. Luis Pérez
Published online: 14 Nov 2010.
To cite this article: C. J. Luis Pérez (2002) Analysis of the surface roughnessand dimensional accuracy capability of fused deposition modelling processes,International Journal of Production Research, 40:12, 2865-2881, DOI:10.1080/00207540210146099
To link to this article: http://dx.doi.org/10.1080/00207540210146099
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int. j. prod. res., 2002, vol. 40, no. 12, 2865±2881
Analysis of the surface roughness and dimensional accuracy capability of
fused deposition modelling processes
C. J. LUIS PE Â REZy
Building up materials in layers poses signi®cant challenges from the viewpoint of material science, heat transfer and applied mechanics. However, numerousaspects of the use of these technologies have yet to be studied. One of theseaspects is the characterization of the surface roughness and dimensional precisionobtainable in layered manufacturing processes. In this paper, a study of rough-ness parameters obtained through the use of these manufacturing processes was
made. Prototype parts were manufactured using FDM techniques and an experi-mental analysis of the resulting roughness average (Ra) and rms roughness (Rq)obtained through the use of these manufacturing processes was carried out.Dimensional parameters were also studied in order to determine the capabilityof the Fused Deposition Modelling process for manufacturing parts.
1. Introductio n
The term rapid prototyping can be de®ned as the manufacture of any physical
model of a part, component, mechanism or product that is carried out using newtechnologies prior to the product’s industrialization, with the aim of validating all or
some of its main characteristics and theoretical functions, or as a functional element
directly applied in a manufacturing process. The use of these technologies means that
prototype manufacturing time is now measured in hours as opposed to days, weeks
or months, which has led to the use of the term `rapid’ and a considerable reduction
in component manufacturing costs (Rhorer et al . 1998, Prinz et al . 1997).
In addition, the number of dierent materials that can be employed has increased
signi®cantly, improving the precision and functionality of the end products.
Therefore, rapid prototype manufacturing techniques are now worthy of considera-
tion as alternative methods of the direct production of parts, components or models
for use in the manufacturing process (Amon et al . 1993).
Since the presentation of the ®rst commercial application in 1987, many pro-
cesses have been developed, the objective of which is to produce prototypes and
functional elements by combining existing manufacturing processes (sintering, con-
sumable electrode welding methods, laser technology, etc) with the versatility oered
by computer-assisted design, manufacture and analysis systems (Malloy 1994, Dorf
and Kusiak 1994).The various prototype manufacturing processes can be classi®ed in dierent
ways: by the material employed, the energy used, or the type of application in
which they are used; thus we have Stereolithography (SLA), Selective Laser
Sintering (SLS), Ink-Jet Printing Processes, Fused Deposition Modelling (FDM),
International Journal of Production Research ISSN 0020±7543 print/ISSN 1366±588X online # 2002 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/00207540210146099
Revision received February 2002.{ ETSIIT-Universidad Pu blica de Navarra, Manufacturing Engineering Section,
C/Campus ArrosadõÂa s/n, 31006 Pamplona, Spain. e-mail: cluis.perez@unavarra.es
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Laminated Object Manufacturing (LOM) and Shape Deposition Manufacturing
Processes (SDM), among others.
The surface ®nish of parts obtained through these manufacturing processes is
often highly important, especially in cases in which the components will be in contact
with other elements or materials in their service life, as in the case of moulds made
up of components manufactured by means of Solid Free Form Manufacturin g
Processes, or the case of other functional elements whose surface characteristics
will have a signi®cant eect on mechanical properties such as fatigue, wear, corro-
sion, etc.
One of the most commonly employed methods for characterizing roughness
involves assessment of the roughness average by means of pro®le rugosimeters.This roughness is eective roughness; that is, the roughness actually measured by
the gauging apparatus. Dimensional precision is also very important; therefore, in
order to determine the capability of the FDM equipment, an analysis of dimensional
precision has been performed.
Prototype manufacture using the Fused Deposition Modelling (FDM) manu-
facturing process was carried out. Figure 1 shows a manufacture d prototype in
the inner chamber of the FDM equipment. Once the parts were obtained, an experi-
mental study of eective roughness and dimensional precision was carried out in
order to determine the capability of the FDM equipment.
2. FDM Process description
Fused Deposition Modelling (FDM) is a rapid prototyping process to produce
three-dimensional solid objects directly from a CAD model. It was ®rst developed by
Stratasys Inc (USA). The machine is basically a CNC-controlled robot carrying a
miniature extruder head. The material is heated and then, in controlled amounts,
deposited directly on the previous layers. Eventually layers are built up to complete
the entire part (Dorf and Kusiak 1994).
2866 C. J. Luis Pe rez
Figure 1. Manufactured prototype.
