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doi:10.1016/j.ijm

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(W. Zhang).

International Journal of Machine Tools & Manufacture 47 (2007) 873–883

www.elsevier.com/locate/ijmactool

Compound scan mode developed from subarea and contour scan modefor selective laser sintering

Y. Shi�, W. Zhang�, Y. Cheng, S. Huang

State Key Laboratory of Plastic Forming Simulation and Die & Mould Technology, School of Material Science and Engineering,

Huazhong University of Science and Technology, Wuhan-Hubei 430074, PR China

Received 25 May 2006; received in revised form 31 July 2006; accepted 14 August 2006

Available online 6 October 2006

Abstract

Scan mode is an important parameter for selective laser sintering (SLS) processing. The improved mode will optimize scan path and

improve the precision, strength and fabrication efficiency of a SLS part. A compound scan mode, which combines subarea scan mode

and contour scan mode, is proposed. The principle of its hatch (path-planning) algorithm and implementation are presented. To testify

the effectiveness of this compound mode compared to that of subarea scan mode, it has been utilized for researches at a SLS machine

developed at Huangzhong University of Science and Technique (HUST). The results from the researches indicate that the degree of

precision of a SLS part with the compound scan mode is higher than that with subarea one. There is little difference in the tensile

strength, flexural strength, shock strength and fabrication efficiency of a SLS part under the compound scan pattern and the subarea scan

mode. Therefore, implementation of the compound scan mode is of importance to improve the precision of a SLS part.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Selective laser sintering; Improved subarea scan mode; Compound scan mode; Fabrication precision

1. Introduction

Scan mode is one of the important parameters that affectthe precision, strength and fabrication efficiency of aselective laser sintering (SLS) part. Therefore, it is veryimportant to optimize scan mode.

Much study on scan mode has been done and many scanmodes have been created, and they belong to parallel-linescan mode or broken-line scan mode.

1.1. Parallel-line scan mode

Parallel-line scan mode [1] is also called as type Z scanmode whose scanning paths are parallel to x- and y-axis.Its principle is similar to that of filled regions in computergraphics. Though its algorithm can be simply and easily

e front matter r 2006 Elsevier Ltd. All rights reserved.

achtools.2006.08.013

ing authors. Tel.: +86027 87557042;

548581.

esses: shiyusheng@263.net (Y. Shi), zwxwen@163.com

implemented, it has disadvantages. Firstly, laser has to becontinually turned off and on, which shortens its life.Moreover, for a part with holes, cavities have to bespanned frequently and it causes scanners run emptily.Secondly, for the scan direction in layers is the same andthere exists shrinkage stress in the same direction, whichcauses the warp and distortion of a SLS part. Finally, aSLS part with parallel scan mode has anisotropy strength.For subarea scan mode [2,3], scan lines are parallel lines.

Every slice plane of three-dimensional (3D) CAD model isdivided into smaller areas and then they are filled byparallel lines. Empty runs are less than those for parallel-line scan mode. Its algorithm is simple, so it is widely usedin the SLS process, and it has the following disadvantages:First, some micro-ladders appear on a SLS part with thismode, which causes the precision dependent of the spot sizeof laser beam. What is more, there exists the warp anddistortion of a SLS part with this mode. Especially, in apart with a larger slice plane, there appears great shrinkagestresses and even cracks along the scanning directionbecause of longer scanning lines.

ARTICLE IN PRESS

Fig. 1. Subarea scan mode.

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883874

For emanative starlike scan mode and angled emanativestarlike scan mode [4], slice planes are divided into twoareas from the center, which are filled with scan linesparallel to x or y axis or at an angle of 451 to the axisfrom the center to outside. Compared to that with the twoscan modes above, the SLS part with these two modescauses less warp and distortion to some extent, butthey have disadvantages such as that of parallel-linescan mode.

1.2. Fold-line scan mode

For fractal scan mode [5] scan path has the features oflocal and whole comparability. When fractal dimensionsare 2, the whole slice planes can be filled with fractal scanpath. This scan mode overcomes the shortcomings ofparallel-line scan mode and makes the temperature fieldmore uniform, which reduces warp and distortion. But ithas the following disadvantages: low scanning speed, laserscanners frequently accelerated and decelerated, a SLS partbeing getting fabricated with low precision, and frequentspanning of the cavities of the slice planes.

