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International Journal of Machine Tools & Manufacture 43 (2003) 6171

Real time adaptive slicing for fused deposition modelling

P.M. Pandey, N.V. Reddy , S.G. Dhande 1

Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India

Received 27 March 2002; received in revised form 19 August 2002; accepted 20 August 2002

Abstract

Improvement of part surface quality and geometric accuracy in Rapid Prototyping has been a major concern. Reduction in build

time and increase of part surface quality are two factors which contradict with each other as decreasing build time detracts partquality because of staircase effect. There has been a number of attempts to tackle this problem and adaptive slicing procedures areproposed. In these procedures the layer edge profiles are implicitly assumed as rectangular. But in real practice the edge profilesof a layer manufactured part are not rectangular and is found to be parabolic in case of Fused Deposition Modelling. A geometricalparameter known as cusp height is limited to a pre-specified value in existing adaptive slicing procedures, which is defined forrectangular edge profiles only. In this paper, a slicing procedure is proposed for Fused Deposition Modelling based on real timeedge profile of deposited layers. The procedure is implemented and examples are included to explain the adaptive slicing method. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Layered manufacturing (LM); Rapid prototyping (RP); Staircase effect; Fused Deposition Modelling (FDM)

1. Introduction

Layered Manufacturing (LM) or Rapid Prototyping(RP) is a process which automatically generates a physi-cal object by layer-by-layer deposition of raw materialto build up the solid model created in a solid modellerlike Ideas, ProE, AutoCAD etc. In LM the conventionalmanufacturing and tooling techniques are not at allrequired therefore building a prototype takes compara-tively a short manufacturing lead time. The RP processis different as multimaterial structures and parts withembedded electronics can be created. Therefore, for adesigner RP broadens their scope of creation.

In all RP processes a CAD model of the part to bebuilt is required as an input. The possible ways of trans-ferring the CAD model to a RP machine are shown inFig. 1. The figure shows that the CAD model can besliced directly or after tessellation. Today, a tessellatedmodel (stereolithography file format or STL file format[1]), has become the standard of the RP industry to rep-resent CAD data. A STL file (ascii or binary) contains

Corresponding author.

E-mail address: [email protected] (N.V. Reddy).1 Director, Indian Institute of Technology, Kanpur, India

0890-6955/03/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.

PII: S0 8 9 0 - 6 9 5 5 ( 0 2 ) 0 0 1 6 4 - 5

the list of coordinates of vertices of triangles (which

approximate the surface (boundary) of the solid model)and their normals. Fig. 2 shows the tessellated model ofa surface patch.

The tessellated or faceted model is then sliced byintersecting it with a set of horizontal planes. Each slicedplane, which is horizontal is a closed polygon becausethe curved surfaces are approximated by triangles in afaceted model. The material is deposited in the interiorand periphery of the polygon which is at minimum verti-cal level of the part to be deposited and then this poly-meric material is cured. The platform on which the depo-sition has taken place lowered vertically down by anamount of the next horizontal intersection plane. Thematerial is again deposited and cured on the top of pre-viously deposited material. The material deposited inbetween any two horizontal planes is known as a sliceand the region between two adjacent slices is referredas a layer. The process of slicing and depositing layer-by-layer leads to geometric inaccuracies and poor sur-face finish. It can be seen from Fig. 3 that smaller thelayer thickness is, more accurate and smoother the LMpart.

The issues of tessellation [1], staircase effect and theproblem of containment [2] are important as they arerelated to the slicing operation and effects the final part

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62 P.M. Pandey et al. / International Journal of Machine Tools & Manufacture 43 (2003) 6171

Nomenclature

Ai: Area (mm2)

R: Radius of axisymmetric part (mm)Ra: Center line average value of surface roughness (m)

Rai

: Center line average value of surface roughness of i-th area (m)Raav: Average Surface roughness of the part (m)

t: Layer thickness (mm): Build Orientation, angle between vertical and surface tangent (degree)

Fig. 1. Transfer of CAD models to RP machine.

Fig. 2. Tessellated or faceted surface model, chordal error.