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The process starts from a 3D geometric CAD model, which is computer-sliced
into horizontal layers. In the machine, molten thermoplastic material (ABS) or wax
is extruded through a ®ne nozzle. The extrusion head with its nozzle is governed in
the X ±direction and Y ±direction by the computer in accordance with the 3D model’s
slices, to produce the required cross section. At the same time, a second nozzle
creates a supporting structure as required. When the model is ®nished, the support-
ing structure is easily removed. The layers are built on a horizontal table, which is
lowered step by step as each layer is added. Layer thickness depends on the nozzle
ori®ce, the feed rate of the material and the speed of the extrusion head.
Figure 2 shows a photograph of the FDM equipment employed in this work. The
material is fed into the head, heated until melting and then extruded from the tip in
controlled amounts. The extrusion head is moved around the table with an X±Y
positioning system to deposit material on each layer. The part is on a platform that
drops when a layer is complete to allow the addition of a new layer. Many materialscan be employed. These materials include: investment casting wax, ABS, polyester
and elastomer. Layer height is usually between 50 mm and 250 mm. The modelling
envelope is the actual volume of space inside the FDM equipment in which parts are
built. Parts up to 254 £ 254 £ 406 mm3 can be built in the FDM3000 used in thiswork.
2867Dimensional accuracy capability of FDM processes
Figure 2. FDM equipment.
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Semi-liquid material is extruded and then deposited in ultra thin layers, from the
lightweight FDM head, one layer at a time. This builds the model upward from a
®xed base. The material then solidi®es as it is directed into a place with an X±Y
controlled extruding head nozzle, which thus creates a precision laminate. The
material (P400-ABS) leaves the nozzle in a liquid form, which then solidi®es. For
this reason, it is fundamental for the FDM process that the temperature of the liquid
modelling material is maintained just above the solidi®cation point.
The material employed was the P400-ABS which contains: 90±99% acrylonitrile
butadiene styrene resin, 0±2% mineral oils and 0±2% wax. The physical properties
are: tensile strength 0.034 MPa, ¯exural strength 0.066 MPa, tensile modulus 2.48
MPa, ¯exural modulus 2.62 MPa and 50.00% of elongation, among others. The
material ®lament is drawn into the FDM head from the spools by drive wheels
where it is melted by the lique®er. The temperature of the lique®er is around
2708C for the P400 ABS Plastic. The material is extruded out of the FDM Tipswhere it solidi®es (in around 0.1 s), shrinks, and fuses to previously deposited
material as the FDM head is moved in the horizontal (X±Y ) plane. A road width
of 0.60 mm was used and a layer height of 0.25 mm was selected.
The FDM process has the following advantages: a great variety of materials
available, easy change of materials, low maintenance costs, ability to manufacture
thin parts, unattended operation, absence of toxic materials and very compact size.
On the other hand, it presents the following disadvantages: there is a seam line
between layers, the extrusion head must continue moving or else the material
bumps up, supports may be required, part strength is weak perpendicular to thebuild axis, more area in slices requires longer build times, and temperature ¯uctua-
tions during production could lead to delamination.
The application range of FDM comprises: conceptual modelling, functional
applications and models for further manufacturing procedures, such as investment
casting and injection moulding.
3. Surface roughness measurement
Surface ®nish tends to be decisive in a large number of applications, and in
general it must be corrected by means of ®nishing operations. However, there are
materials in which it is not possible to carry out these operations, and therefore an
optimum selection of materials and application conditions is crucial. It is also highly
important that the characteristics required of the products obtained should be deter-
mined beforehand, and on this basis the operating conditions that most closely suit
the materials to be employed and their characteristics should be chosen (Luis Pe rez
et al . 2001). Considerable research has been done in order to reduce the surface
deviation of rapid prototyping components, because these techniques often resultin a loss in geometric integrity before the desired ®nish is achieved (Reeves and
Cobb. 1998). Therefore, it is important to have a priori knowledge, by means of
theoretical models, of the manufacturing process parameters that allow us to predict
the surface ®nish of manufactured prototypes (Reeves et al . 1997). In the work
developed by Reeves and Cobb, experimental roughness results are performed for
dierent rapid prototyping systems and then compared with theoretical values.
These authors have also shown that the surface quality depends upon the intrinsic
characteristic of the dierent rapid prototyping processes, which reduces the theor-
etical accuracy of the manufactured parts (Reeves and Cobb 1995).
2868 C. J. Luis Pe rez
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The surface roughness average (Ra) was taken as a parameter, de®ned on the
basis of the ISO 4287 (1997) standard as the arithmetical mean of the deviations of
the roughness pro®le from the central line (`m) along the measurement. This de®ni-tion is set out in equation (1), where y…x† is the pro®le values of the roughness pro®leand ` is the evaluation length
Ra ˆ1
l
… l 0
y…x†j j dx: …1†
Another parameter with a great deal of industrial interest is rms roughness (Rq). This
parameter is de®ned from the expression shown in equation (2). Unlike the Ra par-
ameter, it is more aected by isolated errors and therefore detects them better.