Scan paths are spiral lines for spiral scan mode [6].Though it overcomes the shortcomings of type z scanmode, and shrinkage stresses can be reduced, the cavitieshave to be spanned frequently.

For contour equidistance path [7,8] no empty runappears which prolongs scanners’ life. The frequentchanging scan direction and shorter scanning lines dispersethe shrinkage stresses and reduce warp and distortion.Its algorithm is complex and it needs more CPU time.Besides, the algorithm is not reliable and someunfilled regions appear, which affects the strength of theSLS part.

This algorithm of the scan path based on Voronoi map[9,10] is suitable for multi-connected domains in sliceplanes, and enhances the scan efficiency to some degree.But it has the same shortcomings as the contour equi-distance path.

As for scan mode using Pythagorean hodograph asfilling lines [11], the intersecting parts of slices are separatedinto some subareas by the Delaunay triangle, and then theyare filled with Hilbert curves [12]. However, it is suitableonly for regular parts, except the fabrication of parts withcomplex contour. Besides, there are also other similar slicefilling modes presented by Wasser et al. [13], Tiller andHanson [14], Ganesan and Fadel [15], Pham [16] andTakashi [17].

To overcome the shortcomings of the scan modes above,a compound scan mode combining subarea scan mode withcontour scan mode is presented in this paper, and it has notbeen reported in the literature.

2. Subarea scan mode and contour scan mode

The compound scan mode, based on the subarea scanmode and cotour scan mode, is presented. Therefore,

we firstly discuss these two scan modes before thecompound one.

2.1. Subarea scan mode

A subarea scan mode is presented in Ref. [2] in order toimprove quality of a SLS part. Strategies for it are as follows:The first step is that the slice planes are divided into

subareas without holes shown in Fig. 1.The second one is that the slice planes are divided into

subareas in terms of the number of intersecting points thatthe scan lines parallel to x or y-axis intersect with theircontours. Fig. 1 is taken for an example. The scan lineswithin area 1 form two intersecting points with thecontour. The number of intersecting points increases intofour when they are within area 2. In the same way, thenumber in area 4 is six, the number in area 7 is eight, andthe number in area 11 is six. So the whole slice area issubdivided into 16 subareas.The third one is that subareas are scanned in the fixed

order from top to bottom, and from left to right. Forexample, the scan order in Fig. 1 is: area 1- area 2- area3- area 4- area 5- area 6- area 7??.Finally, these subareas are filled with parallel lines, but

there is an a angle between two neighboring scan layers inorder to reduce shrinkage stress along the same direction.Generally a ¼ 90�.According to the above strategies, we can implement it

by the following procedure:Initially, intersecting points where (at which) the scan

lines are intersecting with the contours of a slice plane areobtained, and in the order they can be stored in pairs, suchasðP0;P1Þ,ðP2;P3Þ, ðP4;P5Þ,?,ðP2n�1;P2nÞ. If these scanlines are in a connected domain, it can be filled with linesconsisting of point pairs. And those lines are called thefilling lines.Then the filling lines can be grouped. For the

setfCi; 1oioNg, the filling lines in the whole slice can begrouped into m groups from Eq. (1).

ARTICLE IN PRESSY. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883 875

C1 ¼ C2 ¼ � � � ¼ Ck1aCk1þ1;

Ck1þ1 ¼ Ck1þ2 ¼ � � � ¼ Ck2aCk2þ1;

� � �

Ckm�1þ1 ¼ Ckm�1þ2 ¼ � � � ¼ Ckm;

km ¼ N;

8>>>>>><>>>>>>:

(1)

where Ci is the number of segments as filling lines, i.e., thenumber of pairs of intersecting point, and N is the numberof grouped filling lines. So in Fig. 1 there are seven groupsof filling lines.

Though subareas are attained according to the numberof crossing points scan lines intersect with the contours of aslice plane, its principle can be optimized. So the subareascan mode can be developed into an improved subarea scanmode.

The strategies of improved subarea scan mode areexplained as follows:

First of all, subarea zone is grouped as much aspossible. Next the numbers of intersection points varywhen two neighboring scanning lines intersect with thecontours in a slice plane. According to the principleof the scan order, two filling lines are in a connecteddomain.

