ORIGINAL ARTICLE

Evaluation of analytical modeling for improvement of surfaceroughness of FDM test part using measurement results

Sadegh Rahmati & Ebrahim Vahabli

Received: 6 October 2014 /Accepted: 4 February 2015 /Published online: 19 February 2015# Springer-Verlag London 2015

Abstract In additive manufacturing (AM) processes, the tes-sellation of CAD model and the slicing procedure are thesignificant factors resulting unsatisfactory surface quality,where the topics related to surface roughness have been akey issue in this regard. In this paper, analytical models whichhave been presented to express surface roughness distributionin fused depositionmodeling (FDM) are assessed according tothe variations in surface build angle by considering the mainfactors which crucially affect surface quality. Analyticalmodels are verified by implementation and comparison withempirical data derived from the comprehensive FDM fabricat-ed test part. Finally, the most accurate model for estimation ofsurface roughness in the process planning stage for optimiza-tion of effective parameters have been introduced upon calcu-lating the mean absolute percentage error (MAPE) as perfor-mance criteria of each model in various equal ranges.

Keywords AdditiveManufacturing . Surface Roughness .

AnalyticalModel

1 Introduction

Emphasize on reduction of product manufacturing time isfollowed by essential changes in manufacturing processesand resulted in the birth of a new race of manufacturing tech-

nologies. This technology is able to produce the part directlyfrom CAD model on a layer by layer deposition principlewithout any need to tools, dies, jigs and fixtures, and humanintervention. This method therein part manufacturing is addi-tive, introduced as additive manufacturing (AM) technology[1]. AM has also enabled industry to benefit from differentrapid tooling (RT) techniques [2]. Due to the nature of layeredmanufacturing in AM processes, quality of manufacturingpart is usually lower than parts manufactured by NC ma-chines. Furthermore, most of layered manufacturing technol-ogies use support structure for prevention of deviation duringstacking of layers that after support separation, plenty of sep-arated support burrs residue on the part surface and upraise thesurface roughness [3].

Among AM processes, fused deposition modeling (FDM)uses heated thermoplastic filament which is extruded in asemi-molten state from the tip-off nozzle in a prescribed man-ner in a temperature-controlled environment for building thepart through a layer by layer deposition method until comple-tion of part manufacturing. The part is fabricated by deposi-tion of layers contoured in a plane (x-y) two dimensionally.The third dimension (z) results from single layers beingstacked up on top of each other but not as a continuous z-coordinate. Due to the layered production of the part, the sur-face finish of the build part is unavoidably excessively rough.This problem is raised in wide applications of FDM process indifferent industries. Due to the importance of surface rough-ness subject, various studies and efforts have been done tosolve this issue [4, 5].

Poor surface finish in AM processes is often affected bytessellation of the original CAD model and the slicing proce-dure during fabrication process. In slicing of tessellated CADmodel, containment problem results in distortion of the orig-inal CAD model of the designed form. In addition to contain-ment problem, deposition of sliced layers results in anotherproblem called staircase effect or stair-stepping effect [6]. This

S. Rahmati (*)Department of Mechanical Engineering, Majlesi Branch, IslamicAzad University, Isfahan, Irane-mail: rahmati@rapidtoolpart.com

E. VahabliDepartment of Mechanical Engineering, Science and ResearchBranch, Islamic Azad University, Tehran, Irane-mail: Ebrahim.vahabli@chmail.ir

Int J Adv Manuf Technol (2015) 79:823829DOI 10.1007/s00170-015-6879-7

problemmay be varied based on the surface build angle [7]. Inthis paper, upon designing and building the specific test part,well-known analytical models are evaluated. The mean abso-lute percentage error (MAPE) of each model within specifiedranges is calculated in order to introduce the best analyticalmodel. The general model parameters that are used in all an-alytical models are shown in Fig. 1 [6], where, denotes buildorientation (or surface build angle), t is layer thickness (slicethickness), and N is the angle between vertical axis and nor-mal to surface axis.

