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Optimization of process planning for reducing material consumption in additive manufacturing
Journal of Manufacturing Systems 44 (2017) 65–78
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Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys
Technical Paper
Optimization of process planning for reducing material consumption in additive manufacturing Yuan Jin a,∗ , Jianke Du a , Yong He b a b
School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 31 October 2016 Received in revised form 2 May 2017 Accepted 9 May 2017 Keywords: Additive manufacturing Material consumption Sliced data Self-support Skeleton-based path
a b s t r a c t The emergence of Additive Manufacturing (AM) technologies brings in the reduction of material consumption in terms of avoiding the repeated fabrication of dies as well as comparatively high material efficiency. However, despite of widespread application and evident advantages over conventional manufacturing techniques, AM still suffers from long lead time and redundant material usage when fabricating large-volume solid objects. This fact would definitely restrict the diffusion of AM technology. Based on this, a design strategy is proposed in this paper from the perspective of process planning focusing on the material consumption in additive manufacturing of relatively large-volume solid parts. Instead of processing the digital models directly, the sliced data of digital models is adopted for the design and optimization, and finally outputting the paths driving the AM machine to realize the practical fabrication. The sliced contours of the model are obtained based on a given layer thickness at first. Subsequently, the areas to be filled on each layer are determined according to the input contours and the self-supporting capability of the material. The interior regions confined by the generated internal contours do not need to be filled necessarily because they have no effect on the parts’ geometry and the materials can be saved accordingly. At last, a skeleton-based path planning method is utilized to address the long and narrow geometry to improve the deposition performance and surface quality. Several tests are used to verify the proposed strategy and the results show its effectiveness and feasibility in reducing the material consumption, enabling AM to be a more environmental friendly and sustainable manufacturing method. © 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction Additive Manufacturing (AM), also referred to as Rapid Prototyping, Solid Freeform Fabrication, Layered Manufacturing, or 3D printing more popularly, has been utilized in an increasingly variety of industries, including the fabrication of prototypes and functional parts in both biomedical and manufacturing fields. AM is a family of technologies that are capable of fabricating parts by joining and building up material with a layer-by-layer paradigm. The biggest advantage of this emerging technology is the ability to build parts directly from the digital representation of models without any geometrical limitations that enables AM to be an excellent alternative compared to conventional manufacturing techniques like machining, injection molding, and die-casting for fabricating highly customized objects [1]. There are a wide range of materials that are applicable in AM currently, such as metal, plastic, ceramic,
∗ Corresponding author. E-mail address: [email protected] (Y. Jin).
or composite materials with different forms, like powder, filament, or liquid. Based on the used materials and forming processes, seven categories are classified by ASTM International Committee F42: material extrusion, material binding, binder jetting, sheet lamination, vat photo-polymerization, powder bed fusion and directed energy deposition [2]. Although the joining details and the forming equipments of different AM categories vary from each other dramatically, they share the same fundamental forming principle: all parts are built along a single deposition direction(bottom up or top down)with a layer-by-layer joining process. The characteristics of AM make it inherently suitable for building parts with complex geometry and structure in relatively small volumes. But fabricating parts with quite large volumes can be very time consuming since much time is spent on filling the interior areas of each layer and the number of layers is commonly very large to ensure the desirable fabrication accuracy and resolution. Current researches on AM are mainly focusing on two aspects: one is the new forming technique and material [3–6], and the other is the process planning [7–9]. Process planning refers to several techniques and methods of transforming the digital model to
http://dx.doi.org/10.1016/j.jmsy.2017.05.003 0278-6125/© 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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the final part, including the CAD file processing [10], orientation selection [11], support generation [12], slicing [13], path generation [14], and post-processing [15]. All of these steps are critical in affecting the part quality and fabrication efficiency. Many works have been done from the process planning to improve the part quality which has long been criticized compared to conventional machining methods and is the major concern when extending the industrial applications. On the other hand, some researchers aimed to decrease the build time via some optimizations in the process planning, such as reducing the volume of support structures, adaptively slicing to reduce the number of layers, or intelligent path planning. However, few studies, so far, have tried to enhance the AM technology in terms of reducing the material consumption, which belongs to the process sustainability [16]. Based on the analyses from the perspective of life cycle, the adoption of AM could have significant savings in the production and use phases of a product [17]. The savings in the production stage stems from reduced material inputs and shorter supply chains than traditional machining methods. In the use phase, additively fabricated lightweight components enable energy consumption to be reduced. Despite of these advantages, the material waste is still a concern among different AM categories. For example, fabricating parts with overhanging features using Fused Deposition Modeling (FDM) or SLA tends to generate waste in the form of support structure, which is required for successful fabrication of the part, while to be removed in the post processing. Besides, a large volume of material is used for filling the interior of solid parts, but its function is not as significant as that in forming the surface boundary. This part of material, therefore, can be saved on the basis of acceptable geometrical accuracy and mechanical strength. The aim of this work is to optimize the material consumption for AM via some methodologies in the process planning. As mentioned before, process planning serves as a bridge between digital models and machines by transferring the models into codes that can guide and control the hardware. The process planning of different AM technologies usually has similar procedures and mainly consists of four steps: orientation selection, support generation, slicing and path planning. Each step affects the material use from different aspects and the details are demonstrated in Fig. 1 taking a dumbbell as an example. The part orientation refers to the location and direction of the part to be sliced and deposited. Besides the influence on the number of sliced layers and build time, a suitable part orientation can improve the part accuracy and surface finish by affecting the orientation of surfaces and support structure required for building the part [18]. In this step, the required volume of support structures is the major factor affecting the material consumption. Based on the determined orientation, overhangs are recognized to generate support structures that would be removed in the post processing phase [12]. In the support generation, several technical factors should be taken into account, such as material consumption, build time, and surface roughness. As intelligent design of support structures can reduce the required materials, it has become a future direction of AM technologies [19,20]. Additionally, more flexible and robust support generation approaches are required as the objects to be fabricated become increasingly complex and complicated. Afterwards, a slicing procedure is applied on the model with a set of paralleling planes that are perpendicular to the part orientation being adopted to intersect with the model, and the intersected boundaries on the part surface are obtained. The slicing process has little effect on the material consumption since the only related parameter, layer thickness, only affect the number of sliced layers. Path planning is another crucial task in AM to generate the trajectory for deposition work based on the interior filling requirements [21]. Different types of path patterns have been developed and would bring in varying material usage. However, these path patterns are invented mainly