Fig. 3. Effect of layer thickness on surface finish.

quality. Tessellation approximates (piecewise) the sur-

face of the CAD model with planar surfaces i.e. triangles

in 3-D space (Fig. 2). This first order approximation ofthe original CAD model loses the intent of the original

design. The list of triangles without topological infor-

mation often leads to gaps, overlaps (defects in STL file)

etc., requires repair softwares. The chordal tolerance i.e.

the maximum faceted deviation (Fig. 2) from the original

surface of the CAD model, the designer has to accept,which leads to geometric inaccuracy. In LM each

2.5-D layer is generated by sweeping a planar profileand depositing the material in the interior and boundary

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63P.M. Pandey et al. / International Journal of Machine Tools & Manufacture 43 (2003) 6171

of a slice. Since the entire part is fabricated in the same

fashion the boundary (external surface) of the LM part

is stepped [3]. This stepped approximation of CAD

model is known as a staircase effect. The staircase effect

can not be eliminated on a RP part completely. It isbecause of staircase the edges of the slices may be com-

pletely out of the CAD model or they may be completelyinside the CAD model as shown in Fig. 4. This is

referred as a containment problem [2]. The two cases

have their importance as far as the application of theprototype is concerned. A part is deposited as shown in

Fig. 4(a), if it has to be used as master pattern for making

cores, since a smaller core would imply extra material

in the mould enabling a finishing process. Part depositedas shown in Fig. 4(b) is made accurate and smoother by

polishing operation. These finished prototypes are usedfor concept modelling, testing etc.

Accuracy and part surface quality has become the

focus of RP community with the increased requirement

of prototyped functional parts, enhanced material proper-

ties for strength and dimensional tolerance comparable

to conventionally producible parts. This has led to a var-

iety of research. Today, researchers are addressing

strength, accuracy and surface finish issues of RP partsto enhance process capabilities. In order to reduce buildtime of a prototype a number of researchers developed

various versions of slicing. Their approaches are mainly

based on the variable slice thickness instead of constant

thickness.The layer thickness in this method is decided

by the geometry of the solid model and is known as

adaptive slicing. Dolenc and Makela [4] proposed a vari-

able slicing thickness method for slicing tessellated CADmodels and introduced the cusp height tolerance concept.The layer thickness at a point is computed based on the

cusp height, which is always less than the user-specifiedmaximum cusp height. Kulkarni and Dutta [2] developed

relations of layer thickness as a function of the radius

of vertical normal curvature of the surface and the angle

that the surface normal makes to the horizontal at the

point under consideration for a given cusp height.The

layer thickness is obtained by minimization of layer

Fig. 4. Containment issue in layered manufacturing.

thickness expression over a contour Z is equal to con-

stant, where Zis vertical direction. The slicing procedure

is also modified by them and is carried out in two steps.In the first step, the model is divided into distinct sectorsso that sharp features are not missed while in the secondstep these separate sectors are sliced on the basis of

specified cusp height and containment requirement. Jam-ieson and Hacker [5] proposed the direct slicing of CAD

models, in which the planar contours are generated

directly from CSG representations. Sabourin et a1. [6]presented an adaptive slicing method for layered manu-

facturing. The CAD model is first sliced into slabs ofthickness equal to maximum available fabrication thick-

ness. Each slab is then re-sliced uniformly as needed to

maintain the desired surface accuracy. Using this method

of slicing the overall build time was reduced by approxi-mately 50% without reducing overall surface accuracy.

They also proposed an adaptive high precision exterior,

high speed interior slicing procedure based on STL files[7]. Fadel and Kirscman [8] presented the accuracy

issues of CAD to RP translation. In their work software

related errors are discussed with ways to mitigate some

of these errors. Frank and Fadel [9] studied the effect of

the part orientation (for deposition) to reduces geometric

inaccuracies. Hope et al. [10] developed a new systemnamed TruSurf which utilizes the layers with slopingsurfaces and constant layer thickness. Later the

developed algorithm is modified by them [11] with vari-able layer thickness, i.e., adaptive slicing. Improved sur-

face finish and and decreased build time through use ofthicker layers is reported in this work. Tyberg et al. [12]

suggested the use of local adaptive slicing which firstidentifies the individual parts and the features that com-prise each layer in a given part, and then slices inde-

pendent of one another. Tata et al. [13] proposed an

adaptive slicing algorithm that can vary the layer thick-

ness in relation to local geometry of the part. Cormier

et al. [14] suggested the use of variable cusp heights for

different locations of the part to achieve the required

functionality and reduce production time. Recently Zhao

and Laperriere [15] developed direct adaptive slicing of

solid model developed in AutoCAD and written programin C/C++ using AutoCAD Runtime Extension to slice

the CAD model. The relative area deviation for sub-

sequent slice is limited to 5% in their work. Lee and

Choi [16] presented an adaptive slicing scheme for

enhanced accuracy and speed of computing. They used

sampling of points on a sliced contour to find the optimalpoint which decides the next slice thickness. The concept

of character line is introduced by them which can further

increase the speed of computing.