However, the Rq parameter does not distinguish between whether it is an isolated
error or a general tendency towards the worsening of the surface
Rq ˆ
1
l
… l 0
y2…x† dxs
: …2†
Having proposed the models for modelling the surface roughness in layered forming,
we now present the results obtained when manufacturing the prototypes shown in
®gures 3 and 4.
Figure 3 shows the proposed prototype with dierent slope variations in order todetermine the in¯uence of the angle in manufacturing the prototypes. The width of
the prototypes is 20 mm. Figure 4 shows the STL geometry used to determine the
slices in order to build the prototype layer by layer.
The technology employed, an FDM machine (FDM 3000) from Stratasys Inc, is
shown in ®gure 2. The material employed was ABS FDM3000. As can be observed,
2869Dimensional accuracy capability of FDM processes
Figure 3. Proposed prototype.
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the prototypes exhibit slope variations that allow analysis of the eect of slope
variations with regard to roughness and dimensional parameters.
Once the prototypes were manufactured, eective roughness was measured withan ALPA TL±70 pro®le rugosimeter, using a nominally 3 mm stylus tip. In addition,
a 2RC cut-o ®lter was used to evaluate the Ra and Rq parameters. A stylus speed of
1 mm/s was used in conjunction with a 0.12 mN static stylus force.
An evaluation length of 9.6 mm (12 £ 0:8 mm) and an 0.8 mm cut-o ®lter wereused to evaluate the Ra and Rq parameters when ’ was 08, 308, 458, 608, 858 and 908,and a 2.5 cut-o ®lter to evaluate the Ra and Rq parameters when ’ was 158, where ’is the angle used to de®ne the slope variations in the prototypes shown in ®gures 3
and 4.
The total length of surface traversed by the stylus in making the measurements is
greater than the evaluation length due to the necessity of allowing a short overtravel
at either end to ensure that mechanical and electrical transients are excluded from
the measurements. In this case, two cut-os are needed in order to perform the
measurements. Therefore, the total length is two cut-os longer than the evaluation
length.
The fact that two dierent types of cut-o were employed was due to the need to
include the appropriate wavelengths for the sampling length, labelled ``’ in ®gure 5,
where hc is the layer height and d c is the horizontal space between layers, which isde®ned by the slope variation. Given that this length will increase as the value of
angle ’ tends to zero, a measure of Ra with a greater cut-o is needed. This is why acut-o of 0.8 mm was employed along with a 2RC ®lter to evaluate the average
arithmetical roughness in all the angles considered, except in the case of ’ ˆ 158.This sampling length is that length of the assessment over which the surface rough-
ness can be considered to be representative. The value of the sampling length is a
compromise. On the one hand, it should be long so as to obtain a statistically good
representation of the surface. However, if it is made too big, longer components of
the geometry, such us waviness, will be also considered. The evaluation length is the
2870 C. J. Luis Pe rez
Figure 4. STL geometry.
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length of a pro®le over which data have been collected. This evaluation length
consists of several sampling lengths and it is normally shorter than the total distance
travelled by the stylus instrument during data collection (traverse length).
As can be observed from the values in table 1, the parameters corresponding to 58
cannot be evaluated because of pro®le irregularities whose sizes made it impossible
to obtain the roughness parameters.
Figure 6 shows the eective roughness pro®le obtained by measuring the proto-
type shown in ®gure 3 in the area corresponding to an inclination of ’ ˆ 308 from
2871Dimensional accuracy capability of FDM processes
Figure 5. Evaluation length.
Ra …mm†Angle (8) Part 1 Part 2 Part 3 Part 4
0 24.66 26.29 24.47 22.430 26.27 26.06 25.15 21.480 25.54 26.57 24.95 22.115 Ð Ð Ð Ð 5 Ð Ð Ð Ð 5 Ð Ð Ð Ð
15 47.40 46.89 45.97 48.16
15 53.61 49.56 46.03 47.0315 50.32 49.17 46.80 46.6930 29.84 29.72 30.83 30.4930 30.51 32.00 30.44 30.5930 28.44 31.61 30.46 30.1345 20.41 23.27 22.72 23.3245 20.89 23.00 23.33 23.8745 21.25 22.79 23.13 23.8160 17.90 19.21 19.74 20.0260 16.84 19.44 19.86 19.94
60 17.59 20.05 20.02 20.2375 16.63 17.07 17.21 18.3575 16.97 17.14 17.98 18.0075 17.42 17.88 18.04 19.0485 15.69 16.61 15.82 15.0685 16.12 17.71 15.07 15.1685 17.38 18.17 16.37 16.7690 16.86 17.24 17.30 16.3890 15.66 14.88 16.08 15.4790 15.60 16.06 16.52 15.04
Table 1. Eective Ra values in the prototypes.