from the view of improving the deposition quality and enhancing the fabrication efficiency, while the influence on the material consumption is commonly ignored. Although the issue of material waste belongs to the process sustainability and some literatures are available on AM from sustainability point of view, there has been little research on the optimization of material use in the AM process. [16] pointed out that material waste is very prominent in laser-based AM devices such as selective laser sintering and direct metal laser sintering and they built a mathematical model to quantify the material wastage in the fabrication process. In the optimization of material usage with their established model, the surface quality and geometrical accuracy were additionally considered. [22] presented a method to save materials by optimizing internal lightweight structures of additively fabricated parts, and to improve the process efficiency by optimizing AM process parameters. [23] explained that it was not the reality in the powder-based AM process that the unfused powder could be reused completely and an amount of material would be wasted in fact. To improve the material efficiency, they adopted two different kinds of nozzle with different efficiency. [24] built a layer deposition system with a passive visual sensor and an improved self-learning neuro control of deposition bead width to decrease the material wastes in gas metal arc welding–based AM process. The visual sensor was used to capture the weld bead images and some processing algorithms were applied on the images to pick up the characteristic information. After that, the controller was to keep the deposited bead widths of various layers consistent. The method proposed by them could bring in more than 10% reduction in the material consumption compared with the open-loop control system. To the best of our knowledge, no literature has been published so far about the optimization of material consumption by means of improving the process planning of AM. Besides the sustainable effect, the reduction of employing materials can accordingly shorten the build time that is also important for the enhancement of AM technology. So, it is not only meaningful but also necessary to have some effective methods and strategies to optimize the material consumption in AM process. This paper focuses on the reduction of materials with some strategies in the process planning phase by fully considering the technical characteristics of AM, mainly for the fabrication of large-volume solid parts. Current practice in building solid objects usually uses sparse filling paradigm to fill the whole interior and a large amount of materials are adopted even though they have no specific function under some circumstances. To deal with this issue, a design strategy applied in the process planning to reduce the material for AM processes is proposed. In the present strategy, the sliced layers are used to obtain the areas to be filled based on the input contours of each layer and the self-supporting capability of the material is fully considered. Afterwards, a skeleton-based path is utilized to fill the obtained long and narrow regions. By integrating the proposed strategy in the process planning stage, large amount of materials can be saved at little expense of physical performance, such as mechanical strength and part integrity. Among different AM processes, the extrusion-based AM is chosen for easy illustration in this paper, and it can be easily extended to other types of AM processes with a few modifications based on the detailed technical characteristics. The structure of this paper is arranged as follows. In Section 2, the details of the proposed strategy are described, including three subsections. The first subsection introduces the self-supportingbased strategy to reduce the internal filling volumes; the second subsection presents the implementation of the proposed strategy with sliced data of the model; and the last subsection is about a novel filling path pattern for depositing the obtained areas with long and narrow geometry. Section 3 demonstrates some tests of
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Fig. 1. Illustration of process planning in AM.
the proposed strategy and some discussions. The last section ends the paper with some conclusions. 2. Methods Minimizing the material consumption via the optimization of part orientation is not detailed in this paper since it has been reported elsewhere in some literatures [25]. So our study is based on the assumption that an optimized part orientation has been selected. Our work mainly focuses on the optimization of internal filling to reduce the material consumption. 2.1. Self-supporting-based strategy In the AM process, parts are formed by joining materials layer upon layer, which means each layer is deposited on its prior layers. Such fabrication paradigm would result in an intuitive fact that the current layer cannot be deposited successfully if there are substantial overhanging areas without the assistance of some additional supports underneath. This is the reason why support structure is required among a large group of AM techniques except that some powder-based AM processes can be fully self-supported by the powders. During the deposition process, an overhanging area that can be fabricated without adding support is called self-supported. The angle between the tangent plane along the part surface of the area and the building direction is called the self-supporting angle ␣, as illustrated in Fig. 2(a), whose value is dependent on the material properties and some process parameters. In order to
reduce consumed material volume to the maximum extent, the self-supporting ability of fabricated parts should be fully considered. After the part has been sliced into a large number of layers and deposited with beads, the self-supporting angle ␣ is analyzed as Fig. 2 (b). With a given layer thickness t and the overhang length l, the self-supporting angle is expressed as ˛ = arctan
l t
(1)
The outmost bead on the upper layer is supposed to be balanced under the combining action of gravity, normal force from the below layers, and the lateral and vertical adhesive force with its adjacent beads. As the interaction between bonded materials is quite complex and mutable, the detailed force analysis is difficult to conduct and cannot provide a reliable benchmark for the determination of self-supporting angle. In general, the self-supporting angle is affected by the mass ratio ı of overhanging part and inside part on the outmost deposited bead, namely ı=
l w−l
(2)
where w is the bead width, which is determined by some process parameters as illustrated in Fig. 2(c). For example, the bead width is determined by the nozzle size and the layer thickness in extrusionbased AM processes, while it is affected by the spot diameter of the laser beam in laser-based AM processes. With a given maximum ı
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Fig. 2. Demonstration of self-supporting capability.
