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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

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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 PuÂ blica de Navarra, Manufacturing Engineering Section,

C/Campus ArrosadõÂa s/n, 31006 Pamplona, Spain. e-mail: [email protected]



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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 PeÂ 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 PeÂ 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).




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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,


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


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


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-


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.


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


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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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


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.




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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


’…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


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




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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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