An Efficient Scanning Pattern for Layered Manufacturing Processes

Y.Yang 1 , J.Y.H Fuh 2 , H.T.Loh 2

Department of Mechanical Engineering, National University of Singapore, Singapore 119260

and Y.G.Wang 3 Kinergy Pte.Ltd., Singapore 569871

Abstract

Path generation is an important factor that affects the quality and efficiency of most layered manufacturing processes such as SLS, SLA and FDM. This paper introduces an efficient path generation algorithm. The principle of the algorithm and the implementation are presented. A comparative study is used to analyze the effectiveness of this method. The results of comparison on both path length and processing time between the traditional method and the proposed method are discussed.

Keyword: Rapid Prototyping, Depth Tree, Scanning Pattern, Equidistant Path.

1. Introduction

Satisfactory surface quality and fast processing speed have always been the aim of all the RP manufacturers and researchers. RP processes create a physical object through the building of layers either by depositing (e.g. FDM) or by curing (e.g. SLA). The method of scanning is a key factor that will affect the surface quality and the processing time of the part. In this paper, we will discuss a method to improve the surface quality and accuracy through improving the scanning pattern.

Some research has been done to minimize the shrinkage and to improve the dimensional accuracy. Onuh [1] proposed the Divergent Star Weave (DSW) and Diagonal Divergent Star Weave (DDSW) hatch strategy. In this method, the scanning is commenced from the mid.dle of the part, in such a way that half of the part is first scanned from the middle to the one end and the other half is then scanned. This process is repeated in either x or y direction (in DSW way), or at 45O to the their axes (in DDSW way). This will reduce the shrinkage forces for the whole layer and thereby minimize the part shrinkage and curl effect. This method is also called parallel-line method in essence. The shortcoming of this method is that it causes a highly anisotropic structure, which can be detrimental to the physical property of the final part. On the other hand,

1. Graduate Research Scholar; 2. Associate Professor, correspondence: mpefuhyh@nus.edu.sg; 3. R&D Director.

discontinuous paths will cause the delay of process and the frequent acceleration and deceleration will result in a slower process; furthermore, the end of the path is on the surface of the part. Since it is impossible to control perfectly the nozzle position and its dispensing due to the limitations of the controller, surface structure roughness is thus affected. Therefore in RP processes, a path with random orientation is desired.

Kim [2] and Bertoldi [3] applied the delaunay triangulation to decompose the cross section of a part and fill the triangulation with space filling curves (Hilbert Curves). But this method was limited to highly regular objects and not applicable to arbitrary boundaries. Moreover, the triangulation of the plane polygon can be of at least O(n2) complexity. If the slice information is represented by polygons, for normal accuracy requirement, n cannot be a small number; and the algorithm may not be acceptable for the practical application.

Wasser [4] introduced a fractal-like build style using simulated annealing algorithm, this method is able to generate filling patterns that allow the continuous deposition of a single path to fill arbitrary shaped domain. In his method, the area to be deposited is first decomposed into nodes, and the number of the nodes depends on the accuracy requirement in LM process. Although the complexity of this algorithm is only O(n), it could be very time consuming when the requirement to accuracy is high. Kulkarni proposed a spiral method in [5], however it is difficult to realize when there are pockets or islands inside the contour.

2. Equidistant Path Generation Method

We propose an equidistant path generation algorithm to improve the scanning efficiency and surface quality. Some literature has discussed about this deposition method, but they are limited to simple geometry and no implementation was reported so far. In this paper the algorithm and its detailed implementation will be presented.

Proceedings of the 2001 IEEE International Conference on Robotics & Automation

Seoul, Korea • May 21-26, 2001

0-7803-6475-9/01/$10.00© 2001 IEEE 1340

2.1 Definitions

The following definitions will be needed to describe the algorithm:

Definition 1: Simple Polygon. For a polygon, non-adjacent edges do not intersect with each other. Let ),...,1,0( niei = be the edges of the cycle,

we have φ=ji ee I , for all 1+≠ ij , and then we call it a simple polygon [6]. In Figure 1, these polygons are non-simple polygons.