Fig. 3. The flow chart of the internal optimization method.
and the bead width is considered as w, the maximal self-supporting angle can be obtained as ˛ = arctan
ımax w
1 + ımax t
(3)
The self-supporting capability has been fully considered in the design of the model, as well as the orientation determination stage, but it has not been adopted in the optimization of internal filling yet. To address this, a method to optimize the internal filling can be developed as illustrated in Fig. 3. The input is arbitrary CAD models, which are commonly solid and large-volume. The interior is modified and optimized procedurally to reduce the internal volume to be filled based on the self-supporting angle. Then, the processed parts are undergone general process planning stage to output the codes to control the AM hardware. The consumed material to fill the modified parts is largely decreased due to the reduction of the volume to be filled. Fig. 4 shows a simple example on the optimization of a cube. The input is a solid cube and the general internal filling is as illustrated in Fig. 4(a). The internal volume is the whole interior of the cube which is filled with relatively sparse structures without any optimization. By contrast, the internal volume to be filled can be optimized by modifying its interior topology to give full play of the self-supporting capability, as illustrated in Figs. 4 (b) and (c). It should be noticed that the inclination angle of the generated
internal surface cannot go beyond the maximal self-supporting angle. The self-supporting angle is selected as 45◦ in the example. From Fig. 4, it can be obviously seen that the fabrication of modified parts can save some materials to be consumed in processing a same CAD part. With the modified internal topology, the part itself can be fabricated smoothly without any other additional structures in the internal space due to the consideration of the self-supporting capability. There are two optional optimized internal structures as illustrated in Fig. 4 (b) and (c) based on the locations. For easy classification, they can be termed as inward method and outward method respectively. Specifically, in the inward method, the cross section of the generated internal structure that is used to support the part surface shrinks gradually from top down as illustrated in Fig. 5(a), while the cross section of the generated internal structure spreads out from top down as illustrated in Fig. 5(b) in the outward method. In both method, the solid part is shelled and hollowed firstly based on the requirement of the wall thickness. The inward method uses an umbrella-like structure inside the part to support the top (or inclined) surface. So a pillar-like structure is usually required as shown in Fig. 4 (b), while this issue is rare in the outward method. The outward method adopts a wall thickening strategy to adaptively thicken the wall to assist surfaces with inclination angle larger than maximal self-supporting angle after the hollowing process. Obviously, the latter method would result in much better mechanical integrity as the generated internal structures are combined into the wall. So, the outward method is chosen in this work.
Fig. 4. General internal filling versus optimized internal filling.
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Fig. 5. Demonstration of inward and outward method.
Fig. 6. The practical implementation of the proposed internal optimization method.
2.2. Implementation with sliced data Based on the description of self-supporting-based internal optimization, the key is the generation of internal topology to save the volume to be filled. To achieve this goal, the input 3D models should be analyzed firstly just as illustrated in Fig. 3. The geometrical analysis on the CAD models which are commonly comprised of large number of triangles is time consuming and computational expensive due to three dimensional operations. In our previous study [12], the sliced data of the model was adopted to recognize the external and internal support areas and it was proven that the Boolean operation between adjacent 2D layers could effectively reflect the geometric information of the 3D model. So, we also use the sliced layers of the model in this work to realize the internal optimization. The optimization process is integrated into the process planning as illustrated in Fig. 6. As shown in Fig. 7, the proposed method to generate the internal topology based on the self-supporting capability is arranged into a flowchart. The input tessellated CAD model is firstly oriented and sliced, and then the proposed algorithm is applied on the output 2D layers using a top down process. The subsequent task is an iteration process to find out the internal contour for each layer based on the input boundary and boundaries of its adjacent layers. As the generated internal structures with the outward method are connected to the wall, the wall thickness becomes larger on these layers. Therefore, the outward method can be also called as wall thickening strategy. Two requirements need to be considered in generating the internal contours of each layer, one is that the wall thickness should be guaranteed to meet the strength requirement, and the other is that the inclination angle of internal structures should not go beyond the
maximal self-supporting angle. According to this, the internal contour of each layer is generated with three steps. The first step is to generate an internal contour to satisfy the thickness requirement; and the next step is to obtain another internal contour based on the self-supporting capability; the last step is to unite two internal contours with a Boolean operation. As the wall thickness refers to the nearest distance between the point on internal contours and the exterior surface of the part, the spatial geometric information of the current layer (including the planar geometry and the vertical location) should be involved. Therefore, besides the boundary of the current layer, the boundaries of its adjacent layers should also be considered to obtain the internal contour. The detailed algorithm is illustrated in Fig. 8. Before the implementation, the input boundaries of all the layers are offset inwards by a distance of the required minimal wall thickness T. By doing this, the horizontal thickness can be guaranteed. For a specific layer, the vertical thickness is ensured by considering its above and below layers, these associated layers are termed as influencing layers. The number of influencing layers above the current layer is determined by the required minimal wall thickness T and the layer height t. The total height of all the above influencing layers should be larger than T. So the number of above influencing layer is [T/t] + 1, where [] is the integral symbol. At the same time, the total height of below influencing layers is also larger than T. With the identified influencing layers, an intersection operation is applied on the projections of the offset contours of all the influencing layers to obtain the internal contour of the current layer. Afterwards, the self-supporting capability is adopted to further modify the internal contours. The detailed flowchart is illustrated in Fig. 9. For a given layer Li which has no internal contour Ci1 generated from the last step, it is impossible to generate the internal
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Fig. 9. Flowchart to generate the internal contour based on the self-supporting capability.
Fig. 7. Flowchart to obtain the internal contour with sliced data.
Fig. 10. Demonstration of generating the internal contour Ci 2 according to Ci+ 1 .
Fig. 11. Demonstration of determining the internal contour Ci 2 according to Ci 1 .
Fig. 8. Flowchart of generating the internal contour based on thickness requirement.
contour Ci2 as the solid filling is required on this layer. The generation of another internal contour Ci2 is demonstrated as follows. If the internal contour Ci1 on the current layer Li exists, the next judgment is applied on the internal contour Ci+1 of the directly above layer Li+1 , where Ci+1 is the final internal contour on the layer Li+1 . If Ci+1 does exist, Ci+1 is offset outwards with the offset distance equaling to tan␣*t, where ␣ is the maximal self-supporting angle and t is the layer height. Then the offset contour is projected to Li vertically and the obtainable contour is the internal contour Ci2 of Li . This can be demonstrated in Fig. 10.