According to the strategies of the improved subarea scanmode, we can implement it as follows:

To start with, we could judge whether the neighboringscan lines are in a connected domain. Once they areprojected into the scanning direction and there are someoverlaps, they must be in a connected domain. Otherwise,they are not in it.

According to the above methods, the algorithm ofimproved subarea scan mode needs frequent judgmentwhether the filling lines belong to a connected domainsection. For this reason, much time will be taken by CPUto do this. To spare calculating time, complex polygons in aslice plane in Fig. 2a can be grouped according to the depthtree of the polygons’ contour cycles.

A

B

C

DE

FG

(a)

Fig. 2. (a) Contour polygons in a slice pla

It is known that depth of the cycle, external and internalpolygon, and direction of the polygon are defined asfollows:Depth of the cycle refers to the number of cycles in the

same contour enclosing it. The maximum depth in acontour is called the depth of a contour; the depth of acontour is also an indication of the planar complexity ofthe contour. As illustrated in Fig. 2b, the depth tree showsthe relationship of the cycles to a contour. The depth ofthis contour is 3. For a given contour, we employ the depthtree to describe its complexity.Based on the definition of depth, we can also define the

attribute of a cycle: if the depth of a cycle is even, it is anexternal cycle; otherwise, it is an internal cycle. In Fig. 2a,cycles A, D and E are external cycles, and the rest areinternal cycles.Like most of definitions in the relevant literature, we

define the direction as positive if the solid area is always tothe left when walking along the boundary. Obviously, forexternal cycles, the positive direction is counterclockwise;for the internal cycles, the positive direction is clockwise.The Fig. 1 is taken as a case in point for the improved

subarea scan mode. According to the above principles,Fig. 1 can be united into four subareas: a subarea Iincluding area 1, area 2, area 4, area 7, area 11, area 14 andarea 16; a subarea II consisting of area 3, area 6, area 9 andarea 12; a subarea III including area 10, area 13 and area15; a subarea IV consisting of area 5 and area 8. Therefore,the number of spanning cavity and subareas can bereduced, which is of benefit to SLS process.

2.2. Contour scan mode

Contour scan mode belongs to fold-line scan mode thatthe two neighboring filling lines are not parallel. Fillinglines with equidistance are parallel to the lines of a contourpolygon. For the curves of a contour in a slice plane, theyare approximated by line segments, to which the fillinglines with equidistance are parallel. The principles of

A

B

D E

F

Contour Depth

0

1

2

3G

C

(b)

ne and (b) tree structure of polygons.

ARTICLE IN PRESS

X

Y

y

O

Vi-1

Vi

V' i-1

V'i

V' i+1

Li

L i+1

L'i

L'i+1

x

Vi+1R

o

R

Fig. 3. Offset generations.

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883876

contour scan mode are explained in the followingSection 3.2. Because the solid area in a slice plane is filledwith laser beam spot with constant size, filling lines areconsidered to be equidistant from lines consisting of acontour polygon.

3. Compound scan mode

The compound scan mode is studied, which combinesthe algorithms of subarea scan mode and contour scanmode.

3.1. Strategies of compound scan mode

Most slice planes of a 3D model consist of complexconcave polygons, and most of them compose polygons.For the algorithm of contour scan mode, it happens thatpolygons may intersect each other and lines of concavepolygons may intersect themselves. That is the main reasonwhy the algorithm of a contour scan mode is complex. Inslice planes the contour scan mode cannot be stopped ortransformed into the improved subarea scan until fillingpolygons intersect each other or intersect themselves. Theseare the strategies of this mode.

3.2. Implementation of compound scan mode

According to the strategies, we can implement thealgorithm by the following steps.

The first step is that the contours in a slice plane aregrouped into connected domains and then every one ofconnected domains is filled with lines with the compoundscan mode once. The second one is that filling lines offsetwith equidistance are generated. The third one is that inscan space, the number of contour offset, is defined. Thelast one is that after the contours are filled with contourscanning mode, the unfilled parts are to be filled with theimproved subarea scan mode.

