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Virtual and Physical PrototypingPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t716100703
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: pmpandey@mech.iitd.ac.in
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
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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).
52 K. Senthilkumaran et al.
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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.
54 K. Senthilkumaran et al.
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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.
58 K. Senthilkumaran et al.
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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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