By contrast, if Ci+1 does not exist, the situation is completely different because there is no any reference contour on Li+1 for the generation of Ci2 . To address this case, the internal contour Ci2 is obtained by offsetting the Ci1 inwards iteratively taking tan␣*t as the offset distance. The terminate condition for the offsetting process is that the radius of the minimum circumscribed circle of the offset shape is smaller than tan␣*t. This shape is considered as the Ci2 of current layer. This circumstance usually appears among top layers and is demonstrated in Fig. 11. Next, a judgment is conducted to ensure that the thickness of generated internal structures is larger than the required wall thickness T. The judgment is performed by computing the radius of the maximal inscribed circle of each separate area. If the radius of one
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Fig. 12. Illustration of two general path patterns for filling the long and narrow geometry.
area is smaller than T, the contour is offset taking tan␣*t as the offset distance to enlarge this area until the radius of its maximal inscribed circle is larger than T. With the obtained internal contours Ci1 and Ci2 on the current layer Li , the internal contour Ci is generated by uniting these two internal contours. Specifically, the input boundary and Ci1 define one area Si1 , while the input boundary and Ci2 define another area Si2 , the Boolean union is performed on these two areas and the interior contour of the united area Si is Ci . So far, the internal contour of each layer is identified by considering both the wall thickness and the self-support capability, implying that the volume confined by the internal surface (the enveloping surface defined by internal contours of all the layers) and the exterior surface of the part can achieve desirable wall thickness and the maximal self-support ability. Therefore, only this type of volume needs to be filled, resulting in a large volume of materials can be saved accordingly. The subsequent step is to generate the filling paths inside the volume; the boundary of the filled area on each layer is confined by the generated internal contours and the original contour of input geometry.
2.3. Path planning For a specific layer, the areas to be filled are confined by the exterior boundary and the generated internal contours from last section, and commonly have long and narrow geometrical property. To fill shapes with such type of geometry, general filling path patterns cannot achieve desirable filling quality or long build time is required. As illustrated in Fig. 12, the general contour path would bring in several overfill issues when the distance between adjacent path elements is smaller than the expected path gap. This issue is very common in filling long and narrow geometry with contour parallel path patterns. One of typical direction parallel path patterns, zigzag path, would avoid the overfill issue, but long build time is required due to many sharp turns along the filling paths. In order to address the above mentioned issues, a new path planning method is proposed to fill shapes with long and narrow geometry exclusively; the flowchart is illustrated in Fig. 13. Note that the analyzing unit here is the shape that just has one exterior boundary and several internal contours because it can be easily extend to arbitrary shapes with any number of exterior boundaries. For demonstrative purpose, a shape shown in Fig. 13 (a) is adopted to explain the path generation method step by step.
Step 1: Generate the initial contour parallel paths based on the desired path space w and the input polygon. The input connected region is comprised of one exterior boundary and several internal contours. Generally, the exterior boundary is defined by a large number of line segments in counter-clockwise (CCW), while the internal contour is in clockwise (CW) for distinction. Then the contour parallel paths are generated by repeated offsetting with the distance of path space w as the offset distance. The offset distance of the first contours is half of the path space w for accurate deposition of the first loop. The contour paths are shown in Fig. 13 (b). Step 2: Analyze the potential overfilling and underfilling cases. Based on the parent/child relationship between contours, a tree representing the mutual relation between them can be built [26]. In the relation tree, one parent contour may have more than one children contour, and vice versa. The input exterior boundary and the internal contours are on the top of the established tree. As shown in Fig. 13 (c), the offset contours are indexed based on the information from the offsetting operations. The input contours are named as B1, B2,. . .Bi and their subsequent child contours are named as Bi-1, Bi-2,. . .Bi-j until one child contour has several children, the names are changed to Bi-j-1, Bi-j-2. . . Bi-j-k, etc. If one contour is obtained by offsetting two input contours Bm and Bn, its name is Bmn-1. The corresponding relationship tree is built up as shown in Fig. 13 (d) and the color of each node is the same as that in Fig. 13 (c) for easy visualization. All of the potential overfilling and underfilling cases can be analyzed based on the relationship tree and the geometry of offset contours. To analyze the path gap accurately, the medial axis transform (MAT) is adopted in this work. Medial axis transform (MAT) of a 2D shape can be used to concisely represent the domain shape and is very useful for analyzing the complex domain. The MAT is based on the medial axis, which geometrically bisects the domain and becomes the shape skeleton [27]. So the medial axis is also called as the skeleton. Two examples are shown in Fig. 14; the medial axis is bounded by the planar curve and is the set of the locus of centers of locally maximal circles that are tangent to the curve in two or more points. The red dot lines are the medial axis of the input geometry. The medial axis of a simple polygon can be visually described as a tree whose leaves are the vertices of the polygon, while the edges are either straight segments or arcs of parabolas [28]. From the definition of medial axis, the distance between two adjacent path segments can be approximately represented by the diameter of locally maximal inscribed circles. So it can be judged
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Fig. 13. Flowchart of the proposed path planning method.
from these circles whether overfill or underfill would appear or not. In the implementation, points are sampled on the obtained medial axis based on a predefined period length firstly. Then the diameters of corresponding maximal inscribed circles are computed. If the diameter of one circle is out of a certain range, like [0.8w, 1.25w], the distance between two associated paths at the center of this circle is considered beyond its proper range. If there are a certain
number of consecutive sampling points all satisfying this condition, the segment of medial axis containing these samples is recorded for the subsequent modification. Two cases may occur on the recorded segments of medial axis after the computation and selection. One case is that the diameter is smaller than the defined range, and the other case is that the diameter is larger than the defined range. These two cases are illus-
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Fig. 14. Demonstration of medial axis of shapes with (a) single contour and (b) multi-contours.