2 Analytical modeling

The concept of cusp height tolerance was introduced byDolence et al. [8] and used for interpretation of surface rough-ness. Offering a theoretic formula, they calculated cusp heightin a 2-dimensional and 3-dimensional part. Campbell et al. [9]introduced a mathematical model for estimation of arithmeticmean surface roughness in various AM processes given byEq. (1).

Ra 1000tsin 904

tan 90 1

where Ra is the arithmetic-mean-surface roughness (mi-cron), t is the layer thickness (mm), and is the build angle(degree). This model was tested for a few angles that none ofthem contains downward facing. In their report, this modelpredicts the surface roughness appropriately in a number ofangles. This estimation was reported in the range of 45 to180 for the FDM process. Mason et al. [10] presented amodel for estimation of arithmetic mean surface roughness.

In this model, surface roughness is indeed equal to half of thecusp height presented in the Dolende model which is given byEq. (2).

Ra 1000t2 cos 90 2

where Ra is the arithmetic-mean-surface roughness(micron), t is the layer thickness (mm), and N is thenormal build angle in degree which is equals to (90).Pandey et al. [6, 7, 11, 12] realized that layer thicknessand build orientation are assumed as the most importantprocess variables which affect the surface finish.According to the analytical observations, the edge pro-file of the part built by the FDM process is parabola.According to these observations, a semi-empirical modelwas proposed. However, the formula used in this paperis presented in Eq. (3), where, Ra is the arithmetic-mean-surface roughness (micron), t is the layer thick-ness (mm), is the build angle (degree), Ra 90 is the

equivalent for the roughness of the build angle (90),and w is a dimensionless adjustment parameter for sup-ported facets (chosen to be 0.2 in all FDM systems). Itis notable that for Ra in the build angles between 0 to70 , the average value of the sum is utilized.

Ra 69:28e72:36 t

cos; 0 70

1.

20 90Ra7070Ra90 Ra90Ra70 ; 70 < < 90117:6 t ; 90Ra 90 1 w ; 90 < 180

8>>>>>>>:

3

Ra 0; 0;=2;1000t

4cos 90

R21 R22

14

sin 90

1000t R

21R

22

1 4

21000t 3 tan 90 sin 90 ; O = W

8>: 4

Ra 1000t2cos 90

cos

5

Byun et al. [13] proposed a new roughness profile charac-terizing the surfaces made by layered manufacturing process-es. For the FDM process, R1 and R2 were set to 0.045 and0.01 mm respectively and maximum overhang angle was setto 30 . Likewise, the profile roughness Ra as a function of f(t,,R1,R2) is calculated by Eq. (4), where, Ra is arithmetic-meanFig. 1 Surface roughness estimation parameters model [6]

824 Int J Adv Manuf Technol (2015) 79:823829

surface roughness (micron), t is the constant layer thicknessfor a facet (mm), is the build angle (degree), R1 is the radiusof fillet (mm), and R2 is the radius of the corner (mm). Ahnet al. [14] presented a theoretical model for calculation ofarithmetic mean surface roughness; therein, the edge profilewas assumed as ellipse which is given by Eq. (5); in which tdenotes the layer thickness in millimeters, the build angle indegrees, and is the surface profile angle in degrees.

3 Test part design

To calculate the surface roughness in different build angles, asuitable and comprehensive model is required. In the appliedstudies, researches and papers written for evaluation of surfaceroughness, a pyramid-shaped test part with varied surfacebuild angles was selected by some researchers as a prototypefor measuring the surface roughness. The angle between up-ward vector tangents to surface with the vertical axis is calledthe surface build angle. Pyramid test part is shown in Fig. 2;therein, surface build angles are equal to 10, 15, 30, and 45 ,respectively.