3.2.1. Creation of contour scan path

3.2.1.1. Equidistance contour generation. When the solidpart of a slice plane is filled with a series of equidistancebeam paths, the offset directions to inner loops andexternal loops are opposite. According to the definitionof the direction of a loop [18], the offsets of inner andexternal loops are presented with the vector R

*shown in

Fig. 3. Therefore, the endpoint coordinates of their linescan be calculated according to the following methods:

As shown in Fig. 3, it is assumed that the origin of thetemporary coordinate system xoy is the arbitrary intersect-ing point Vi . Li and Liþ1 are the vector formed by V i�1V i

and V iV iþ1. l*

i and l*

iþ1 are the unit vectors of Li and Liþ1.They are given by

l*

i ¼ ai i*þbi j

*;

l*

iþ1 ¼ aiþ1 i*þbiþ1 j

*;

8<: (2)

where

ai ¼xi � xi�1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðxi � xi�1Þ2þ ðyi � yi�1Þ

2q ,

bi ¼yi � yi�1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðxi � xi�1Þ2þ ðyi � yi�1Þ

2q ,

aiþ1 ¼xiþ1 � xiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðxiþ1 � xiÞ2þ ðyiþ1 � yiÞ

2q ,

biþ1 ¼yiþ1 � yiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðxiþ1 � xiÞ2þ ðyiþ1 � yiÞ

2q ,

Vi�1ðxi�1; yi�1Þ, V iðxi; yiÞ and Viþ1ðxiþ1; yiþ1Þ are, re-spectively, the points of V i�1, Vi and V iþ1in the coordinatesystem XOY. If lines Li and Liþ1 are offset with R

*, the

following equation is derived:

�bixþ aiy ¼ �R;

�biþ1xþ aiþ1y ¼ �R:

((3)

Because L0i is not parallel to L0iþ1, aibiþ1 � aiþ1bia0.After Eq. (3) is solved, we get the point V 0i by

x ¼ �ðaiþ1 � aiÞR

ai bi

aiþ1 biþ1

����������;

y ¼ �ðbiþ1 � biÞR

ai bi

aiþ1 biþ1

����������:

8>>>>>>>>><>>>>>>>>>:

(4)

ARTICLE IN PRESS

Vi

Vi′′

Vi′

Vi-1

Vi-1′

Vi+1′

Vi+1

Fig. 5. Sharp angle.

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883 877

The points in temporary coordinate system xoy can betransformed into the points in XOY with the transforma-tion equation:

X ¼ xi þ x;

Y ¼ yi þ y:

((5)

Thus we can get the coordinate values of all offsetpoints.

3.2.1.2. Self-intersection and sharp angle. After theboundary cycle is offset inwardly, self-intersection mayhappen in Fig. 4. It causes the distortion of contours, soself-intersection should be eliminated [19].

To calculate the intersecting points, the method is to goaround the offset polygon edge by edge, and check whetherthere are two no-adjacent edges intersecting each other,and store a list of intersection points along the path in theorder, in which they appear in their parent cycle. Thencheck whether the vector direction of a newly offsetting lineis the same as that of the offset line. Otherwise, it isconsidered that the newly offset lines are self-intersections,which cause polygon distortion; and laser beam cannotreach and therefore, they should be eliminated. Forinstance, in Fig. 4 the vector directions for contour lines10 and 40 are the same as those of the original contour lines1 and 4, respectively. Contour lines 20 and 30, whosedirections are opposite to the lines 2 and 3, should beremoved. Then a newly intersecting point d00 between no-adjacent contour lines 10 and line 40 is added. Self-intersections can be eliminated in this way.

Furthermore, sharp angles must be processed beforefurther offsetting. If the lines form a sharp angle (angleV i�1V iV iþ1 in Fig. 5), which means aibiþ1 � aiþ1bi � 0, thevalues of x and y in Eq. (4) are so large that a newly offsetcontour will be distorted. The sharp angle can be processedas follows: the endpoint Vi+1 of the shorter edge of sharpangle Vi�1ViV iþ1 is gone through by the line V iþ1V

00i

perpendicular to the line V iV0 in Fig. 5. Substituting V 00i for

V 0i may eliminate the distortion of the newly offset sharpangle.

a

1

b

2

c

3

db′d′

c′

a′ee′

4

4′

2′

3′

1′

d′′

Fig. 4. Self-intersections.