The literature survey reveals that substantial amount

of work has been done to achieve reduced build time bypre specifying cusp height through adaptive slicing, but

most of these adaptive slicing procedures use, in one

or another form, the concept of cusp height tolerance

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developed by Dolenc and Makela [4]. Dutta and Kulk-

arni [2] used the same concept but without approximat-

ing the CAD model with triangles. The use of vertical

normal curvature is introduced by them for calculation

of slice thickness. In all the procedures developed forthe adaptive slicing, it is implicit that the build edge pro-

file of the deposited slice is rectangular. But in real timethe edge profile is not rectangular. Bharath et al. [17]and Pandey et. al. [3] established in their work that these

edge profiles can be approximated as parabola. Based onthis assumption Pandey et al. [3] came up with a simple

model of surface roughness of Fused Deposition Mod-

elled (FDMed) part.

It is obvious that the build edge profiles of depositedslices can not be rectangular for an LM process as it

involves curing of raw material and hence uncontrolledflow of molten or softened material. The authors havecarried out microscopic study of a Solid Ground Cured

(SGC) part and observed that the build edges are not

rectangular. These edges are comparable to parabola

with a sharp vertex. Therefore approximating the edge

profiles of a LM part with rectangle is the most optimis-tic approximation. This approximation ultimately leads

to finer layers and hence more build time. The achievedsurface quality also can not be understood in terms ofsurface roughness obtained on the part.

The geometric inaccuracies and surface finish prob-lems on RP part can be controlled by minimizing the

layer thickness. But minimization of layer thickness

leads to maximization of build time of the part. There-

fore, there is a need to limit the layer thickness and to

compromise with part quality. Hence a scheme of vari-able slice thickness for a specified upper bound of sur-face roughness i.e. a measure of part quality in case of

FDMed part, is presented in the present research work.

The paper describes two methodologies of adaptive slic-

ing. First is direct adaptive slicing of axisymmetric parts

and the second is adaptive slicing of a tessellated

CAD model.

2. Slicing method

Existing methodologies of adaptive slicing are based

on two concepts. First is the limiting cusp height and

the second is the limited deviation of cross-sectional area

(plane normal to Z axis) of the part. The layer thickness

is increased from minimum to maximum slice fabri-cation thickness which is given as one of the input para-

meters. In both these procedures the measure of the part

surface quality does not come into picture explicitly.

Therefore, a method based on limiting surface roughness

(Ra) value, which describes part surface quality is pro-posed in the present work.

The surface roughness at a point on the FDMed part

is given by [3]

Ra(mm) (71 to 93)t(mm)

cosq(1)

where Ra is local surface roughness in m, t is layer

thickness in mm and is build orientation i.e. angle

between and vertical and surface tangent at that point.

The above equation is based on deterministic evaluationof the height of the edge profile i.e. taken as 30-35% ofthe t/cosq i.e. base length. It is realized that the heightof the edge profiles is random in nature, therefore theheight of the edge profile is determined stochastically.It is carried out by analyzing the part surface on Surf-Analyzer-5000 and determining the height of edge pro-

files as percentage of base for different . The frequencyplot of these edge profile heights in terms of percentageof base is shown in Fig. 5. From the frequency plot it

can be concluded that the distribution of these heights

is normal. The mean of the distribution is obtained as

30.10589, standard distribution 4.069661 along with

skewness 0.027821. For a 99% confidence the height ofedge profiles is ranging from 29.45972 to 30.75205%.Thus the expression of Ra for 99% confidence isgiven by

Ra (69.28 to 72.36)t

cosq(2)

therefore in the present work the expression used fordetermination of slice thickness is,

tRa cosq

70.82(3)

using 30.10589% (mean) of t/cosq as the height of edgeprofiles. From the stochastic analysis it is obvious thatdeterministically developed equation of Ra by Pandey et

al. [3] is conservative.

The effect of radius of curvature on surface roughness

is also studied in the present work. For the purpose, the

part shown in Fig. 6 is fabricated in FDM-1650 machine.