trated in Fig. 15. Corresponding methods are presented to generate the paths under these two circumstances in the next step. Besides the area confined by one contour and its child/parent contours, some areas confined by two adjacent contours that do not have containing/contained relationship also need to be analyzed to compute the diameter of the maximally inscribed circles. Specifically, if a contour has more than one parents and several brothers, all of these contours are required to be analyzed together. For
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example, in the relationship tree as shown in Fig. 13(d), the parents of contour B12-1 are B1-2 and B2-2, and it also has a brother contour B12-2, so the area confined by B1-2, B2-2, B12-1 and B122 requires the further geometrical analysis. The same situation appears on B12-1, B3-3, B123-1 and B123-2. Step 3: Generate a skeleton-based path. The subsequent step is to use a skeleton-based path to replace the associated contour path segments for the case where the diameter of maximally inscribed circles is smaller, or to insert into the areas where the diameter of maximally inscribed circles is larger. Fig. 16 illustrates the steps of the skeleton-based path generation for the former case. Step 3.1: The first step is to identify the segment of the medial axis selected from Step 2 based on the diameter of maximally inscribed circles. As the segment in Step 2 is selected according to a given range, it should be extended (or shortened) from two ends to enable the diameter of the maximally inscribed circle to equal to a proper limit value, like w. However, there are two exceptional situations. The first is that if the selected segment is closed, it is impossible to extend it and unnecessary to shorten it. Another exception is that the end of segment may extend to the whole medial axis to identify the end points if the diameters of all maximal inscribed circles within this contour are all smaller than the limit value. Fig. 16(a) shows the original ends and the extended ends and Fig. 16(b) shows the exceptions. Step 3.2: The next step is to get the corresponding tangent points on the contours by considering the maximally inscribed circles taking the end points as centers and tangent to the contours, as illustrated in Fig. 16(c); Step 3.3: Delete the segment of the original contour between two tangent points and connect the adjacent end points of the contour with a Hermite curve which can ensure smooth transition between them;
Fig. 15. Demonstration of two cases where the distance between paths is out of defined range.
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Fig. 16. Illustration of the wavy path generation process.
Step 3.4: Generate a new path based on the medial axis and the distance between the end point and the contour path is w/2, so it is called the skeleton-based path, as show in Fig. 16(d). As the medial axis transform is a complete shape descriptor and can be used to reconstruct the shape of the original domain[29], the geometric information of MAT allows the generation of path inside the domain to be very effective and feasible. Actually, there are some similar researches on the combination of skeleton-based path and contour parallel-based path in the traditional machining and these can be effectively adjusted to fit the path generation for additive manufacturing [30,31]. With the present method, the modified path for the shape in Fig. 12 is shown in Fig. 17. 3. Demonstration and discussion In this section, two 3D objects are used to validate the proposed process planning methodology. In the case studies, mainly two aspects are emphasized: one is the implementation of the optimized internal filling from the sliced file; another is the difference on the material consumption before and after optimization. In the evaluation of consumed materials, the length of generated paths, as well as the weight of printed parts is used for calculation. Fig. 17. Optimized filling path for long and narrow geometry.
3.1. Case study 1 In the first case, the proposed internal optimization strategy is applied to a non-rotational part. The selected part is symmetrical and has three roofs and two inclined surfaces that require additional supports for fabrication. The dimensions of the object along three axes are 112.3 mm, 50 mm and 70 mm respectively and the volume is 182278.058 cubic millimeter, as shown in Fig. 18(a). The layer height for slicing is 0.2 mm and there are totally 350 slices shown in Fig. 18(b). In the generation of internal contours, the maximal self-supporting angle is set as 45◦ and the desired wall thickness is set as 4 mm to determine the internal contour of the underneath layer based on the internal contour of the current layer,
this process is illustrated in Fig. 18(d). After all the layers are processed, the sliced model is shown in Fig. 18(c). The red polygons are the generated internal contours of each layer. To further demonstrate the self-supporting strategy, the cross section of the sliced modal in the front view is shown in Fig. 18(e). We can see that the maximal self-supporting angle can be reflected from the cross section and the part can be deposited smoothly with the consideration of the self-supporting capability. With the modified sliced data, including the input boundary and the generated internal contour, the next step is to generate the deposition path to fill areas for each layer. The path space is 0.55 mm here to generate the dense filling and the density for the
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Fig. 18. Demonstration of a non-rotational part (a) 3D part; (b) sliced data of the model; (c) generation of internal contours based on the sliced data; (d) internal contour generation; (e) cross section of (c).
Fig. 19. Comparison of filling path at different layers in the case study I.
sparse filling is 40%. For comparison purpose, three layers (20th, 100th and 302th) at different heights are chosen. As illustrated in Fig. 19, the first row shows the paths without optimization, while the second row is the layers with optimized internal structure. It can be observed that some areas which are filled in the former do not need to be filled in the latter and the deposition material can be saved accordingly.
3.2. Case study 2 The purpose of the second case study is to demonstrate the application of the proposed method to a rotational part which has pagoda-like geometry in the illustrated example. The part has
a volume of 284858.55 cubic millimeter with the dimensions in three axes are 107 mm, 107 mm and 76.346 mm respectively, as illustrated in Fig. 20(a). The layer thickness is 0.2 mm and there are totally 382 layers as shown in Fig. 20(b). The maximal selfsupporting angle is considered as 45◦ and the wall thickness is 4 mm in the generation of internal contours, as illustrated in Fig. 20(d). After the internal contours of all the layers have been generated, the sliced model is shown in Fig. 20(c). The interior red polygons are the generated internal contours. As the object can be obtained by rotating a cross section around a vertical axis, the self-supporting property can be observed from one of its cross sections, as illustrated in Fig. 20(e).
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Fig. 20. Demonstration of a rotational part (a) 3D part; (b) sliced data of the model; (c) generation of internal contours based on the sliced data; (d) internal contour generation; (e) cross section of (c).
Likewise, the subsequent step is to plan the deposition path to fill areas which is confined by the exterior boundaries and the generated internal contours for each layer. The path space is also set as 0.55 mm for the dense filling and the density for the sparse filling is 40%. Three layers (80th, 200th and 320th) belonging to different height ranges are selected and their deposition paths are generated based on the determined parameters. From Fig. 21, it can be observed that some filled areas in the former case remain as unfilled areas in the latter case, while the part can be build successfully, so materials can be saved in the practical deposition process using the proposed methodology.