Pandey et al. [6] reported the surface roughness measure-ment for the pyramid test part with side angles of 10, 15, 30,and 45 and layer thickness of 0.254 mm. In their research, byoffering a formula, they introduced a solution for estimation ofsurface roughness using layer thickness and build orientationparameters. Mason et al. [10] developed a customized FDMmachine with the nozzle thickness of 2 mm for building thetest part therein resulted in very rough surfaces with high

surface roughness indexes. Other researchers such asCampbell et al. [9] and Ahn et al. [14] presented a more com-prehensive test part for assessment of their analytical models.This test part, therein, was firstly introduced by Reeves andCobb [15] as depicted in Fig. 3, called Truncheon, has a suit-able geometry which enables the measurement of surfaceroughness for a wide range of surface build angles.

In the present study, with the choice of a step angle of 5 ,the truncheon test part in total consists of 36 cuboids to spansurface build angles between 0 to 180 , where the test partwas designed in CATIAv5. The dimension of each cuboid isassumed 103030 mm3 for accurate measurement by sur-face scanner and considering machine platform dimension of254254305 mm3, where the overall dimension of the trun-cheon is 2203030 mm3.

3.1 Fabrication and measurement of the test part

The prototype is fabricated by FDM-Dimension sst 1200es.The test part is sliced in CatalystEx and is made horizontallywith layer thickness of 0.254 mm. Model interior is solid andsupport sparse method used for fabrication. The material usedfor fabrication is ABSPLUS. Inside, the test part is filled andfabricated with support sparse method. At the final stage, thetest part is put into the chemical solution for 1 day and supportmaterial dissolved therein thoroughly. Due to the estimation ofsurface roughness, no surface polishing operation is imple-mented as depicted in Fig. 4. The surface roughness measure-ment is done by surface scanner MahrSurf MFW250 and Ravalues are derived accordingly (Table 1).

Fig. 2 Pyramid-shaped test part for measurement of surface roughness[9]

Fig. 3 Schema of the truncheon test part [14]

Fig. 4 Final test part after washing and assembly operation

Table 1 Scanning parameters

No. Parameter Value

1 Sampling length (lr)/cut off length (lc) 0.8 mm

2 Evaluation length (ln) 4 mm

3 Traversing length (lt) 5.6 mm

4 Profile resolution(measuring range)

250 m/7 nm

5 Traversing speed (vt) 0.5 mm/s

6 Points 11200

7 Direction Perpendicular to thedeposition direction

Int J Adv Manuf Technol (2015) 79:823829 825

3.1.1 The surface roughness

The surface roughness values measured by the scanner for thetest part with layer thickness of 0.254 mm are presented inFig. 5. Two separate roughness measurements are performedfor the test part on the same surface for each build angle aspresented in Table 2, while the scanning parameters set for this

study (according to DIN EN ISO 4287 standard) are presentedin Table 1.

4 Accuracy assessment of analytical models

In the present study, MATLAB software is used for modeling,whereas Figs. 6 to 10 exhibit the performance of the Mason,Campbell, Pandey, Byun, and Ahn models for estimation ofsurface roughness in layer thickness of 0.254 mm for variedsurface build angles in comparison with the measured empir-ical data for the truncheon test part. As it is observed in theMason model, a weak estimation of surface roughness is ob-tained therein for prototype with layer thickness of 0.254 mm.This model provides an appropriate estimation in angles of 0to 15 and 165 to 180 .