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horizontal, selecting an evaluation length of 9.6 mm and in the conditions described
previously, for the cut-o and the ®lter. From the values shown in ®gure 6, it can be
seen that the traverse length is Lˆ
11:2 mm (12£
0:8‡
2£
0:8), where the evalua-tion length is `ev ˆ 9:6 mm (12 £ 0:8). Similarly, it is possible to observe that thenumber of peaks contained in this ®gure is approximately 20, so the evaluation
length divided by the total number of peaks is `ev=20 ˆ 0:48. In addition, in thecase of angle ’ ˆ 308, and from ®gure 5, it is determined that hc ˆ ` sin…30†. Giventhat the layer height employed in this study is hc ˆ 0:25 mm, we then ®nd that` ˆ 0:25 £ 2 ˆ 0:50 mm. As can be seen, the theoretical value coincides with themean experimental value. Similar behaviour is obtained for ®gures 7 and 8 corre-
2872 C. J. Luis Pe rez
Figure 6. Eective roughness for ’ ˆ 308, with an evaluation length of 9.6 mm(12 £ 0:8 mm) and a 2RC cut-o ®lter.
Figure 7. Eective roughness for ’ˆ
458, with an evaluation length of 9.6 mm(12 £ 0:8 mm) and a 2RC cut-o ®lter.
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sponding, respectively, to ’ ˆ 458 and ’ ˆ 608, where the values deduced from thegraphs are 0.36 mm (9.6/27) for 458 and 0.29 mm (9.6/33) for 608, while the theor-
etical values are, following a similar line of reasoning to the previous case, 0.35 mm
and 0.29 mm respectively.A surface pro®le is composed of a set of frequency components. The highest
frequency components correspond to those that are perceived to be rough and hence
are called `roughness’. The lowest frequency components are often associated with
the terms `waviness’ or even `form errors’. The easiest way to separate the com-
ponents of a signal is the use of ®lters. The term `cut-o ’ numerically speci®es the
frequency bound below or above which the frequency components are eliminated.
Therefore, a cut-o is a method of ®ltering the components of a signal. For example,
a 0.8 mm cut-o ®lter will allow only the wavelengths below 0.8 mm to be assessed
and wavelengths above this value will be removed. On the other hand, a 0.8 mm cut-o will allow only the wavelength above 0.8 mm to be assessed.
For the case of ’ ˆ 158, we get ` ˆ hc=sin…15† ˆ 0:25=sin 15 ˆ 0:9659, which isgreater than the cut-o of 0.8 mm, making it necessary to employ a larger cut-o. In
this case, by employing a cut-o of 2.5 mm along with a 2RC ®lter, length ` may besuciently encompassed. Figure 9 shows the eective roughness for the case of
`ev ˆ 7:5 mm, ’ ˆ 158 and a 2.5 mm cut-o. As can be seen in ®gure 9, the repre-sented length divided by the total number of peaks `ev=8 ˆ 0:94. Given that thetheoretical value corresponding to this angle is 0.96 mm, a correspondence similarto that of the previous case is obtained between the theoretical and experimental
values. If we consider a periodic function as shown in ®gure 1, the expected number
of peaks compressed in an evaluation length of 9.6 mm is given by 9:6=sin…’†. Forexample, if ’ is equal to 308 the theoretical number of peaks is equal to 19.2 peaks.
That is, the wavelength is equal to 9:6=19:2 ˆ 0:5 mm. Therefore, if we consider acut-o ®lter of 0.8 mm the irregularities are included.
This study was carried out by means of a surface characterization in which
average arithmetic roughness Ra and rms roughness Rq were used as parameters,
since they are the parameters of greatest technological interest.
2873Dimensional accuracy capability of FDM processes
Figure 8. Eective roughness for ’ ˆ 608, with an evaluation length of 9.6 mm(12 £ 0:8 mm) and a 2RC cut-o ®lter.
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With the aim of comparing the results obtained from the theoretical models
presented previously, four prototypes were manufactured, incorporating the geome-
try shown in ®gures 3 and 4. Once the prototypes were prepared, three measurementswere carried out in the study zones which, as indicated previously, were de®ned by
the variation in angle ’. These measurements were performed for parallel, equallyspaced lines, with the aim of achieving a characterization of the manufactured
surfaces. In this way, it is possible to obtain good surface characterization as far
as roughness is concerned. In the case of ’ ˆ 908, the roughness measurement s wereperformed according to the straight wall of the prototypes.