The rules of judging the sharp angle are as follows:Firstly, judge whether angle V i�1ViViþ1 value is small

enough to form a sharp angle. Secondly, area ofDV i�1V iV iþ1 is also chosen as the criteria, for sometimesthe sharp angle can be the feature of the contour geometry.Lastly, the points of a newly offset contour are stored in

the order in which they appear in their parent cycles.

3.2.2. Transformation of scan modes

The rules of stopping contour scanning are as follows:First, two contours intersect each other. Second, a

contour self-intersects. Last, the direction of externalcontour is changed or the contour scan ends.If one of the first two rules is attained, stop contour scan

mode and start improved subarea scan mode in slices.

3.2.2.1. Contour intersection. Contour intersection maybe divided into the intersection among contours and self-intersection. Actually, these two kinds of intersections canbe processed in the way as we judge whether lines areintersecting.

3.2.2.2. Intersection of lines. If two points of a line lie intwo sides of the other line, the two lines intersect [20,21].Lines CD and AB intersect, points C and D lie in the twoareas of the line AB and vice versa. As for a line AB

y ¼ f ðxÞ, if Dðx; yÞ ¼ f ðxÞ � y, the following expressionshold:

Dðx; yÞ40 above a line;

Dðx; yÞ ¼ 0 on a line;

Dðx; yÞo0 below a line:

8><>: (6)

We can now derive the following relation, where C:xandC:y derive the coordination x and y of endpoint C of

ARTICLE IN PRESSY. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883878

line CD respectively, and D:x and D:y stands for thecoordination x and y of endpoint D of line CD,respectively:

DABðC:x;C:yÞ � DABðD:x;D:yÞ40 The line CD is in the same side of the line AB;

DABðC:x;C:yÞ � DABðD:x;D:yÞ ¼ 0 The point C or D is on the line AB;

DABðC:x;C:yÞ � DABðD:x;D:yÞo0 The line CD is in two side of the line AB:

8><>: (7)

For the same reason, for which point A and point B ontwo sides of the line CD, the following equation is valid.

DCDðA:x;A:yÞnDCDðB:x;B:yÞo0. (8)

To increase the efficiency of the algorithm, a rectanglewindow is constituted by the points in Eq. (9). If a line spansthe window or its endpoints are in it, we can further judgewhether they are intersecting lines according to Eq. (7):

ymax ¼ maxðyA; yBÞ;

ymin ¼ minðyA; yBÞ;

xmax ¼ maxðxA;xBÞ;

xmin ¼ minðxA; xBÞ:

8>>>><>>>>: (9)

The mean time complexity of the algorithm is Oðn log nÞ.For the object consisting of convex polygon, when theexternal loop offsets inward, it does not happen that linesintersect each other. But the direction of the external loopmight change into the counterclockwise when the externalloop offsets to a certain. If it continues to be offset, it can beamplified in the opposite direction. To avoid the situation,whether the direction of a loop is in the opposite directionshould be judged. If the direction of a loop is changed intothe opposite direction, contour scan must be stopped.

3.2.3. Filling after contour loop scan

After a solid area in a slice plane is filled with contourscan path, the remainder will be filled with the improvedsubarea scan mode presented in Section 2.1.

3.2.4. Laser parameters and scan order for this mode

3.2.4.1. Scan speed and laser power. When complexcontour curves are scanned, laser scan speed for contourscan mode is required to be less than that for improvedscanning mode in order to increase the scan precision.Besides, because the scan time interval between twoneighboring contour cycles is longer, there much heat lossoccured. For these reasons laser power for contourscanning mode is required to be high to improve thesintering density.

Because the center part of a slice plane is scanned withthe improved subarea scan mode, the scan paths are short,which shortens the scan time interval between twoneighboring scanning paths and reduces heat loss. There-fore, the laser power for improved subarea scan mode maybe lower to avoid the center parts to be overly sintered [22].

According to the characteristics of these two scanmodes, the scan speed and laser energy should not be thesame. In this paper, the scan speed and laser power for the

two scan modes are summarized from the experiments. Ifreference scan speed and laser power is set as laser speedand laser power, the scan speed and laser power for theimproved subarea scan mode are laser speed and0.85� laser-power, respectively, while for the contour scanmode they are laser-speed and 1.2� laser-power, respec-tively.

