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New model for shrinkage compensation in selective laser sinteringK. Senthilkumarana; Pulak M. Pandeya; P. V. M. RaoaaDepartment of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India

To cite this ArticleSenthilkumaran, K. , Pandey, Pulak M. and Rao, P. V. M.(2009) 'New model for shrinkage compensationin selective laser sintering', Virtual and Physical Prototyping, 4: 2, 49 62

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New model for shrinkage compensation in selective laser sintering

K. Senthilkumaran, Pulak M. Pandey* and P. V. M. Rao

Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, India

(Received 9 May 2008; in final form 5 August 2008)

This paper presents a new model for shrinkage and a new approach for shrinkage

compensation to enhance the accuracy of parts produced by selective laser sintering (SLS)

a solid freeform fabrication process. The present prevailing approach as proposed by

machine manufacturers is simple but not accurate. A new shrinkage model which

accounts for part geometry as well as beam offset is proposed in this work. A new

compensation scheme which accounts for nonlinear shrinkage is proposed, implemented

and validated. The proposed compensation scheme compensates for shrinkage at everylayer and at every hatch length, unlike a uniform compensation scheme applied to entire

part. A new algorithm which accounts for this is developed and implemented.

Experiments carried out with the new shrinkage model as well as with the new

compensation scheme have shown significant improvement in the accuracy of the parts

produced which establishes the effectiveness of the proposed methodology.

Keywords: rapid prototyping; selective laser sintering; shrinkage compensation; beam

offset; scan length

Notation

a Beam offset for hatch line (mm)

DCAD Desired dimension of CAD model (mm)

DCSM Dimensions obtained using machine manufacturer

suggested shrinkage compensation factor (mm)

DLSM Dimensions obtained using shrinkage models (mm)

Ia Percentage improvement in accuracy (%)

L Compensated length (mm)

Lc Original Hatch length (mm)

Lm Measured length (mm)

Ls Actual sintered length (mm)

LX Hatch length along Xdirection

LY Hatch length along Ydirection

s Percentage shrinkage (%)SX Shrinkage in Xdirection (%)

SY Shrinkage in Ydirection (%)

SZ Shrinkage in Z direction (%)

Dc Compensation length (mm)

Dl Deviation from nominal dimension (mm)

1. IntroductionSelective laser sintering (SLS) is one among many different

rapid prototyping (RP) processes where the parts are built

in a layer by layer fashion. Recently, SLS has gained

importance due to its ability to process a wide variety of

materials. SLS can produce functional prototypes and rapid

tooling components, which necessitates the production of

high-quality parts. The majority of its applications are in

aerospace and rapid tooling, where high accuracy levels

have to be met in order to ensure proper functional

requirement. Due to this new constraint imposed on SLS

in terms of part quality, there is a need to study the process

in detail and to improve part accuracies.

Among all types of process-related errors, the effects

caused by shrinkage are found to have major influence on

the accuracy of parts produced. Materials exhibit shrinkage

during thermal cycles, which varies from material to

material. The shrinkage of crystalline polymer is found to

*Corresponding author. Email: [email protected]

Virtual and Physical Prototyping, Vol. 4, No. 2, June 2009, 4962

Virtual and Physical PrototypingISSN 1745-2759 print/ISSN 1745-2767 online # 2009 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/17452750802393659

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be higher than that of amorphous polymers (Venuvinod

and Ma 2004). The SLS process is always accompanied by

shrinkage as a result of thermal and phase change effects. In

practice, the shrinkage is experimentally calibrated and the

same is compensated during data preparation stage of rapid

prototyping. The purpose of compensation seems to be that

of reducing the inaccuracies due to shrinkage and not to

attempt to eliminate those (Yang et al. 2002). However,notwithstanding the complexity of shrinkage, the basic

approach used today in most of the RP processes involves

some form of simple shrinkage compensation. Before

making the part, users are allowed to set a constant

shrinkage compensation factor, which is different for

different direction to overcome the shrinkage effect (Tong

et al. 2003). The shrinkage compensation factor is found by

fabricating standard test specimens and deriving a linear

relationship between the nominal dimensions and fabri-

cated part dimensions. Here when dealing with shrinkage

compensation, a fundamental assumption usually made is

that shrinkage is orthotropic and the shrinkage compensa-

tion scaling factors are constant for all X, Y and Zdimensions. However, this constant scaling factor is not

realistic because of the dynamic nature of the SLS process

and varying layer geometry in part building. Therefore in

this paper it is proposed to compensate nonuniform

shrinkage in sliced layer files rather than compensating

the STL files.