In Fig. 7, the Campbell model shows a better estimation ofsurface roughness in surface build angles of 45 to 135 and

Fig. 5 Measured Ra for the truncheon test part with layer thickness of0.254 mm

Table 2 Empirical surface roughness (Ra) values for each build anglewith layer thickness of 0.254 mm

Buildangle(degree)

Ra-report no. Raavea

(micron)Buildangle(degree)

Ra-report no. Raave(micron)

Ra-A Ra-B Ra-A Ra-B

0 17.56 17.82 17.69 90 1.4 2.72 2.06

5 17.72 19.1 18.41 95 18.55 17.77 18.16

10 20.37 19.33 19.85 100 18.2 17.56 17.88

15 21.94 20.56 21.25 105 18.68 18.4 18.54

20 20.06 22.82 21.44 110 19.14 20.02 19.58

25 26.98 20.32 23.65 115 17.14 23.54 20.34

30 24.48 25.32 24.9 120 21.1 21.22 21.16

35 27.43 27.63 27.53 125 22.55 22.63 22.59

40 28.56 29.52 29.04 130 24.63 23.37 24

45 32.52 28.74 30.63 135 24.66 26.92 25.79

50 31.92 32.54 32.23 140 26.63 25.45 26.04

55 34.52 34.4 34.46 145 21.86 26.22 24.04

60 39.26 40.1 39.68 150 27.83 30.11 28.97

65 42.01 39.55 40.78 155 29.61 30.45 30.03

70 38.42 42.5 40.46 160 32.5 30.82 31.66

75 31.3 31.4 31.35 165 33.21 35.63 34.42

80 23.08 20.38 21.73 170 20.22 20.74 20.48

85 18.27 17.59 17.93 180 18.78 17.92 18.35

a It is notable that Raave is denoting the average value between the Ra-Aand Ra-B values which is considered as Ra value and used in evaluationprocedure

Fig. 6 Estimation of surface roughness by Mason model for thetruncheon test part with layer thickness of 0.254 mm

Fig. 7 Estimation of surface roughness by Campbell model for thetruncheon test part with layer thickness of 0.254 mm

826 Int J Adv Manuf Technol (2015) 79:823829

also it overestimates the surface roughness for the build anglesbetween 0 to 30 and also 155 to 180 .

Moreover, according to Eq. (1), this model cannot predictthe surface roughness for angles between 0 to 180 . As it isobserved in Fig. 8, the Pandey model provides a relativelyappropriate estimation of surface roughness more than othermodels; this model has an appropriate estimation performancefor surface build angle range within 0 to 65 and 95 to 135,while this model has a weak performance for 80 to 95 andalso 155 to 180 .

Figure 9 shows the Byun model performance for surfaceroughness estimation which demonstrates overestimation ofsurface roughness within 95 to 135 , while estimation perfor-mance within 0 to 45 and 135 to 180 is more fitted.According to Eq. (2) and Eq. (5), the Ahn model has a phaseshift of (degree) relative to the Mason model; thus as pre-sented in Fig. 10, the Ahn model provides a similar estimationlike the Mason model with phase shift () of 5 .

4.1 Performance of surface roughness estimation for differentanalytical models

The estimation error values in different models are calculatedfor four angle ranges including 0 to 45, 45 to 90, 90 to 135,and 135 to 180 in layer thickness of 0.254 mm. Analyticalmodels are compared by using mean absolute percentage error(MAPE) criteria. MAPE gives a normalized error, permittingefficiency comparison of different models coming from dif-ferent data sets, as presented in Eq. (6).

MAPE % 1NX

i

X actX estX act

100 6

where Xact is the actual value of Ra, Xest is denoting modelsestimation value ofRa, andN is the number of patterns. As it isobserved in Table 3, within 0 to 45 angles, minimum error isobtained for the Pandey model (13.56 %) and later the Byunmodel (39.88 %), and other models have higher errors. Within45 to 90 angles, minimum error is obtained for the Campbellmodel (67.88 %). Within 90 to 135 , the Pandey model(16.54 %) has the minimum error. Within 135 to 180 , theByun model (45.57 %) shows lower error than the other

Fig. 8 Estimation of surface roughness by Pandey model for thetruncheon test part with layer thickness of 0.254 mm

Fig. 9 Estimation of surface roughness by Byunmodel for the truncheontest part with layer thickness of 0.254 mm

Fig. 10 Estimation of surface roughness by Ahnmodel for the truncheontest part with layer thickness of 0.254 mm