Tables 1 and 2 show the roughness values obtained by measuring the prototypes
represented in ®gures 3 and 4, which were obtained from the manufacture of four
prototypes. These measurements represent the results obtained from the evaluationof the roughness average and rms roughness in each of the zones de®ned by the
variation of the angle ’ from 08 to 90, the layer height being 0.25 mm. The roughnesscorresponding to ’ ˆ 908 was measured on the vertical wall of the prototypes andthe roughness corresponding to ’ ˆ 08 was measured on the upper side of the pro-totypes. The measurements were recorded to two decimal places.
Tables 3 and 4 present the mean value corresponding to the roughness meas-
urements for each of the slopes and the typical deviation occurring therein. The
previous values were obtained from equation (3),
·xx ˆXn j ̂ 1
x j and S 2 ˆ 1
n ¡ 1Xn j ̂ 1
·xx ¡ x j ¡ ¢2
: …3†
Similarly, uncertainty has been incorporated into the roughness evaluation with
the aim of providing the measurements with traceability and providing a value that
will account for the variability of the manufacturing process. This is done by taking
into account the variability associated with the measurement instrument, the varia-
bility in the measurements performed in a single part and the variability associated
2874 C. J. Luis Pe rez
Figure 9. Eective roughness for ’ ˆ 158, with an evaluation length of 7.5 mm (3 £ 2:5 mm)and a 2RC cut-o ®lter.
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2875Dimensional accuracy capability of FDM processes
Rq …mm†Angle (8) Part 1 Part 2 Part 3 Part 4
0 28.07 30.86 25.32 24.120 29.85 30.48 24.98 23.930 29.06 31.11 24.34 24.775 Ð Ð Ð Ð 5 Ð Ð Ð Ð 5 Ð Ð Ð Ð
15 54.40 54.02 55.67 55.3415 59.93 56.96 55.05 52.8115 57.43 55.30 54.21 54.2530 34.30 34.27 33.07 34.9330 34.90 36.62 33.74 35.0130 33.00 36.43 32.52 34.73
45 23.75 26.65 25.33 26.7545 24.43 26.45 25.84 27.4645 24.76 26.30 24.99 27.4560 20.81 22.15 22.99 23.0760 19.98 22.44 23.23 23.0860 20.77 23.26 23.05 23.3975 19.44 19.82 20.95 21.0775 19.79 19.93 20.23 20.8175 20.44 20.63 20.22 22.0685 18.34 19.42 19.59 17.63
85 18.80 20.48 18.57 17.9485 20.16 21.03 20.34 19.7690 20.40 20.01 19.93 19.5690 18.16 17.53 18.10 17.9790 18.36 19.15 19.25 17.68
Table 2. Eective Rq values in the prototypes.
Parameter ’…8† FDM 1 FDM 2 FDM 3 FDM 4·RRa (mm) 0 25.49 26.31 24.85 22.01
u2W ˆ u2c ‡ s2W 2.28 1.81 1.68 1.45
15 50.44 48.54 46.26 47.2916.03 7.99 5.58 6.20
30 29.60 31.11 30.57 30.403.32 3.92 2.40 2.38
45 20.85 23.02 23.06 23.671.27 1.39 1.44 1.5060 17.44 19.57 19.87 20.06
1.06 1.15 1.01 1.0475 17.01 17.36 17.74 18.46
0.89 0.96 1.01 1.1485 16.40 17.50 15.75 15.66
1.45 1.41 1.05 1.5390 16.04 16.06 16.63 15.63
1.15 2.04 1.08 1.09
Table 3. Mean eective Ra and uncertainty values within the prototypes.
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with the manufacturing process itself (by means of the variability existing between
dierent parts). Tables 3 and 4 present the results obtained on incorporating the
measuring instrument uncertainty into the process of measuring roughness, consid-
ering the variability in the dierent samples.
As mentioned earlier, the roughness measurements were performed with an
ALPA TL±70 pro®le rugosimeter, in which the maximum value of uncertainty as-
sociated with the Ra and Rq parameters is obtained from equation (4), where 5%
refers to the mean value of the roughness parameters.
uc ˆ §…5% ‡ 0:004† mm: …4†The data obtained when equations (3) and (4) are applied to the data shown in
tables 1 and 2 are shown in tables 3 and 4, incorporating the total uncertaintyassociated with the roughness measurement process in a single part. For evaluation
of the total uncertainty associated with the measurement in a single part and for an
angle of a given slope, the recommendations set out in EAL-R2 (1997) and ISO
(1993) with regard to the expression of uncertainty in measurements were followed,
and they lead to equation (5).
u2W ˆ u2c ‡ s2W ; …5†
where u2W is the total uncertainty in the same series of measurements, within a single
part, (uwithin†, s2W is the variability associated with the measurement according to thethree dierent lines over the surface considered and u2c is the uncertainty associated
with measurement due to use of the rugosimeter described previously.