3.2.4.2. Scan order. Outside powder material is firstlysintered when laser scans powder inward, which causesinner heat stress. So the scan order inward causes warp anddistortion, and even crack in the SLS parts [23]. Therefore,in order to release the inner heat stress, compound scanorder is outward.

3.3. The results of simulation

The results of simulating the process of compound scanmode are shown in Fig. 6. Fig. 6a is the 3D CAD standardtest piece. The result of simulating filling the slice plane atthe height of 7mm with contour scan mode is in Fig. 6b.Fig. 6c is the result of simulating filling the remainder partof the slice with improved scan mode. While the Figs. 7a–care the amplified filling result of parts I, II, and III inFig. 6c. In the process of SLS polystyrene (PS) powder issintered outward with the compound scan mode.

4. Experiment and results

We have tested the effect of subarea scan mode andcompound scan mode on fabrication efficiency or scanefficiency, strength and precision of SLS parts.

4.1. Scan efficiency

4.1.1. Experimental equipment and conditions

Experimental equipment was a HRPS-IIIA type SLSmachine built at Huazhong University of Science andTechnology (HUST), Wuhan, PR China. A CO2 lasersource with a wavelength of 10.6 mm and maximum outputpower of 50W is used. Other conditions, such as thelaser power of 14W, scan space of 0.1mm, layer thicknessof 0.2mm and the scanning speed of 2000mm/s, arecarefully set. The powder used in this study was PSpowder with grain size below 74 mm. It was sintered at95–110 1C.

ARTICLE IN PRESS

Fig. 6. Simulating the process of a slice with compound scan mode: (a) 3D CADmode of standard test piece with the size of 200� 200� 20mm3; (b) filling

the slice plane at the height of 7mm with contour scan mode, and the dashed presenting the tracks of beam spanning cavities; (c) filling the remainder

cycles 1–6 of the slice with improved scan mode.

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883 879

4.1.2. Experimental methods

General standard test parts in Fig. 8 were sintered. Twoscan modes are used to fabricate the test parts with theheight of 6mm. They have the area of valid fabricationlayers of 9080mm2. The scan efficiency Z can be defined asZ ¼ ðvalid sintering areas S=laser scan areaÞ. The numberof scanning location point is defined as the number ofendpoints of filling lines, and the area of laser empty run isequal to: mean run length� the number of emptyrun� scan spacing.

4.1.3. Experimental results

Table 1 shows the results of the scan efficiency of thesame test part with the compound scan modes and thesubarea scan mode.

In Table 1 for the same test part the scan efficiency of thecompound scan mode is less than that of the subarea scanmode.

The fabrication time taken for the standard test part inFig. 8 with the compound scan modes and the subarea scanmode are shown in Table 2.

For the same test part fabricated with two scan modes,the fabrication time with the compound scan mode islonger than that with the subarea scan mode.

4.2. Strength tests

4.2.1. Experimental methods and test instruments

Experimental equipment and conditions are the same asthose of testing scan efficiency in Section 4.1.1. The testinstruments include the MDM-20 electron pulling forcemachine and the XJJ-5 freely supported beam hammerstrength machine with a resolution of 0.005J. They are usedfor testing tensile strength, flexural strength and shockstrength under 20 1C air temperature with 60% humidity.

SLS test part with simple structure cannot reflect theeffect of scan modes on the strength of SLS part. Forexample, effects of different scan modes, such as thecompound scan mode and the subarea scan mode, on the

strengths of simple shock test piece, simple flexural testpiece and simple tensile test piece have little difference. Sothe complex structure test pieces with scan modes havelarge difference in their characteristics.For this reason, to simulate the strength of complex SLS

parts, standard test pieces were made as in Figs. 9 and 10,in the light of the experimental standards of the strength ofplastic parts. In Fig. 10, the SLS standard test pieces forflexural strength have the height of 10mm, while they havethe height of 5mm for shock strength.

4.2.2. Results of strength tests

Test results for tensile strength, flexural strength and shockstrength of SLS PS testing parts are shown in Tables 3–5.