Nearly all the commercial RP systems available in the market build the 3D objects from layers obtained through the slicing of 3D CAD models (in STL format). When the slicing algorithm is performed on the STL model without any fault, the result must be a series of simple polygons that do not intersect with each other.

Definition 2: Depth of the cycle. It refers to the number of cycles in the same contour that enclose it. The maximum depth in a contour is called the depth of a contour; the depth of a contour is also an indication of the planar complexity of the contour. As illustrated in Figure 2, the depth tree shows the relationship of the cycles to a contour. The depth of this contour is 3. For a given contour, we employ the depth tree to describe its complexity.

Definition 3: External and Internal polygon. 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 an external cycle; otherwise it is an internal cycle. In Figure 3, cycles a, b, e, f, j are external cycles, and the rest are internal cycles.

Definition 4: Direction of the polygon and chains. Like most of definitions in the relevant literature, we define the direction as positive if the solid area is always to the left when walking along the boundary. Chains are the segments along the boundary of the polygon.

Obviously, for external cycles, the positive direction is counter clockwise; for the internal cycles, the positive direction is clockwise. Accordingly, we define the areas besides the chains as left side and right side when walking along the polygon in the positive direction. We can infer from the above definitions that the left side of a chain is a solid part, and the right side of the chain is a void part.

2.2 Domain Partition

In a typical RP process, in order to realize the physical model, the cross section area of each layer has to be identified and filled with a pattern of vectors. In Figure 3 the shaded area is to be hatched. The cross section should be partitioned into different continuous areas that will be processed at the same time. Continuous area can be taken as the area bounded by the external cycle and the outmost internal cycles interior to it. In a depth tree, we can easily identify the continuous area boundaries; they are those cycles with the even depth and the cycles just below it in the depth tree. In Figure 3, a, c, d and f, g, h are all the boundaries of continuous area, and they can be processed together. This is also the pre-processing procedure of this algorithm.

2.3 Offset Generation

Since the diameter of nozzle is constant during the deposition process, we assume the motion velocity of the nozzle is also constant. To get the constant deposition thickness, the basic requirement to the path generated is that the distance between the adjacent paths must be constant. The main idea of this algorithm is to offset the contour and get a series of equidistant path.

The algorithm begins from the offset of an external cycle. Without loss of the generality, set the origin of the temporary coordinate system at the arbitrary vertices of

a b

i c d

e f

h g

Contour

j

Depth

0

1

2

3

Figure 2. Depth tree structure

b

i

Figure 3. Partition of areas inside a layer

ad

f g h

j

c

e

Figure 1. (a) Simple polygon and (b) non-simple polygon

(a) (b)

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the cycle iV . iL and 1+iL are the vectors formed by ii VV 1− and 1+iiVV (Figure 4).

ilr

and 1+ilr

are the unit vectors of iL and 1+iL , i.e.

+=

+=

+++ jyixl

jyixl

iii

iiirrr

rrr

111 (1)

Let 'iL and '

1+iL be the equidistant line of iL and 1+iL . If the offset is R, then the following equations are derived:

=+−=+−

++ RyxxyRyxxy

ii

ii

11 (2)

Since iL and 1+iL are not parallel to each other, 011 ≠− ++ iiii yxyx . Solve equation (2) to get:

−=

−=

+

+

+

+

1

1

1

1

)(

)(

i

i

i

i

ii

i

i

i

i

ii

yy

yx

Ryyy

yy

yx

Rxxx

(3)

Thus we can get the coordinate values of all the offset points.

2.4 Self-intersection

After the boundary cycle is offset inwardly, self-intersection may happen (See Figure 5). To keep the resulting cycle always the simple cycle, the self-intersections should be eliminated.

To calculate the intersection points, the method is to go around the offset polygon edge by edge and check whether there are two non-adjacent edges intersecting with each other, and keep a list of intersection points along the path. After checking all the intersection points, a list of intersection points is formed (e.g., point A and B in Figure 5). Then construct some simple cycles with the chains between the two intersection points (as seen the new cycles A1, A2 and A3 in Figure 5). It is necessary to store the points in the order in which they appear in their parent cycle. Then determine the direction of the newly formed cycles, and eliminate the cycles whose direction is negative (e.g., A3 in Figure 5).