Jacobs (2000) discussed the effects of shrinkage variation

on the accuracy of rapid tooling inserts. He found that a

noise component is present along with mean percentage

shrinkage for most of the RP processes, and termed it as

random noise shrinkage. He mainly concentrated on

random noise shrinkage and found that standard deviation

of the random shrinkage is directly proportional to the

mean process shrinkage. He also found that nonuniformity

in shrinkage is mainly attributed to geometry of the part.

He concluded that key to accuracy and repeatability of such

techniques is the reduction of mean process shrinkage to

the smallest possible level.

Zhuet al. (2006) studied the shrinkage behavior in metal

powders. They quantified the two shrinkages namely

thermal shrinkage and sintering shrinkage. They found

that in-plane shrinkage (X and Yshrinkage) is very small

compared to shrinkage in the build direction. The sintering

shrinkage was mainly caused by densification and is a kind

of elastic compressive shortening. They suggested thatthermal shrinkage due to cyclic heating can be reduced by

controlling process parameters. In their work, the thermal

shrinkage increases with increase in laser power and

shrinkage decreases with increase in scan speed and scan

spacing.

Ning et al. (2006) considered the effect of geometry on

the shrinkage of the metallic parts. They introduced the

speed compensation technique based on the scan length. In

their method, when building a part, the laser scan speed is

adjusted dynamically according to the scan length which

varies with geometric shape of the part. The different scan

speeds for the scan lengths are chosen based on their

shrinkage values at different speeds. Wang (1999) discussed

the issues in calibration of shrinkage and beam offset for

the SLS process. Expressions for shrinkage and beam offset

in terms of the nominal diameter and error after sinteringwere developed. They also discussed the effect of part

weight on the percentage shrinkage.

Manetsbergeret al. (2003) studied the effect of tempera-

ture, time and pressure on the shrinkage of polymer parts.

They used a thermal simulation as a basis for shrinkage

compensation in SLS process. They expressed shrinkage

values as a function of temperature and also showed a

linear dependency to the pressure applied. Yang et al.

(2002) proposed compensation test pieces for the X, Yand

Zaxes to compensate for the shape distortions caused by

phase changes during the sintering process and they

measured shrinkage rates experimentally. With those

shrinkage rates, a set of equations is proposed which givesthe scale factors of the X, Yand Z axes. The scale factors

obtained from the compensation test pieces ofX, Yand Z

axes satisfy the required dimensional accuracy even if there

are changes in the build positions and in the size of the SLS

parts. Their work is mainly focused on the study of the

location of the part on the part bed and does not aim at

shrinkage variation with process parameters.

Ning et al. (2005) conducted a series of experiments for the

direct metal laser sintering (DMLS) process to find the effect

of hatch length on the material anisotropy, heterogeneity and

part strength. They concluded that short hatch lines cause

serious shrinkage and the part becomes less homogeneous.

They proposed an algorithm to find out optimal hatch

direction for a typical layer by considering the shrinkage as a

function of hatch length. Ragunath and Pandey (2007)

studied the effect of process parameters on the process and

material shrinkage. They found that scan length influences

shrinkage in theXdirection. They also predicted that scaling

factors can have a linear relationship with scan length

(Figure 1). They derived empirical relations for percentage

shrinkage in terms of scan length using Taguchi method.

However they used scaling factors based on the maximum

dimensions not on the individual scan lengths.

Several attempts have been made to improve the accuracy

of RP parts made by other processes like stereolithographyand fused deposition modeling (FDM) by controlling the

effect of shrinkage. Dao et al. (1999) calculated shrinkage

compensation factors for FDM parts with varying lengths.