4.2.3. Analysis of test results

The strength of a SLS part is related to the energyabsorbed by powder [24]. Within some range, the moreenergy powder absorbs, the more strength of a SLS partincreases. The energy absorbed by powder mainly dependson the energy directly supplied and the dissipated energy.The supplied energy depends on laser energy and preheat-ing temperature, while the dissipated energy depends onthe sintering time in a layer. It can be seen from Tables 3–5that the compound scan mode and the subarea scan modehave little difference on the absorbed energy.

4.3. Dimensional accuracy

4.3.1. Experimental methods

Experimental equipment and conditions are the same asthose of testing scan efficiency in Section 4.1.1. Thestandard test pieces in Fig. 8 are sintered with thecompound scan mode and the subarea scan mode.

4.3.2. Test results

Test results of the dimensional accuracy of the SLSstandard test piece in Fig. 8 with the subarea scan modeand the compound scan mode are listed in Tables 6 and 7.

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-10270

-9775

-9280

-8785

-8290

-7795

-72100

-102 -97 -92 -87 -82 -77 -72

70 75 80 85 90 95 100

30

35

40

45

50

55

60

65

70

30 35 40 45 50 55 60 65 70

(a) (b)

(c)

Fig. 7. Amplification of Fig. 6c: (a), (b), and (c) are the amplification of part I, II, III, respectively.

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883880

4.3.3. Analysis of experimental results

4.3.3.1. Dimensional accuracy. Tables 6 and 7 show thatthe dimensional accuracy of the SLS part with thecompound scan mode is higher than that of the SLS partwith the subarea scan mode. Therefore, scan modes have agreat effect on the dimensional accuracy. According to theprinciple of the working laser scan system, the laser beamscanning on the edge of a SLS part will cause great errorbetween its practical position and the theoretical positiondue to the inertia force of the system. Areas with thesubarea scan mode are filled with parallel scan lines, so thelaser beam will produce a position error to some degree.However, areas with the compound scan mode may havean error only on the turning point of the borderline of theSLS part. Because the whole contours are filled with line

segments with the compound scan mode, there exists noinertia force. Therefore, its dimensional accuracy is higher.

4.3.3.2. Shape accuracy. Shape error is mainly caused bythe shape change or warp and distortion of a SLS part.Tables 6 and 7 show that the diameter of circular hole ofthe standard test piece fabricated by the subarea scan modehas great variable errors at different positions, but a goodcircular degree can be guaranteed for the parts with thecompound scan mode. It is obvious that the compoundscan mode is of benefit to reducing the shape error.Warp and distortion of the SLS part are dependent on

the temperature. Scan modes directly affect the tempera-ture field, so the warp and distortion of the SLS part varywith different scan modes. From the results the warp and

ARTICLE IN PRESS

Fig. 8. Standard test pieces.

Table 1

Scan efficiency with the compound scan mode and the subarea scan mode

Laser locating

points

Number of laser

on–off

Area of scan empty

run (mm2)

Area of practical scan

(mm2)

Laser scan

efficiency

Subarea scan 8820 16 640 9720 0.93

Compound scan 11872 87 3480 12560 0.72

Table 2

The fabrication time with the compound scan mode and the subarea scan mode

Scan mode Fabricated

height (mm)

Layered

number

Laser power

(W)

Scan spacing

(mm)

Fabrication

time (h:m:s)

Subarea Scan 15.03 75 14 0.10 02:18:22

Compound scan 15.00 75 14 0.10 03:06:56

Fig. 9. SLS test pieces for tensile strength.

Fig. 10. SLS test pieces with H ¼ 10mm for flexural strength, SLS test

pieces with H ¼ 5mm for shock strength.

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883 881

ARTICLE IN PRESS

Table 3

The results of tensile tests

Scan mode Tensile strengths (MPa) Mean tensile

strengths (MPa)

Test 1 Test 2 Test 3

Subarea scan 3.057 2.862 2.667 2.862

Compound

scan

1.823 1.450 1.928 1.734

Table 4

The results of bending tests

Scan mode Flexural strengths (MPa) Mean flexural

strengths (MPa)

Test 1 Test 2 Test 3

Subarea scan 0.453963 0.454774 0.492338 0.467025

Compound

scan

0.316846 0.396634 0.442507 0.385329

Table 5

The results of shock tests

Scan mode Shock strengths (J/m2) Mean shock

strengths (J/m2)