This part has a number of hemispheres of differentradius. Surface roughness on these hemispheres is meas-

Fig. 5. Frequency curve.

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Fig. 6. FDM part to study effect of radius of curvature.

ured by SurfAnalyzer-5000 at different locations (Buildorientation is different at different locations). Standard

neural network software is used to study the effect ofradius of curvature on Ra. The obtained experimental

values of Ra are used to train the network as t/cosq andradius of curvature as input and Ra value as output. The

network is trained for maximum square error of 2.5%.Once the network is trained the Ra values are evaluated

from neural network model and are plotted as shown inFig. 7. It can be seen from the Fig. 7 that the variation

in Ra values is within 5% over a large variation of radius

of curvature therefore the effect of radius of curvature

on Ra can be assumed insignificant. For a RP processthe layer thickness must lie within the minimum and

maximum fabrication layer thickness available in that

machine i.e.

tminttmax

Eq. (3) is used to determine slice thickness in adaptive

slicing algorithm. Evaluation of cosq can be done for

Fig. 7. Radius of curvature Vs Ra.

any point on the boundary of the CAD model (By para-

metric equation of enclosing surface in case of direct

slicing and by normal vector for a facet in case of tessel-

lated CAD model), and for a pre-specified value Ra onthe surface of the part the slice thickness can be calcu-lated by Eq. (3).

The average part surface quality is given by

Raav RaiAi

Ai(4)

where Raav is average surface roughness of the part, Raiis the roughness of the ith slice (for axisymmetric part)

or trapezium (for tessellated CAD model) and Ai is the

area of the surface of the cylinder, which belongs to i

th slice i.e. 2pRtslice in case of direct slicing and is areaof the ith trapezium in case of slicing of tessellated

CAD model (refer Fig. 8).

2.1. Direct adaptive slicing of axisymmetric CAD

models

Rapid Prototyping models are now used for a varietyof applications like design verification, flow testing foraerodynamic applications, casting applications etc. In

these applications a method of direct slicing is more suit-

able. These applications mainly involve axisymmetric

parts. The other advantages of direct slicing include

reduced file size, decreased RP machine pre-processingtime, greater model accuracy, and elimination of repair

routines. But in direct slicing, the addition of a support

structure because of nested sections, ability to reorient

the model is difficult. In this method more designerknowledge is required as he has to decide on his own

about optimum build orientation for accuracy, least sup-

port structure and least cost [5]. The combination of

direct slicing and adaptive slicing improves the accuracy

and surface quality of the final RP part. Currently, mostRP machines uses linear interpolation for traversing of

their X and Y axes. Therefore, the curves resulting fromdirect slicing must be interpolated again to linear seg-

ments so that RP hardware can understand it. In the

Fig. 8. Definition of Ai.

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present work a software is developed which does slicing

of a CAD (surface) model created by sweeping a Bezier

curve around an axis. The flowchart shown in Fig. 9explains the working of the developed software.

The software for direct slicing of axisymmetric partstakes the control points of Bezier curve, minimum and

maximum fabrication thickness available in FDMmachine and maximum Ra value desired on the part sur-

face as input. The software gives the variable slice thick-

ness list, overall part surface roughness and the graphicsof the slices formed. It also gives the corresponding cusp

height [4], and the relative difference in the subsequent

slice areas [15]. The output of the program helps in

understanding the developed procedure and gives a feel-

ing of how this methodology is comparable with the

other two existing [4,15] adaptive slicing procedures.

2.2. Adaptive slicing of tessellated CAD models

A general RP component, may be complex enough,

involving many features, is difficult to slice directly bythe CAD model as it needs the parametric equation of

the enclosure. Therefore, the tessellation of CAD models

is widely accepted by the RP industry. The tessellation

involves first order approximation of the CAD modelenclosure; at the same time implementation of plane-

plane intersection algorithm is also easier. The other

advantages of tessellation include simple way of rep-

resenting CAD data with existing de facto standard, and

sometimes, for certain geometries the STL file is smallerin size. The need of a large disk size for storing STL

file, repair softwares and a large time requirement for

Fig. 9. Flowchart: direct adaptive slicing software.

slicing are limitations of faceted representation of

CAD data.