They observed that mean error after shrinkage compensa-

tion follows a linear trend and is increasing for increasing

nominal dimensions. Also the residual errors are found to

be scattered due to lack of process stability. They attributed

this trend to the noise shrinkage which is not compensated

50 K. Senthilkumaran et al.

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by the scaling factors used. Wang et al. (1996) investigated

the relationship between post-cure shrinkage and thevarious process parameters for stereolithography by using

least-square method. They concluded that, as the curing

degree of the green-state prototype increases, the shrinkage

encountered reduces. They also found that the curing

degree is a function of laser power, layer pitch, scan pitch

and scanning speed. Wenbin et al. (2005) presented finite

element simulation for stair stepping effect caused by

material shrinkage in a new process called step less rapid

prototyping which combines stereolithography and conven-

tional milling. They reported that the layers had a small

initial expansion before a large shrinkage. They concluded

that the light intensity does not have significant effect on

staircase control. The decrease in layer thickness affects thestair stepping significantly.

It is evident from the literature review presented above

that part accuracy is affected highly by shrinkage. Some

studies (Manetsberger et al. 2003, Wenbin et al. 2005) use

simulation as a basis for shrinkage compensation. However

due to the dynamic nature of the process, a realistic

simulation of shrinkage occurring in the process using

FEM is often difficult. In most of these approaches which

use standard test specimen, the assumption is that shrink-

age is constant. Two important research issues identified are

nonuniform shrinkage along every Y direction and its

dependency on geometry and these two are not explicitly

studied in any previous works.

2. Nonuniform shrinkage

The total shrinkage in the SLS process is due to material

shrinkage, process shrinkage and thermal shrinkage. Dur-

ing polymer crystallisation, the molecules arrange them-

selves and occupy less volume thus leading to material

shrinkage. During processing the powder particles fuse

together to produce dense parts, leading to a decrease in

porosity and volume. During heating, the part expands due

to the co-efficient of thermal expansion and then shrinks

during cooling. Shrinkage is strongly influenced by the laser

parameters, powder bed properties, cooling rate and

geometry. Therefore the total shrinkage b (Shi et al. 2004)

is expressed as a sum of three shrinkages.

bbtbsbc (1)

where bt is the thermal shrinkage, bs is the sintering

shrinkage and bc is the crystalline shrinkage. The linear

thermal shrinkage bt (Zhu et al. 2006) can be written in

terms of the process parameters.

bta

AP

Vh

1

rcpLt

L (2)

where a is the thermal expansion co-efficient, A is

absorbtivity of the powder bed, P is the laser power, V is

the velocity of the laser beam,his the hatch spacing, r is the

density of the powder bed,cpis the specific heat capacity of

the powder material, Lt is the layer thickness and L is the

original scan length.

The crystalline shrinkage occurring during cooling can be

highly nonuniform along each direction due to strong

temperature gradient inside the powder bed. There can be

expansion-shrinkage behavior during the time history of

sintering. A particular layer can shrink nonuniformly due to

its position, i.e., high or low temperature regions.

In order to understand the effect of geometry on

shrinkage in SLS process, a brief introduction to the

compensation procedure in injection molding process is

essential. In injection molding process, different wall

thicknesses of the part produces different shrinkage.

When wall thickness increases, more time is required to

cool the centre of the thicker wall. As polyamide cools more

slowly, there is more time for crystallisation and stress

relaxation leading to higher crystallisation and higher

shrinkage (Jansen et al. 1998). The shrinkage values are

specified either as a normalised value (mm/mm) or as

percentage values to the original part dimensions. Different

percentage shrinkage values are specified for different wall

thicknesses for a polyamide material. ASTM D955-00 is an

American standard for measurement of shrinkage in

molded plastics which specifies that shrinkage values differ

in directions along the flow to the direction across the flowand it should be measured separately for semi-crystalline

materials like polyamide (Fisher 2003).

It is interesting to note that the shrinkage factor is not a

constant value but it varies according to the geometry in

many similar processes. Moreover, there is a directional

effect considering the direction in which laser scanning

takes place and the direction perpendicular to it. In this

work, an attempt is made to study the effect of geometry i.e.

20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

Scan length in mm

Percentage

Shrinkage(%)

cX Ls 009647.00302.1 =

Figure 1. Scan length and percentage shrinkage relation

(Ragunath and Pandey 2007).