Test 1 Test 2 Test 3 Test 4

Subarea scan 933.33 1000.00 933.33 1000.00 966.67

Compound

scan

866.67 1333.33 933.33 933.33 1016.67

Table 6

Test results of the dimensional accuracy of the SLS standard test piece with t

Items Theoretical

values (mm)

Measured values (mm

Length of part 200 199.80 199.4

Width of part 200 199.20 199.4

Inner diameter of central hole 20 19.50 19.4

External diameter of central hole 30 29.82 29.7

Inner diameter of external circle 20 19.60 19.6

Inner length of square hole 20 20.00 19.7

External length of square hole 30 30.00 30.0

Width of external rib 5 5.30 5.0

Width of inner rib 5 5.00 5.3

Table 7

Test results of the dimensional accuracy of the SLS standard test piece with t

Items Theoretical

values (mm)

Measured values (mm

Length of part 200 200.00 200.1

Width of part 200 200.20 200.0

Inner diameter of central hole 20 19.60 19.8

External diameter of central hole 30 30.00 30.0

Inner diameter of external circle 20 19.80 19.8

Inner length of square hole 20 19.60 19.8

External length of square hole 30 29.82 29.6

Width of external rib 5 5.00 5.0

Width of inner rib 5 4.80 4.9

Y. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883882

distortion with the compound scan mode are less than withother scan modes.

4.3.3.3. Surface quality. The sintered seam occurs only inthe place where two scans meet. For the subarea scan mode,there are subareas where the melted seams occurs, and forthe compound scan mode there are less subareas, and theyare in the center of slice planes. Therefore, the surface finishof the SLS part with compound scan mode is higher.

5. Conclusions

The thesis presents the principle of a compound scanmode and its implementation. The compound scan pathgeneration combines the algorithms of contour pathgeneration and subarea path generation. The results ofthis compound scan mode for a standard test piece aregiven. It proves that the compound scan mode is available.Some experiment on the effectiveness of the compoundscan mode and subarea scan mode on fabricationefficiency, strength and precision were made. The resultsrestate that

(1)

he su

)

0

0

8

2

2

0

0

0

0

he co

)

0

0

0

0

0

0

8

0

8

For the same part the former (compound scan mode)has less fabrication efficiency than the latter (subareascan mode) does; i.e., it needs more time to befabricated with the former than the latter.

(2)

The part with the former has slightly less tensilestrength, flexural strength, and shock strength, than

barea scan mode

Average

values (mm)

Dimensional

errors (mm)

199.90 199.80 199.72 0.28

199.70 199.50 199.45 0.55

19.62 19.54 19.53 0.47

29.80 29.82 29.79 0.21

19.80 19.90 19.73 0.27

19.78 19.92 19.85 0.15

30.40 30.20 30.15 0.15

5.00 5.50 5.20 0.20

5.94 5.30 5.38 0.38

mpound scan mode

Average

values (mm)

Dimensional

errors (mm)

200.20 200.20 200.12 0.12

199.80 199.64 199.91 0.09

19.60 19.84 19.71 0.29

30.00 30.10 30.02 0.02

19.80 19.76 19.79 0.21

19.60 19.88 19.72 0.28

29.80 30.00 29.82 0.18

5.10 5.20 5.07 0.07

4.82 5.00 4.90 0.10

ARTICLE IN PRESSY. Shi et al. / International Journal of Machine Tools & Manufacture 47 (2007) 873–883 883

that of the latter; i.e., the former has no superiority onthe strength of a SLS part.

(3)

The part with the former has more precise on thedimensional accuracy, shape accuracy and surfacequality, than the latter.

(4)

The SLS part with high fabrication precision should bescanned with the compound scan mode, and the SLSpart with high fabrication efficiency and lower fabrica-tion precision should be scanned with the subarea scanmode. The presented compound scan mode has beenutilized on SLS system built at HUST. It can also beapplied to other RP systems. Though the algorithm inthis paper can improve the quality of SLS parts to someextent, there are algorithms to be developed for SLSprocessing.

Acknowledgments

This work was supported by the key project under the863 program of China (2002AA6Z3083), the key R&Dprogram of Hubei Province of China (2001A107B02), andthe key technological project under the tenth five-year planof Guangdong Province of China (A1040201).

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