3.3. Discussion To evaluate the material consumption, the length of generated path is firstly used to approximately represent the volume of consumed materials. In the extrusion-based AM, the volume of consumed materials can be obtained from the path length and the cross-sectional area of the deposited filament. In the first case study, the path length for depositing the non-optimization model is 644.14m, while it is reduced to 513.43 mm with the optimized internal topology. In this case, material saving can reach 20%. In the second case study, the path length is changed from 882.72 m to 574.26 m after using the proposed method. The comparison of the
Fig. 21. Comparison of filling path at different layers in case study II.
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due to the internal optimization. One main reason for the gap is the appearance of sharp edge in the internal surface where there are stress concentrations. This can be verified by the fact that the failure began from these zones during the experiments. In theory, this issue can be alleviated by rounding these edges, which can also be achieved using sliced data. Therefore, the slight reduction of the mechanical properties is reasonable and acceptable. Based on the above analysis, it appears that the proposed strategy can reduce the material consumption to additively fabricate parts without much compromise in the part’s mechanical performance. The reduction of the material consumption mainly owns to the optimization of internal topology which can be implemented with the sliced data and fabricated with layer-based manufacturing paradigm.
Fig. 22. Comparison of filling path length before and after optimization in two case studies.
material consumption before and after the optimization is shown in Fig. 22. To investigate the influence on the mechanical strength of fabricated parts brought by the internal optimization, the part in the case study I is additively fabricated using a Lulzbot TAZ3 FDM machine. The sliced files of the part before and after optimization are shown in Fig. 23(a) and the corresponding fabricated parts are shown in Fig. 23(b). The measured weight of the part without internal optimization is 80.7 g while the weight of the part after optimization is 64.5 g. Then, the compressive strength of fabricated parts is measured as illustrated in Fig. 23(c) and the load versus displacement data is collected as shown in Fig. 23(d) respectively. First failure is observed at 18.576 and 16.364 kN for part I and part II respectively. The second failure can be found at 11.834 and 10.92 kN from the stress-strain curve generated from the load displacement data as given in the figure. From the result, it is observed that the compressive strength and compressive stiffness are slightly decreased
4. Conclusion An AM process planning approach emphasizing on the internal optimization and the path planning has been developed in this paper to reduce the material consumption of additively fabricated parts, particularly for large and solid objects. The developed framework proposes an optimal internal topology considering the requirement of minimal wall thickness and the self-supporting capability. The optimal internal topology minimizes the total consumed materials by reducing the volume of the whole part to be filled, and thus saves the build time. Instead of the input CAD file itself, its sliced data is adopted in the internal optimization to reduce the computational cost and avoid errors in addressing 3D geometric operations. Meanwhile, the filling quality is enhanced by utilizing a skeleton-based method for evaluation and path optimization. Two case studies are demonstrated to validate the feasibility and effectiveness of the proposed methodology with acceptable mechanical strength and integrity. The proposed process planning method can help different AM technologies to be more environmental friendly and suitable manufacturing methods with less environmental impacts.
Fig. 23. Investigation of the influence on the mechanical strength of the proposed internal optimization method.
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Contents lists available at ScienceDirect
Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys
Technical Paper
Optimization of process planning for reducing material consumption in additive manufacturing Yuan Jin a,∗ , Jianke Du a , Yong He b a b
School of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
a r t i c l e
i n f o
Article history: Received 31 October 2016 Received in revised form 2 May 2017 Accepted 9 May 2017 Keywords: Additive manufacturing Material consumption Sliced data Self-support Skeleton-based path
a b s t r a c t The emergence of Additive Manufacturing (AM) technologies brings in the reduction of material consumption in terms of avoiding the repeated fabrication of dies as well as comparatively high material efficiency. However, despite of widespread application and evident advantages over conventional manufacturing techniques, AM still suffers from long lead time and redundant material usage when fabricating large-volume solid objects. This fact would definitely restrict the diffusion of AM technology. Based on this, a design strategy is proposed in this paper from the perspective of process planning focusing on the material consumption in additive manufacturing of relatively large-volume solid parts. Instead of processing the digital models directly, the sliced data of digital models is adopted for the design and optimization, and finally outputting the paths driving the AM machine to realize the practical fabrication. The sliced contours of the model are obtained based on a given layer thickness at first. Subsequently, the areas to be filled on each layer are determined according to the input contours and the self-supporting capability of the material. The interior regions confined by the generated internal contours do not need to be filled necessarily because they have no effect on the parts’ geometry and the materials can be saved accordingly. At last, a skeleton-based path planning method is utilized to address the long and narrow geometry to improve the deposition performance and surface quality. Several tests are used to verify the proposed strategy and the results show its effectiveness and feasibility in reducing the material consumption, enabling AM to be a more environmental friendly and sustainable manufacturing method. © 2017 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction Additive Manufacturing (AM), also referred to as Rapid Prototyping, Solid Freeform Fabrication, Layered Manufacturing, or 3D printing more popularly, has been utilized in an increasingly variety of industries, including the fabrication of prototypes and functional parts in both biomedical and manufacturing fields. AM is a family of technologies that are capable of fabricating parts by joining and building up material with a layer-by-layer paradigm. The biggest advantage of this emerging technology is the ability to build parts directly from the digital representation of models without any geometrical limitations that enables AM to be an excellent alternative compared to conventional manufacturing techniques like machining, injection molding, and die-casting for fabricating highly customized objects [1]. There are a wide range of materials that are applicable in AM currently, such as metal, plastic, ceramic,
∗ Corresponding author. E-mail address: [email protected] (Y. Jin).