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hatch length on shrinkage in the direction of the laser

scanning and in a direction orthogonal to scan direction.

3. Development of shrinkage model

The details of the experimentation for developing a new

shrinkage model are discussed in next section. As a

shrinkage model relating hatch length and percentage

shrinkage needs to be developed, the shrinkage calibration

part should contain strips of different length to capture the

effect of scan length. Figure 2 shows some of the common

geometries used by researchers and RP machine manufac-

turers for in-plane shrinkage calibration. In order to

accommodate longer dimensions than older shrinkage

models a shrinkage calibration part with large variations

in scan length as shown in Figure 3 is designed. Moreover,

two shrinkage models are developed by considering the

direction of scanning. The first model is developed for the

shrinkage along the scanning direction (X direction) and

the other across the scanning direction (Ydirection).

The length of the strips in shrinkage calibration part

varies from 20 to 200 mm. In order to develop models for

shrinkage in the Xand Ydirection, two parts were fabricated

in each case to check the repeatability in each direction.Specimens used in the study were fabricated using

PA2200 which is a modified nylon 12 developed for use in

SLS machines by EOS GmbH, Germany. The material is

semi-crystalline in nature. The material used was refreshed

powder and the ratio of mixing is 70% used powder and

30% virgin powder. The schematic of the equipment used is

shown in Figure 4. It uses a combination of two bins and a

slot feeder to dispense powder onto the platform. Extra

powder is collected through two bins situated on both sides

of the removal chamber. Moreover the environment main-

tained in the study includes the processing chamber and the

removal chamber. Nitrogen purging is done and infra red

heat radiators maintain the required temperature of both

environments. All the parts are oriented and placed at the

centre of the platform for building.

Maximum power available with CO2 laser in the SLS

machine used for the study is 58 W. Only 62% (36 W) of the

maximum power is used in the present experiment. This is

mainly due to the fact that curling is observed at higher

laser powers. A maximum scan speed of 4500 mm/s is

chosen for minimum build time. The laser spot size is kept

around 0.6 mm. The energy density used in the experiment

is 26.66 KW/m2. The process parameters used for contour

are low laser power and scan speed compared to hatching in

order to achieve a good surface finish. If the part is not

allowed to cool in a controlled environment for long time,

the part tend to warp due to faster cooling in the outside

environment. During faster cooling significant stresses

develop causing post-build warpage. So the part is allowed

to cool inside the platform for five hours. There are four

types of exposure strategy available with the current SLS

equipment used for the study. The scanning lines aregenerated and exposed (1) along Xdirection only, (2) along

Ydirection only, (3) exposure along both Xand Ydirection

and (4) along Xdirection in one layer and along Yin next

layer (parallel toXand Yon alternate layers). The exposure

strategy used in the present study has scan lines only along

Xdirection (type 1).

There are considerations in fabricating shrinkage calibra-

tion parts using different process parameters for contour

Figure 2. Some shrinkage calibration parts found in the literature: (a) part used by Wang (1999); (b) part used by Yanget al.

(2002); (c) part used in EOS method (EOS 2003); (d) part used in DTM method (Pham and Dimov 2001).


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lines and hatch lines (Figure 5). Mostly the contour lines

are scanned with a low laser power and high beam speed as

compared to the hatch lines. For the present experiments,

the contouring option is switched off to accurately capture

the shrinkage behavior of the hatch lines. The diameter of

the sintered zone is usually larger than the laser diameter

and is called as spot diameter. In order to compensate the

dimensional error due to spot diameter, the laser beam

should be offset from the boundaries of the cross section of

the object and is called beam offset. The estimation of these

beam offset values for the SLS process is described in Wang

(1999). In the present work, in order to estimate the beam

offset for the hatch lines, a part is designed with dimensions

250.66 mm. The dimensions of this part are chosen

such that when fabricated, this part will have single line

exposure of laser beam. The design, arrangement and

fabricated specimen are shown in Figure 6. The process

parameters used for this experiment is listed in Table 1. The

thickness of the single hatch line part is measured and its

value is found to be 0.555 mm. No beam compensation is

applied while fabricating specimens. It is incorporated while

calculating percentage shrinkage.