Therefore, as shown in tables 3 and 4, for each group of measurements, uncer-
tainty appears within the sample (u2W ) and a mean value of the roughness meas-
urements ( ·RRa j and ·RRq j ). However, the uncertainty associated with measurement of a
single prototype is not sucient for the evaluation of uncertainty in the process and
for comparison of theoretical and experimental results. To achieve this, as pointed
out previously, four dierent prototypes were manufactured (termed FDM 1, FDM
2876 C. J. Luis Pe rez
Parameter ’…8† FDM 1 FDM 2 FDM 3 FDM 4·RRq (mm) 0 28.99 30.82 24.88 24.27
u2W ˆ u2c ‡ s2W 2.91 2.49 1.81 1.68
15 57.25 55.43 54.98 54.13
15.89 9.88 8.12 8.9630 34.07 35.77 33.11 34.89
3.86 4.92 3.13 3.0845 24.31 26.47 25.39 27.22
1.75 1.79 1.80 2.0360 20.52 22.62 23.09 23.18
1.28 1.62 1.36 1.3975 19.89 20.13 20.47 21.31
1.25 1.21 1.23 1.5885 19.10 20.31 19.50 18.44
1.82 1.71 1.75 2.1890 18.97 18.90 19.09 18.40
2.44 2.49 1.77 1.88
Table 4. Mean eective Rq and uncertainty values within the prototypes.
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2, FDM 3 and FDM 4, in tables 3 and 4) and roughness was measured in each of the
prototypes according to equally spaced lines. From these measurements, the rough-
ness values set out in tables 3 and 4 were obtained, as was the corresponding uncer-
tainty for each of the four prototypes.
Another source of uncertainty is the limited resolution of the instrument. Since
the scale interval of the rugosimeter is 0.01 mm, the value of one indication can lie
with equal probability anywhere in the interval (x § 0:005). A rectangular probabil-ity function can be used to describe this variation and its uncertainty is then given by
equation (6):
ulr ˆ 0:01
12p mm: …6†
With the aim of expressing the manufacturing process variability once the uncer-
tainty within the samples had been determined, total variability was determined fromequation (7), bearing in mind that the model was developed to evaluate variability in
a process subject to variability in the samples.
u2T ˆ S 2B ‡m ¡ 1
m S 2P ‡ u2lr; …7†
where u2T is the total uncertainty of the process, S 2B is the variability observed
between the mean values of the various roughness measurements, that is,
…·xx1 . . . ·xxm
†, where m is the number of prototypes manufactured, and S 2P is the
mean value of the standard deviations shown in tables 3 and 4; that is,…u2W 1 ‡ ¢ ¢ ¢ ‡ u2Wm†=m.
Once the process uncertainty has been evaluated by the procedure described
previously, it is assigned a coverage factor of k ˆ 2 so that total uncertainty isevaluated by equation (8).
U T ˆ k £ uT : …8†This coverage factor `k’ is a numerical factor used as a multiplier of the combined
standard uncertainty in order to obtain an expanded uncertainty; that is, a quantity
de®ning an interval on the result of a measurement that may be expected to encom-
pass a large fraction of the distribution of values that could reasonably be attributed
to the measurand. This fraction may be viewed as the coverage probability or level of
con®dence of the interval. Associating a speci®c level of con®dence, with the interval
de®ned by the expanded uncertainty, requires implicit assumptions regarding the
probability distribution characterized by the measurement result and its combined
standard uncertainty (EAL-R2 1997, ISO 1993). The value of the coverage factor ` k’
that produces an interval having a level of con®dence 95.45% assuming a normal
distribution is 2. If this value has to be increased then a greater k value should beconsidered. For instance, if k ˆ 3 then the level of con®dence is 99.73%.
From equations (7) and (8) we obtain the data shown in table 5, which represents
total process uncertainty and the mean value of the average roughness values (Rˆ
a
and Rˆ
q) in each of the sections corresponding to variations in angle ’.For expression of the results R
ˆa j
and Rˆ
q j the nearest value on a decimal scale was
employed as, when taking rugosimeter uncertainty into account in the measure-
ments, according to equation (7), it can be seen that there is no advantage to be
gained in working with higher accuracy. Subsequently, the bias between the calcu-
lated value of R̂ a j and the value of R̂ a j to one decimal place is evaluated.