2.5 Sharp Angle Another problem that is often encountered is a sharp angle. Sharp angles must be processed before further calculation. On one hand, a sharp angle is too small for deposition; on the other hand, it may become a source of instability of the next offsetting. If the lines form a very sharp angle, the x and y values in Eq. (3) can be unreasonable large, which will cause the deformation of offset polygon (as shown in Figure 6).

Criteria 1: Angle 11 +− iii VVV . This is to determine whether a sharp angle has formed;

Criteria 2: Area of 11 +−∆ iii VVV . Sometimes the sharp angle can be the feature of the contour geometry, if ruled out without differentiating, accuracy will be lost, or big void space will be created when hatching. To avoid the mistake, the area of 11 +−∆ iii VVV is also chosen as the criteria.

1+iL

'iL

'1+iLiV

'iV

R

Figure 4. Offset generation

1−iV

1+iV

A 1 A 2

A 1 A 2

A 3

A B

Figure 5. Self-intersection and polygon degradation

Figure 6. Sharp angle

iV

'iV

1+iV

1−iV

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2.6 Intersection with Internal cycle:

When the external contour is offset inwardly, it is likely that the path will intersect with the cycles interior to it. Calculating the resulting area to be hatched becomes the problem of finding the difference of two cycles.

Without loss of generality, we assume that cycle P (L vertices) is an external cycle and cycle Q (M vertices) an internal cycle (Figure 7). Then according to the computational geometry theory, the intersection of P and Q is a polygon having at most L+M vertices [6]. Both P and Q will be divided into some chains by the intersection points, and the boundary of QP ∩ is a series of chains that are alternatively obtained from the two polygons. For the chains, we define the area to the left of it as lC and the area to the right as rC . By this definition and the definition of direction, we know that lC is the solid area and rC is the void area.

We can seeintersection facing to eaBased on ou

For every coffsetting tdescribed prFigure 8.a). 3. Performa The followinthe parallelprocessing cross section 3.1 Total Pa We assume between thethe two adja

A

Where 1l an δ is t d is t

piC

P

Q

qiC

Figure 7. Polygon difference

1l

F

(a)

(b)

Figure 8. Comparison of two scanning path (a) equidistant method (b) parallel line method

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Figure 9. Model used for testing

from Figure 7 that between each pair of points, there are two chains ( piC and qiC ) ch other; one is of P and the other is of Q. r definition, we can get:

)(:0

qilpilni

iCCQP IU

=

=−

)(:0

qirpirni

iCCPQ IU

=

=−

ontinuous area, the algorithm begins from he external cycle and repeats the above-ocess until all the area is filled (as shown in

nce Evaluation

g performances are tested in comparison with line method: they are total path length, time and surface finish. Figure 9 shows the from the test model of a hand-phone shell.

th Length

that there is no overlap or crevice produced paths generated. The overlap area covered by cent segments (See Figure 10) is:

)2

tan2

sin(4

*)(2

21δδ −−+= ddll (4)

d 2l are the length of segment, he angle between 1l and 2l , and he width of the path.

δ d

igure 10. Area of the paths covered

o

2l

For the path generated by the parallel-line hatch method, all the 0=δ , and the area of hatched area is

∑=

=

=ni

iip ldA

0

* (5)

For the other hatch method,

∑∑=

=

=

=

−−=ni

i

iini

iio

dldA0

2

0

)2

tan2

sin(4

* δδ (6)

If d is a constant, for a given area 0A , the factor that affects the path length is iδ . For normal path, ild << , thus we get:

po AA ≈ , and

∑=

=

≈=ni

ii d

AlL0

(7)

where A is the area to be hatched, thus we get: Theorem: For all hatch methods, if there is no overlap or crevice produced, the total path lengths are approximately equal.