Figure 3. Shrinkage calibration specimen: (a) design (b) length of strips (c) arrangement in platform and (d) fabricated

specimen.

Figure 4. Schematic of the SLS process.


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The percentage shrinkage is calculated from the following

relation:

sLc a Lm

Lc a100 (3)

where Lm is the measured dimension of the part after

sintering and cooling and a is the beam offset.

The exposure strategy used for shrinkage calibration

experiments is type 1. The process parameters used for thisexperiment are given in Table 1. The dimensions of the

strips in calibration specimen are measured and the

percentage shrinkage is calculated using equation (3). The

percentage shrinkage is plotted against nominal dimensions

of the strips. The results showed good repeatability of the

shrinkage pattern between the two specimens fabricated in

each direction. The orientation of the specimen and the

results of these experiments are presented in Figure 7.

Percentage shrinkage increases with nominal dimensions for

strip lengths between 20 to 160 mm and becomes constant

after 170 mm. Also significant amount of expansion rather

shrinkage is found between strip lengths 20 to 110 mm. As

discussed earlier, there is a shrinkage-expansion behavior

during time-history of sintering. Between the strip lengths

20 to 110 mm, the expansion dominates the shrinkage. Thisexpansion or increase in dimension is attributed to the fact

that sintering is unconstrained. In most of the SLS systems,

the laser scans the top surface of a heated powder bed to

form the area enclosed by contours of the layered object in

raster scan mode (hatching) in combination with the

outlining of the cross sections of the part in vector scan

Figure 5. Exposure strategy showing contouring and hatching (type 4).

Figure 6. Beam offset calibration parts (a) single line exposure (b) design (c) arrangement and (d) fabricated specimens.


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mode (contouring). In hatching, the laser scans across the

powder surface in one dimension, turning the laser on and

off at the boundaries of the contour. The complete length of

laser scan in one dimension is dependent upon of the size

and shape of contours dictated by part geometry. As the

exposure strategy used for experimentation had only

hatching lines and no contour lines, the expansion during

sintering is not constrained by the contour lines as shown in

Figure 8. A more detailed hypothetical explanation for this

in-plane expansion is dealt by Zhu et al. (2006).

Moreover, the pattern of shrinkage obtained shows that

the percentage shrinkage is lower for lower scan lengths and

higher for higher scan lengths unlike the pattern obtained in

literature (Ning et al. 2005, 2006, Jacobs 2000). This

reversal of trend is mainly due to the fact that lower strip

length receives less energy in the present experiments

compared to works reported in literature. The length of

scan during which acceleration and deceleration of galvano

mirrors takes place, while the laser takes turn at the

boundaries, is compensated in the present work and the

laser is switched off while scanning these lengths and hence

no exposure. This length of unexposed compensated region

is independent of part size, shape and location. This method

produces less energy in smaller strip lengths unlike the

earlier approaches and produce less densification and

shrinkage.

In addition, the scans are incremented in a manner suchthat the present scan overlaps the previous scan to obtain

structural integrity of the part. Accordingly, the time

between adjacent and overlapping scans of the two hatch

lengths will widely vary according to the different lengths of

scan. Such variation in this time is the prime cause for

greater temperature deviation, inconsistent sintering rates

leading to nonuniform shrinkage. Also larger length of scan

will have enough time for sintering to happen and produce

more shrinkage. In order to compensate this nonuniform

shrinkage, a shrinkage model is developed relating percen-

tage shrinkage and length of scan along the Xdirection.

Figure 9 shows the shrinkage pattern for calibration

specimens oriented along the Ydirection of the platform. It

is to be remembered that this pattern is obtained with parts

where the scanning direction is still parallel to the X

direction and only the variation in length of strips is in Y

direction. The percentage shrinkage increases with increase

in strip length until the strip length is 110 mm and then

starts to decrease with increase in strip length. Unlike the

trend in the X direction, there is no expansion which is

Table 1. Process parameters set for the experiments.

Parameter Value

Laser power (W) 36

Hatch spacing (mm) 0.3

Scan speed (mm/s) 4500

Part bed temperature (oC) 176

Hatching Parallel to X

Figure 7. (a) Orientation of specimen; (b) percentage shrinkage versus strip length alongXdirection.