2877Dimensional accuracy capability of FDM processes
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4. Dimensional precision measurementAs mentioned earlier, four prototypes were manufactured incorporating the geo-
metry shown in ®gure 3, and three measurements were carried out in the zones to be
studied. Equally spaced lines have been selected with the aim of characterizing the
manufactured parts. Tables 6 and 7 show the angle and width values obtained by
measuring the prototypes represented in ®gures 3 and 4. Similarly, uncertainty has
2878 C. J. Luis Pe rez
’…8† …Rˆa § 2 £ uT † mm…k ˆ 2† …Rˆ
q § 2 £ uT † mm…k ˆ 2†0 …24:7 § 4:6† mm …k ˆ 2† …27:2 § 7:0† mm …k ˆ 2†
15 …48:1 § 7:0† mm …k ˆ 2† …55:4 § 7:1† mm …k ˆ 2†30 …30:4 § 3:7† mm …k ˆ 2† …34:5 § 4:5† mm …k ˆ 2†45
…22:6
§3:4
† mm
…k
ˆ2† …
25:8§
3:7† mm
…k
ˆ 2
†60 …19:2 § 3:2† mm …k ˆ 2† …22:4 § 3:4† mm …k ˆ 2†75 …17:6 § 2:4† mm …k ˆ 2† …20:4 § 2:6† mm …k ˆ 2†85 …16:3 § 2:9† mm …k ˆ 2† …19:3 § 3:1† mm …k ˆ 2†90 …16:1 § 2:5† mm …k ˆ 2† …18:8 § 3:0† mm …k ˆ 2†
Table 5. Expression of process uncertainty, taking samplevariability into account.
Angle values
Angle (8) Part 1 Part 2 Part 3 Part 4
0 0.1832 0.0640 0.0196 0.13100 0.1226 0.0715 0.0713 0.13140 0.3520 0.0612 0.0760 0.20585 4.5214 4.1751 5.1264 4.56065 5.3107 5.3423 4.1934 5.04095 4.4130 3.3453 4.3457 4.3107
15 15.1206 15.2339 15.0555 15.0920
15 15.3442 15.2442 15.2000 15.045515 15.1006 15.4624 15.1110 15.151430 29.5442 30.1105 29.6572 30.151430 30.0731 30.2142 29.9189 30.164830 30.0641 29.5628 30.1827 30.115045 45.0023 45.1525 45.0532 45.062445 45.0641 45.0417 45.0345 44.595845 44.5239 45.2331 44.8212 45.101460 60.0937 60.2915 59.9062 60.243760 60.1025 60.3247 60.2454 60.3033
60 60.0814 60.0307 59.7414 60.204775 75.0406 75.1421 74.9889 75.105375 75.0312 75.2600 75.3048 75.294075 75.1936 75.1644 74.8552 75.062685 85.4325 85.3935 85.3278 85.410185 85.4949 85.5128 85.4768 86.043685 85.3715 84.5640 85.0801 85.361790 90.2828 90.1431 90.0544 90.243990 90.2640 90.1032 90.4704 90.272590 90.3044 90.2022 90.3098 90.1611
Table 6. Angle values in the prototypes.
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been incorporated into the evaluation of the dimensional parameters with the aim of
providing the measurements with traceability and providing a value that will account
for the variability of the manufacturing process. This is done by taking into accountthe variability associated with the measuring instrument, the variability in the meas-
urements performed in a single part and the variability associated with the manu-
facturing process itself (by means of the variability existing between dierent parts).
Table 8 presents the results obtained upon incorporating the measuring instru-
ment uncertainty into the process of measuring angle and width, considering the
2879Dimensional accuracy capability of FDM processes
Width values
Angle (8) Part 1 Part 2 Part 3 Part 4
0 19.7461 19.8681 19.7390 19.76610 19.8110 19.8500 19.8300 19.8125
0 19.8354 19.8932 19.8100 19.82985 19.6879 19.7937 19.7373 19.69645 19.6973 19.8012 19.8610 19.70135 19.6855 19.8221 19.8225 19.7220
15 19.7936 19.8231 19.8430 19.786815 19.7466 19.8205 19.7482 19.739715 19.7454 19.8091 19.7300 19.711730 19.8000 19.8567 19.8281 19.768630 19.8071 19.8252 19.8240 19.775430 19.7862 19.8443 19.7565 19.7711
45 19.8199 19.8328 19.8465 19.828145 19.7970 19.8210 19.7564 19.832945 19.8857 19.8320 19.8211 19.824060 19.8642 19.8569 19.7908 19.835560 19.8600 19.8265 19.8527 19.816260 19.8350 19.8337 19.7427 19.816475 19.8791 19.8332 19.7155 19.937775 19.8351 19.8321 19.7865 19.836075 19.8485 19.8393 19.7818 19.871085 19.8212 19.8336 19.8160 19.917085 19.8430 19.8626 19.7532 19.881385 19.8881 19.9100 19.8334 19.875890 19.8144 19.8850 19.8205 19.827990 19.8075 19.8601 19.7801 19.813590 19.7912 19.8540 19.8910 19.8030
Table 7. Width values in the prototypes.