Figure 11 illustrates the relationship on the total path length versus offset value from a simulation result. It shows that if the path width is the same, the total path

length resulted from equidistant method is slightly longer than the parallel line way. The difference between them comes from the different overlaps in these hatch methods, which is quantified as the second part of Eq. 6. Since the value of this part is very small, the difference is negligible. 3.2 Processing Time

The aim for the optimized scanning path generation is to find a solution that requires the shortest processing time.

For a given continuous path, the motion starts from zero velocity at the starting point, accelerates to a specified velocity, keeps that velocity to a point along the path and then decelerates toward the end point of the path, where the velocity becomes zero. Usually for a given path, the motion controller [7] can adjust the vector velocity along a trapezoidal profile automatically no matter it is linear or nonlinear path (as illustrated in Figure 12). The length of path generated also limits the motion velocity. If the length is not long enough to allow the motion be accelerated to the specified velocity, then the constant speed stage can not be achieved, i.e. the velocity begin to be decelerated before it is accelerated to the specified value. On the other hand, the shorter the paths, there will be more starts and stops. So the longer the single path is, the higher the motion velocity will be, and thus less processing time is needed therefore the equidistant method has the advantage in terms of the process speed.

We use the SB214 [7] series of multi-axis motion controller to control the motion of nozzle. A comparison on processing time is shown in Figure 13. We can see that processing time of our proposed method is significantly reduced. Additionally, for both hatch strategy, the required processing time drops with the increase of vector velocity, but as the velocity increase to a certain point, this drop will stop.

3.3 Surface Quality

The ends of the scanning path on the surface are the main factors that affect the surface quality. With the parallel line hatch method, all the path ends are on the surface of the final parts, so the surface quality is not so satisfactory.

Velocity

Time

Vector Velocity (VV)

Vector Acceleration (VA)

Figure 12. Velocity profile of SB214 motion controller

Offset (mm)

Total Path Length (m)

0.1 0.2 0.3 0.4 0.5 0.6

1530456075

105Equidistant method

Parallel line method

Figure 11. Relationship between path length and offset value

90

Vector Velocity (m/s)

Processing Time (s)

0.2 0.4 0.6 0.8 1

800

1200

1600

2000

Figure 13. Relationship between processing time and vector velocity

0

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With this hatch pattern we have introduced, only one end of the path is on the surface for a continuous area, and therefore the surface quality can be improved significantly. 4. Conclusion

Different hatch strategies for the layered manufacturing process are analyzed in this paper, and an equidistant hatch algorithm is put forward and implemented in this work. Some experimental and simulation analysis were performed based on this algorithm, which shows that this method can bring significant improvements to the present RP process both in processing efficiency and parts quality. This algorithm was tested on the FDM system. It can also be applied to some other RP process, such as SLA and SLS with little modification. References [1] S. O. Onuh, K.K.B.Hon (1998), Application of the Taguchi method and new hatch styles for quality improvement in stereolithography, Proc. of the Inst. of Mechanical Engineers Part B, v212, 461-471.

[2] Deok-Soo Kim (1998), Polygon offsetting using a voronoi diagram and two stacks, Computer-aided Design, v30, n14, 1069-1075. [3] M. Bertoldi, M.A.Yardimci and C.M.Pistor (1998). Domain Decomposition and Surface Filling Curves In Tool-path Planning and Generation, Solid Freeform Fabrication Symposium Proceedings. Austin, Texas 267-274. [4] T. Wasser, A. Dhar Jayal, and C. Pistor (1999). Implementation and Evaluation of Novel Buildstyles in Fused Deposition Modeling (FDM), Solid Freeform Fabrication Symposium Proceedings, Austin, Texas, 95-102. [5] P. Kulkarni and D.Dutta (1999), Deposition Strategies and Resulting Part stiffnesses in Fused Deposition Modeling, ASME. Journal of Manufacturing Science and Engineering, v121 93-103. [6] J. O’Rourke (1994). Computational Geometry In C, Cambridge, Cambridge University Press, Cambridge. [7] ACS Motion Controllers Software Guide, A.C.S Elec- tronics Ltd.

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