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found in the specimens. As the first scan line itself acts as a

barrier to expansion during sintering along the positive Y

direction, the sintering is usually partially constrained in theY direction of the platform while scanning direction is

parallel to the X direction. More crystalline structures are

formed when the material is kept longer in the temperature

range of 140 to 160oC. The shrinkage of the material will be

higher if the material is undergoing a slow cooling in this

temperature range. Moreover, as the width of the specimen

is small, the time interval between two consecutive scan

lines is not sufficiently long for the surface to cool down;

the temperature in the region will gradually build up,

resulting in higher temperature and longer liquid-phase

time. This will cause greater gradients in temperature to the

surrounding and a relatively faster cooling than the longer

length strips (Ning et al. 2006). Therefore the material

shrinkage is lesser for smaller strip lengths as the part cools

rapidly allowing minimum time to form the crystallinestructures.

The magnitude of shrinkage in the Xand Ydirections is

less compared to shrinkage along the build direction (Z

direction). Apart from that, the process parameters that

affect the in-plane shrinkage does not affect the Zdirection

shrinkage. For example, the effect of scan length on the Z

shrinkage is negligible (Ragunathet al.2006). In addition to

that nonuniformities in shrinkage in the Z direction

depends upon the placement of the part in the build

chamber, i.e. a part placed at the bottom of the platform

will have more shrinkage than the same part placed at the

top of the build chamber due to the weight of the powderacting upon it. It is observed from the authors previous

studies that part bed temperature, and scan spacing mostly

influence the Z shrinkage (Ragunath and Pandey 2007). So

in this study shrinkage models are developed for Xand Y

directions only and for compensating Zdirection shrinkage

a constant shrinkage factor is calculated using the method

suggested by the machine manufacturer (SZ3.5%).

Unconstrained sintering without contour exposure

Constrained sintering with contouring and hatching

Figure 8. Expansion in X direction owing to exposure

strategy

Figure 9. (a) Orientation of specimen; (b) percentage shrinkage versus strip length alongYdirection


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For fitting a model, to the percentage shrinkage as a

function of scan length, the data from the experiment

conducted using a specimen shown in Figure 3 with

parameters listed in Table 1 is used. A model is fit between

percentage shrinkage and scan length in both the Xand Y

directions using curve fitting toolbox in MATLAB. The

fitted shrinkage model for X and Ydirections (SX and SY

in%) are given below

SX0:292428:5

LX(4)

SY3:12105L2Y0:007271LY0:09478 (5)

Figure 10 shows the fitted curves for the shrinkage in X and

Ydirection. The coefficient of determination (Montgomery

20 40 60 80 100 120 140 160 180 200

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Strip length (mm)

Percentageshrinkage(%)

X direction

Y direction

Negative shrinkage

Figure 10. Comparison of shrinkage model in X and Y

direction.

Figure 11. Illustration of new compensation method: (a) STL file; (b) slicing; (c) contour showing hatch lines; (d) offsetting

hatch lines based on shrinkage model; (e) comparison of original and final compensated geometry.


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and Runger 2007) for the fitted shrinkage model in the X

andY direction are 98.67% and 81.67% respectively.

4. Proposed compensation procedure

When the shrinkage scaling factors are constant, shrinkage

compensation is relatively easy. The scaling transformation

can be used to offset the vertices of the triangles of the STL

file to the single scaling factor value in each X, Yand Z

direction. However if the shrinkage scaling factors vary

with hatch length, shrinkage compensation requires off-

setting each scan line of the part. Therefore a sliced layer

file is preferred rather than a STL file for the ease of

compensation. Compensating on sliced data is proved

successful by Tong et al. (2008) for compensating machine

errors for SLA and FDM processes.

In order to achieve this, the STL file of the part is sliced

into layers and is stored in a layered file format called CLI

file. In order to generate the scan lengths, entire scan path

of the laser has to be calculated. The contour information is

extracted and all the co-ordinate points of the contour are

sorted based on whether the contour is internal or external

contour. After reading the contour information hatch lines

and its lengths are found using intersection of hatch lines

with the contours. Then compensation value for every hatch

length is calculated using the fitted shrinkage models. Hatch

lengths are compensated at its two ends. After offsettingeach contour at its end points, the contour is rebuilt with its

new vertices and a new compensated CLI file is written.