’…8† …angle § 2 £ uT † mm …k ˆ 2† …width § 2 £ uT † mm …k ˆ 2†
0 …0:12 § 0:20†8 …k ˆ 2† …19:82 § 0:11† mm …k ˆ 2†5 …4:56 § 1:34†8 …k ˆ 2† …19:75 § 0:14† mm …k ˆ 2†
15 …15:18 § 0:28†8 …k ˆ 2† …19:77 § 0:10† mm …k ˆ 2†30 …29:98 § 0:58†8 …k ˆ 2) …19:80 § 0:07† mm …k ˆ 2†45 …44:97 § 0:50†8 …k ˆ 2† …19:82 § 0:07† mm …k ˆ 2†60 …60:13 § 0:40†8 …k ˆ 2† …19:83 § 0:08† mm …k ˆ 2†75 …75:12 § 0:31†8 …k ˆ 2† …19:83 § 0:12† mm …k ˆ 2†85 …85:37 § 0:78†8 …k ˆ 2† …19:85 § 0:10† mm …k ˆ 2†90 …90:23 § 0:26†8 …k ˆ 2† …19:83 § 0:08† mm …k ˆ 2†Table 8. Expression of process uncertainty, taking sample variability
into account.
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variability in the dierent samples. These measurements were performed with a
Mitutoyo MMC, in which the maximum value of uncertainty associated with
these measurements, from the certi®cate of calibration, is 4 mm.
To evaluate the associated total uncertainty, a similar procedure to that shown in
the previous section has been used; that is, the total uncertainty in the same series of
measurements, the total uncertainty within a single part, the variability associated
with the dierent measurement performed over the surface considered, and the
uncertainty associated with measurement due to the use of the instrument described
previously. The contribution of uncertainty due to the limited resolution of the
instrument was also considered.
As we know, the uncertainty associated with the measurement of a single pro-
totype is insucient for the evaluation of uncertainty in the process. To achieve this,
dierent prototypes were manufactured and the dimensional parameters of each of
them were measured. From these measurements, the values of the dimensional par-ameters set out in tables 6 and 7 were obtained, as was the corresponding uncertainty
for each of the dierent prototypes.
Therefore, following the procedure shown in previous sections we obtain the data
shown in table 8, which present total process uncertainty and the mean value of the
dimensional parameters under consideration. Finally, once the process uncertainty
has been evaluated by the procedure described previously, it is assigned a coverage
factor of k ˆ 2.
5. Conclusions and future work
The present study reports an uncertainty analysis of roughness and dimensional
parameters resulting from Fused Deposition Modelling processes.
Two dierent roughness parameters have been considered in order to analyse the
surface quality of manufactured parts (Ra and Rq). To achieve this, an uncertainty
analysis taking into account not only the manufacturing process variability but also
the measurement variability was carried out. The recommendations given in the ISO
standard were followed. Therefore, we have demonstrated a methodology to follow
when evaluating the capacity of a speci®c process that considers both the measuring
uncertainty and the uncertainty due to the manufacturing process.
It can be veri®ed that the rms surface is greater than the average surface rough-
ness, as was expected, since the rms surface is more aected by isolated errors and
therefore detects them better. Moreover, a greater degree of variability has been
observed in this latter parameter. In addition, a larger degree of variability is
observed in the Rq values. For the case of ’ ˆ 158, we get Ra ˆ 48:1 mm, which isgreater than the rest of the values. In order to obtain this parameter, it was necessary
to employ a larger cut-o so that the surface irregularities may be suciently encom-passed. A better surface ®nish could have been obtained by reducing the layer height.
Nevertheless, this means more manufacturing time and costs.
As can be observed, surface roughness parameter uncertainties are more or less
the same with dierent slope variations of the angle. This behaviour is also observed
when considering dimensional parameters in which a similar degree of variability is
observed.
Taking into account the analysis performed, it has been shown that the dimen-
sional precision of FDM parts is quite good, considering the diameter of the depos-
iting material. Moreover, the surface roughness is deeply aected by the layer height
2880 C. J. Luis Pe rez
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of the prototypes. This parameter could be maintained at its lower value so that
better roughness values are obtained, but this would take a great deal of time.
The future aim of this work is to develop theoretical models that take into
account the experimental results obtained with this rapid prototyping technology
related to surface roughness and dimensional precision. From these models, it will be
possible to predict accurately the surface roughness and dimensional precision of a
FDM prototype before it has been built, since the proposed methodology combines
the variability within a single prototype, the variability associated with the manu-
facture of dierent prototypes, and the uncertainty associated with measurement due
to the use of the measuring instruments. This will lead us to time and cost savings, by
reducing the need for ®nishing operations on the model.
Acknowledgements
The author acknowledges the support given by the Engineering Project Section of the Public University of Navarre.
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2881Dimensional accuracy capability of FDM processes
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