or composite materials with different forms, like powder, filament, or liquid. Based on the used materials and forming processes, seven categories are classified by ASTM International Committee F42: material extrusion, material binding, binder jetting, sheet lamination, vat photo-polymerization, powder bed fusion and directed energy deposition [2]. Although the joining details and the forming equipments of different AM categories vary from each other dramatically, they share the same fundamental forming principle: all parts are built along a single deposition direction(bottom up or top down)with a layer-by-layer joining process. The characteristics of AM make it inherently suitable for building parts with complex geometry and structure in relatively small volumes. But fabricating parts with quite large volumes can be very time consuming since much time is spent on filling the interior areas of each layer and the number of layers is commonly very large to ensure the desirable fabrication accuracy and resolution. Current researches on AM are mainly focusing on two aspects: one is the new forming technique and material [3–6], and the other is the process planning [7–9]. Process planning refers to several techniques and methods of transforming the digital model to
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the final part, including the CAD file processing [10], orientation selection [11], support generation [12], slicing [13], path generation [14], and post-processing [15]. All of these steps are critical in affecting the part quality and fabrication efficiency. Many works have been done from the process planning to improve the part quality which has long been criticized compared to conventional machining methods and is the major concern when extending the industrial applications. On the other hand, some researchers aimed to decrease the build time via some optimizations in the process planning, such as reducing the volume of support structures, adaptively slicing to reduce the number of layers, or intelligent path planning. However, few studies, so far, have tried to enhance the AM technology in terms of reducing the material consumption, which belongs to the process sustainability [16]. Based on the analyses from the perspective of life cycle, the adoption of AM could have significant savings in the production and use phases of a product [17]. The savings in the production stage stems from reduced material inputs and shorter supply chains than traditional machining methods. In the use phase, additively fabricated lightweight components enable energy consumption to be reduced. Despite of these advantages, the material waste is still a concern among different AM categories. For example, fabricating parts with overhanging features using Fused Deposition Modeling (FDM) or SLA tends to generate waste in the form of support structure, which is required for successful fabrication of the part, while to be removed in the post processing. Besides, a large volume of material is used for filling the interior of solid parts, but its function is not as significant as that in forming the surface boundary. This part of material, therefore, can be saved on the basis of acceptable geometrical accuracy and mechanical strength. The aim of this work is to optimize the material consumption for AM via some methodologies in the process planning. As mentioned before, process planning serves as a bridge between digital models and machines by transferring the models into codes that can guide and control the hardware. The process planning of different AM technologies usually has similar procedures and mainly consists of four steps: orientation selection, support generation, slicing and path planning. Each step affects the material use from different aspects and the details are demonstrated in Fig. 1 taking a dumbbell as an example. The part orientation refers to the location and direction of the part to be sliced and deposited. Besides the influence on the number of sliced layers and build time, a suitable part orientation can improve the part accuracy and surface finish by affecting the orientation of surfaces and support structure required for building the part [18]. In this step, the required volume of support structures is the major factor affecting the material consumption. Based on the determined orientation, overhangs are recognized to generate support structures that would be removed in the post processing phase [12]. In the support generation, several technical factors should be taken into account, such as material consumption, build time, and surface roughness. As intelligent design of support structures can reduce the required materials, it has become a future direction of AM technologies [19,20]. Additionally, more flexible and robust support generation approaches are required as the objects to be fabricated become increasingly complex and complicated. Afterwards, a slicing procedure is applied on the model with a set of paralleling planes that are perpendicular to the part orientation being adopted to intersect with the model, and the intersected boundaries on the part surface are obtained. The slicing process has little effect on the material consumption since the only related parameter, layer thickness, only affect the number of sliced layers. Path planning is another crucial task in AM to generate the trajectory for deposition work based on the interior filling requirements [21]. Different types of path patterns have been developed and would bring in varying material usage. However, these path patterns are invented mainly
from the view of improving the deposition quality and enhancing the fabrication efficiency, while the influence on the material consumption is commonly ignored. Although the issue of material waste belongs to the process sustainability and some literatures are available on AM from sustainability point of view, there has been little research on the optimization of material use in the AM process. [16] pointed out that material waste is very prominent in laser-based AM devices such as selective laser sintering and direct metal laser sintering and they built a mathematical model to quantify the material wastage in the fabrication process. In the optimization of material usage with their established model, the surface quality and geometrical accuracy were additionally considered. [22] presented a method to save materials by optimizing internal lightweight structures of additively fabricated parts, and to improve the process efficiency by optimizing AM process parameters. [23] explained that it was not the reality in the powder-based AM process that the unfused powder could be reused completely and an amount of material would be wasted in fact. To improve the material efficiency, they adopted two different kinds of nozzle with different efficiency. [24] built a layer deposition system with a passive visual sensor and an improved self-learning neuro control of deposition bead width to decrease the material wastes in gas metal arc welding–based AM process. The visual sensor was used to capture the weld bead images and some processing algorithms were applied on the images to pick up the characteristic information. After that, the controller was to keep the deposited bead widths of various layers consistent. The method proposed by them could bring in more than 10% reduction in the material consumption compared with the open-loop control system. To the best of our knowledge, no literature has been published so far about the optimization of material consumption by means of improving the process planning of AM. Besides the sustainable effect, the reduction of employing materials can accordingly shorten the build time that is also important for the enhancement of AM technology. So, it is not only meaningful but also necessary to have some effective methods and strategies to optimize the material consumption in AM process. This paper focuses on the reduction of materials with some strategies in the process planning phase by fully considering the technical characteristics of AM, mainly for the fabrication of large-volume solid parts. Current practice in building solid objects usually uses sparse filling paradigm to fill the whole interior and a large amount of materials are adopted even though they have no specific function under some circumstances. To deal with this issue, a design strategy applied in the process planning to reduce the material for AM processes is proposed. In the present strategy, the sliced layers are used to obtain the areas to be filled based on the input contours of each layer and the self-supporting capability of the material is fully considered. Afterwards, a skeleton-based path is utilized to fill the obtained long and narrow regions. By integrating the proposed strategy in the process planning stage, large amount of materials can be saved at little expense of physical performance, such as mechanical strength and part integrity. Among different AM processes, the extrusion-based AM is chosen for easy illustration in this paper, and it can be easily extended to other types of AM processes with a few modifications based on the detailed technical characteristics. The structure of this paper is arranged as follows. In Section 2, the details of the proposed strategy are described, including three subsections. The first subsection introduces the self-supportingbased strategy to reduce the internal filling volumes; the second subsection presents the implementation of the proposed strategy with sliced data of the model; and the last subsection is about a novel filling path pattern for depositing the obtained areas with long and narrow geometry. Section 3 demonstrates some tests of
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Fig. 1. Illustration of process planning in AM.