Then this file is used for part building.

Figure 11 illustrates this procedure with an example of a

sphere. The STL file of the sphere (Figure 11(a)) is sliced

with uniform slice thickness of 150 mm (Figure 11 (b)).

Hatch vectors (dexels) are generated with a hatch gap of 300

mm for circular slice geometry (Figure 11(c)). The hatch

vectors along Xdirection corresponds to scan path of the

laser and the hypothetical hatch vectors along Ydirection

are perpendicular to these scan lines. It should be remem-

bered that there is no exposure on these hatch lines along

the Ydirection and these are virtual hatch lines generated

for the purpose of the compensation.

Most of the degenerated cases in calculating intersections

of hatch vector with contour geometry are solved with thehelp of odd/even parity checking. The generated hatch

vectors are compensated depending upon their hatch

length. When a dexel with length Lc is fabricated, due to

linear shrinkage, the dexel length reduces to Lm. The

deviation due to shrinkage of original length Lc is Dl.

From Figure 11(d), it is observed that in order to obtain a

length Lc a dexel with length L has to be used. Thus the

compensated value is LLcDc, where DcsLc1 s

is the

compensation length to be added to every dexel of the part.

For a part having scan length Lc, Dc is calculated using the

shrinkage model and appended at the two ends of the dexel

by the amountDc/2. First, the dexels in the Xdirection arecompensated using shrinkage model (SX) developed in the

X direction (equation (4)). Then compensated contour is

reconstructed from the end points of the hatch vectors.

Following this dexels in Ydirection for this new compen-

sated contour are generated and compensated using shrink-

age model (SY) developed for the Ydirection (equation (5))

and then compensated contour is reconstructed from the

end points of the hatch vectors. The comparison of original

and compensated contour is illustrated in Figure 11(e). All

the compensated contours are then written into a CLI file

for fabricating the slices.

Unlike the conventional compensation techniques, the

compensation length varies nonlinearly with the originalhatch length. As percentage shrinkage is a function of hatch

length and during compensation it is again multiplied by the

hatch length, the amount of compensated length varies

nonlinearly with hatch length. Figure 12 compares the

original and compensated geometry for a semi-circular

section with a magnification in compensation length. The

implementation of this compensation methodology for X

directionis illustrated in theformof a flow chart in Figure 13.

Thesame procedure is repeatedfor thecompensation in theY

direction. This new method of compensation can be used for

any four types of exposures mentioned earlier in section 3.

But for each type of exposure new shrinkage models need to

be developed following the steps outlined in section 3.

5. Results and discussion

The shrinkage compensation algorithm and the developed

shrinkage models are verified by conducting experiments.

Improvement in accuracy is quantified by fabricating parts

following two different compensation methods:

-20 0 20 40 60 80 100 120 140 160 180 200-20

0

20

40

60

80

100

120

140

160

180

200

Compensated geometry

Original geometry

Y

X

Figure 12. Comparison of geometry before and after

compensation using the developed shrinkage model.


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. The first part is compensated by applying a scaling

transformation to STL file with a constant shrinkage

scaling factor (calculated using method suggested by

SLS machine manufacturer (EOS 2003)).

. and the other part is compensated using the shrinkage

model and new compensation method

The improvement in accuracy for the model developed in

this work for both the Xand Ydirection is studied using a

standard benchmark part as suggested by Ippolito et al.

(1995). A comparison experiment is conducted to quantify

the improvement in accuracy due to the inclusion of the

nonuniform shrinkage term. In one part a machine

Start

Input CLI file

Read layers, contours, vertices and their attribute

Find the max and min values of x & y for each contour

Generate Hatch lines

Find Intersection points of hatch

lines with contours

Sort the intersection points in ascending order of X co-ordinates

Generate scan lines from the intersection points

Offset scanline by c

Write new contour data from compensated scan line

Output compensated CLI file

Stop

IF hatchline> H

Initialise first layer & contour

Increment layer_no

Increment

contour_no

If layer_no

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