Table 3 Mean absolute percentage error values (%) of surfaceroughness of 0.254-mm layer thickness for different analytical models

0 45 45< 90 90< 135 135< 180

Byun 39.88 96.13 175.93 45.57

Ahn 138.33 950.35 434.21 76.30

Campbell 1279.15 67.88 59.28 1299.83

Mason 112.91 932.79 451.24 89.29

Pandey 13.56 183.03 16.54 99.49

Int J Adv Manuf Technol (2015) 79:823829 827

models. Considering the calculated values as presented inTable 3, the Pandey and Byun models may be used due tolower errors for surface roughness prediction.

In the designed parts with surface build angles of 0 to 45and 90 to 135 with the specified layer thickness, the Pandeymodel provides an appropriate estimation for optimum designand also for the surface build angles of 135 to 180 ; the Byunmodel is a proper choice for desirable and optimum design.But, in surface build angles within 45 to 90 , all abovemodelshave higher errors for prediction of roughness. In Fig. 11,different models are compared and their estimation perfor-mance can be seen. Therefore, based on these assessments,the Pandey and Byun models exhibit lower prediction errorthan other models and the best estimation performance be-longs to the Pandey model as presented in Fig. 11.

The Ahn and Campbell models despite benefitting from thesimilar test part in their model evaluation, nevertheless do notlead to desirable results. It may be due to the changes made inthe test part design and higher accuracy of surface measure-ment device utilized in this research. Although, in ref [14], anempirical model is used for perusing the surface roughnessdistribution in accordance with the measured data that pro-vides more precise prediction, but due to the assessment ofthe theoretical estimation models, models introduced in thispaper are utilized merely for comparison of the derived theo-retical data with measured data.

5 Conclusion

In layered production processes, the tessellation of the CADmodel and the slicing procedure are assumed as the majorfactors affecting creation of rough surfaces. In slicing a tessel-lated CAD model, containment problem results in distortionof the original CAD model from the designed form. In addi-tion to the containment problem, deposition of the slicedlayers leads to another problem called staircase effects. Toimprove the FDM part surface roughness, modeling of thesurface roughness distribution for optimizing the effective

parameters before the fabrication process is used for moreprecise planning of AM process.

In the present paper, the most well-known models used forimprovement of surface roughness are utilized based on ana-lytical modeling. Later, the specific test part called truncheonis designed to evaluate the above models. Analytical modelsare evaluated by the comparison of the performance criteria(MAPE) in different ranges. According to the provided assess-ments, best model for prediction of each range is introduced,where altogether, Pandeys model exhibits the best predictionfor surface roughness. It is notable that although different testparts are used for model evaluation in their research (pyramidshape), results demonstrates high predictability of this modelfor varied parts.

The main advantage of this research is the use of a compre-hensive test part which enables the assessment of surface rough-ness in all surface build angles, including all factors affecting thereal rough surface creation such as roughness arising out ofstaircase effects, support burrs, material properties, and otherfactors which is not possible to achieve them in other ways.

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0

200

400

600

800

1000

1200

1400

0 45 45< 90 90< 135 135< 180

39.88 96.13175.93

45.57

138.33

950.35

434.21

76.3

1279.15

67.88 59.28

1299.83

112.91

932.79

451.24

89.2913.56

183.03

16.54 99.49

Byun model

Ahn model

Campbell model

Mason model

Pandey model

Fig. 11 Mean absolute percentage error values (%) for different analytical models

828 Int J Adv Manuf Technol (2015) 79:823829

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Int J Adv Manuf Technol (2015) 79:823829 829

Evaluation of analytical modeling for improvement of surface roughness of FDM test part using measurement resultsAbstractIntroductionAnalytical modelingTest part designFabrication and measurement of the test partThe surface roughness

Accuracy assessment of analytical modelsPerformance of surface roughness estimation for different analytical models

ConclusionReferences