Any part that can be solid modeled in I-deas, ProE or

AutoCAD can be sliced by the developed software in

the present work. The input to the software is the STLfile. The flowchart given in Fig. 10 explains the working

of the software.The software for tessellated CAD model slicing takes

a standard de facto STL file as input. It also takes mini-mum and maximum fabrication slice thickness availablein the FDM machine and maximum Ra value needed on

the FDMed part surface. The output of the software is

the list of the slice thickness and average part surface

roughness which is a measure of part surface quality.

3. Result and discussion

Two parts are chosen to describe the working of the

developed methodology of adaptive slicing. The first partis the axisymmetric component which is sliced by direct

adaptive slicing algorithm. The second part is a typical

part which has convex, and concave surfaces, splined

slot and through hole is sliced after exporting its tessel-

lated CAD model. Details of the two considered casesare given below.

3.1. Direct adaptive slicing

The proposed method of direct adaptive slicing is

implemented and the sliced model is shown in Figs. 11

and 12. The part is sliced for minimum and maximum

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Fig. 10. Flowchart: slicing of tessellated CAD model.

Fig. 11. Direct sliced Part (3D View).

fabrication thickness 0.254 and 1.27 mm respectively.

The maximum Ra value permitted on the part at anylocation is 30 m. The output of the proposed method-

ology is presented in Table 1.

It can be seen from the results presented in Table 1that the proposed method of slicing is able to directly

slice the CAD model. The output also shows the com-

parison between Ra of proposed methodology and Dol-

Fig. 12. Direct sliced part (xz plane).

enc and Makelas [4] cusp height, as well as the relativedeviation in area of Zhao and Laperriere [15]. The vari-ation of maximum cusp height on internal and external

surfaces obtained for the part, and maximum relative

deviation in area with respect to the bound kept on Ra

is presented in Figs. 13 and 14. The two curves are flatat their ends and in between they can be approximated

as straight lines. This straight line portion of the curves

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Table 1

Output of direct slicing softwarea

No. Slice thickness by present Ra outer surface Ra inner surface Cusp height outer cusp height inner Area deviation Zhao[15]

work mm m m surface by Dolenc[4] surface by Dolenc[4]

mm mm

1 0.298778 23.717083 30.000002 0.133617 0.211268 0.0011692 0.311327 24.771584 30.000000 0.140533 0.210489 0.003422

3 0.321539 25.645258 30.000000 0.146487 0.208608 0.005548

4 0.329946 26.378904 30.000000 0.151682 0.206114 0.007555

5 0.336947 27.003023 30.000000 0.156272 0.203313 0.009446

6 0.342839 27.540468 30.000000 0.160372 0.200393 0.011227

7 0.347848 28.008476 30.000000 0.164069 0.197471 0.012902

8 0.352145 28.420179 30.000000 0.167431 0.194615 0.014477

9 0.355862 28.785698 30.000000 0.170511 0.191865 0.015955

10 0.359101 29.112915 30.000002 0.173350 0.189242 0.017338

11 0.361942 29.408026 30.000000 0.175981 0.186757 0.018629

12 0.364451 29.675982 30.000000 0.178432 0.184412 0.019833

13 0.366678 29.920759 29.999998 0.180725 0.182204 0.020949

14 0.366884 30.000000 29.855122 0.181994 0.179261 0.021875

15 0.366140 30.000000 29.651949 0.182749 0.176126 0.022660

16 0.365416 30.000000 29.467178 0.183470 0.173254 0.02336717 0.364712 30.000000 29.298122 0.184159 0.170615 0.024001

18 0.364027 29.999998 29.142611 0.184818 0.168182 0.024568

19 0.363361 30.000000 28.998871 0.185449 0.165932 0.025073

20 0.362712 30.000000 28.865446 0.186053 0.163846 0.025517

281 0.254000 31.903843 31.168831 0.209528 0.207167 0.013405

282 0.254000 31.507502 31.393667 0.208279 0.207910 0.012408

283 0.254000 31.067156 31.601135 0.206825 0.208579 0.011269

284 0.254000 30.583221 31.789719 0.205142 0.209174 0.010107

285 0.254000 30.056105 31.958551 0.203198 0.209696 0.008859

286 0.254000 29.486477 32.106560 0.200956 0.210146 0.007558

287 0.254000 28.876236 32.232929 0.198375 0.210525 0.006224

288 0.254000 28.227011 32.336540 0.195401 0.210831 0.004810

289 0.254000 27.541109 32.416786 0.191973 0.211066 0.003361

290 0.254000 26.822067 32.472939 0.188018 0.211230 0.001896

291 0.254000 26.074059 32.504379 0.183448 0.211321

a Maximum cusp height on internal surface=0.211321 mm, maximum cusp height on external surface=0.214315 mm, maximum deviation in

area=0.027574, average part roughness=28.797332 m.

Fig. 13. Bound on Ra vs maximum cusp height.

Fig. 14. Bound on Ra vs maximum relative area deviation.

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excluding the flat regions is working region of the meth-odology. It corresponds to minimum and maximum aver-

age Ra that can be obtained on the part, once the part

is sliced by minimum slice thickness only and maximum

slice thickness only. It is clear from these figures thatincreasing the bound of Ra, the maximum cusp height

and relative deviation in area increases proportionally inthe working range.

Parametric study is carried out by varying the bound

on Ra from 15-170 m. The variation of number ofslices (which is an indirect parameter to have an idea

about build time), with the bound on Ra and average Ra

of the part is shown in Fig. 15. It is obvious from the

figure that by choosing a little higher bound on Ra thenumber of slices can be reduced drastically. Therefore

one should use an adaptive slicing scheme as it reducesnumber of slices and hence results into reduction in build

time. It is also clear from the Fig. 15 that there exist a

minimum and a maximum average value of part surface

roughness corresponding to all slices of minimum slice

thickness and all slices of maximum slice thickness

respectively.

3.2. Slicing of tessellated CAD model

Part shown in Fig. 16 is modeled in I-deas and a STL

file is exported. The STL file is used as an input to thedeveloped system of slicing. The part is sliced taking

minimum and maximum fabrication thickness 0.254 and

1.27 mm respectively. The graphical output of the

software and the list of slice thickness is presented in

Fig. 17 and Table 2. The overall average part surfaceroughness is also predicted by the software. The vari-ation of number of slices vs Ra shown in Fig. 18, which

predicts that there is comparatively more reduction in

number of slices as compared to increase in roughness.

At this stage reader may be confused that the part used

Fig. 15. Number of slices vs surface roughness (direct slicing).

Fig. 16. Sliced part after tessellation (3D view).

Fig. 17. Sliced part after tessellation (xz plane).

here to validate the procedure can be sliced in another

orientation to have a better surface finish. It may be true,but in order to show the working of the procedure thisorientation of the part is chosen. It is obvious that the

optimum orientation of the part should be decided

before slicing.

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Table 2

Output of slicing of tessellated CAD modela..

No. Slice thickness by No. Slice thickness by

present work mm present work mm

1 0.254000 447 0.422531

2 0.254000 448 0.4225313 0.254000 449 0.422531

4 0.254000 450 0.422531

5 0.254000 451 0.422531

6 0.254000 452 0.422531

7 0.254000 453 0.422531

8 0.254000 454 0.422531

9 0.254000 455 0.422531

10 0.254000 456 0.422531

11 0.254000 457 0.422531

12 0.254000 458 0.422531

13 0.254000 459 0.422531

14 0.254000 460 0.422531

15 0.254000 461 0.422531

16 0.254000 462 0.422531

17 0.254000 463 0.42253118 0.254000 464 0.422531

19 0.274713 465 0.422531

20 0.274713 466 0.422531

a. Average part roughness after layered manufacturing is

24.617872 m

Fig. 18. Number of slices vs Surface roughness.

4. Conclusions

An approach for adaptive slicing based on the realistic

build edge profile is implemented using two approaches,namely direct slicing and tessellated model (STL). In

comparison to earlier approaches of adaptive slicing

based on cusp height and area deviation using the rec-tangular build edge profiles, it can be easily seen thatthe present methodology can reduce the number of

slices, and hence build time. The major advantage of the

present methodology is that the part quality is expressed

in terms of standard Ra value which is used in design

and manufacturing. The different variations of the adapt-

ive slicing appeared in literature like stepwise refinement[6], local adaptive slicing [12], specifying nonuniformRa values at different locations [14] of the part can be

implemented easily by the addition of a feature recog-nition module.

It can be concluded from the studies carried out that

for most of the RP process the Ra value is proportionalto t/cosq. It is only the constant of proportionality whichwill be different for different RP processes. Therefore,

the presented procedure can be used for different RP sys-

tems.

Acknowledgements

Authors are thankful to Mr. Vivek Srivastava, under-graduate student of Mechanical Engineering Department

of I.I.T. Kanpur for his help in implementation.

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