the proposed strategy and some discussions. The last section ends the paper with some conclusions. 2. Methods Minimizing the material consumption via the optimization of part orientation is not detailed in this paper since it has been reported elsewhere in some literatures [25]. So our study is based on the assumption that an optimized part orientation has been selected. Our work mainly focuses on the optimization of internal filling to reduce the material consumption. 2.1. Self-supporting-based strategy In the AM process, parts are formed by joining materials layer upon layer, which means each layer is deposited on its prior layers. Such fabrication paradigm would result in an intuitive fact that the current layer cannot be deposited successfully if there are substantial overhanging areas without the assistance of some additional supports underneath. This is the reason why support structure is required among a large group of AM techniques except that some powder-based AM processes can be fully self-supported by the powders. During the deposition process, an overhanging area that can be fabricated without adding support is called self-supported. The angle between the tangent plane along the part surface of the area and the building direction is called the self-supporting angle ␣, as illustrated in Fig. 2(a), whose value is dependent on the material properties and some process parameters. In order to
reduce consumed material volume to the maximum extent, the self-supporting ability of fabricated parts should be fully considered. After the part has been sliced into a large number of layers and deposited with beads, the self-supporting angle ␣ is analyzed as Fig. 2 (b). With a given layer thickness t and the overhang length l, the self-supporting angle is expressed as ˛ = arctan
l t
(1)
The outmost bead on the upper layer is supposed to be balanced under the combining action of gravity, normal force from the below layers, and the lateral and vertical adhesive force with its adjacent beads. As the interaction between bonded materials is quite complex and mutable, the detailed force analysis is difficult to conduct and cannot provide a reliable benchmark for the determination of self-supporting angle. In general, the self-supporting angle is affected by the mass ratio ı of overhanging part and inside part on the outmost deposited bead, namely ı=
l w−l
(2)
where w is the bead width, which is determined by some process parameters as illustrated in Fig. 2(c). For example, the bead width is determined by the nozzle size and the layer thickness in extrusionbased AM processes, while it is affected by the spot diameter of the laser beam in laser-based AM processes. With a given maximum ı
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Fig. 2. Demonstration of self-supporting capability.
Fig. 3. The flow chart of the internal optimization method.
and the bead width is considered as w, the maximal self-supporting angle can be obtained as ˛ = arctan
ımax w
1 + ımax t
(3)
The self-supporting capability has been fully considered in the design of the model, as well as the orientation determination stage, but it has not been adopted in the optimization of internal filling yet. To address this, a method to optimize the internal filling can be developed as illustrated in Fig. 3. The input is arbitrary CAD models, which are commonly solid and large-volume. The interior is modified and optimized procedurally to reduce the internal volume to be filled based on the self-supporting angle. Then, the processed parts are undergone general process planning stage to output the codes to control the AM hardware. The consumed material to fill the modified parts is largely decreased due to the reduction of the volume to be filled. Fig. 4 shows a simple example on the optimization of a cube. The input is a solid cube and the general internal filling is as illustrated in Fig. 4(a). The internal volume is the whole interior of the cube which is filled with relatively sparse structures without any optimization. By contrast, the internal volume to be filled can be optimized by modifying its interior topology to give full play of the self-supporting capability, as illustrated in Figs. 4 (b) and (c). It should be noticed that the inclination angle of the generated
internal surface cannot go beyond the maximal self-supporting angle. The self-supporting angle is selected as 45◦ in the example. From Fig. 4, it can be obviously seen that the fabrication of modified parts can save some materials to be consumed in processing a same CAD part. With the modified internal topology, the part itself can be fabricated smoothly without any other additional structures in the internal space due to the consideration of the self-supporting capability. There are two optional optimized internal structures as illustrated in Fig. 4 (b) and (c) based on the locations. For easy classification, they can be termed as inward method and outward method respectively. Specifically, in the inward method, the cross section of the generated internal structure that is used to support the part surface shrinks gradually from top down as illustrated in Fig. 5(a), while the cross section of the generated internal structure spreads out from top down as illustrated in Fig. 5(b) in the outward method. In both method, the solid part is shelled and hollowed firstly based on the requirement of the wall thickness. The inward method uses an umbrella-like structure inside the part to support the top (or inclined) surface. So a pillar-like structure is usually required as shown in Fig. 4 (b), while this issue is rare in the outward method. The outward method adopts a wall thickening strategy to adaptively thicken the wall to assist surfaces with inclination angle larger than maximal self-supporting angle after the hollowing process. Obviously, the latter method would result in much better mechanical integrity as the generated internal structures are combined into the wall. So, the outward method is chosen in this work.
Fig. 4. General internal filling versus optimized internal filling.
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Fig. 5. Demonstration of inward and outward method.
Fig. 6. The practical implementation of the proposed internal optimization method.
2.2. Implementation with sliced data Based on the description of self-supporting-based internal optimization, the key is the generation of internal topology to save the volume to be filled. To achieve this goal, the input 3D models should be analyzed firstly just as illustrated in Fig. 3. The geometrical analysis on the CAD models which are commonly comprised of large number of triangles is time consuming and computational expensive due to three dimensional operations. In our previous study [12], the sliced data of the model was adopted to recognize the external and internal support areas and it was proven that the Boolean operation between adjacent 2D layers could effectively reflect the geometric information of the 3D model. So, we also use the sliced layers of the model in this work to realize the internal optimization. The optimization process is integrated into the process planning as illustrated in Fig. 6. As shown in Fig. 7, the proposed method to generate the internal topology based on the self-supporting capability is arranged into a flowchart. The input tessellated CAD model is firstly oriented and sliced, and then the proposed algorithm is applied on the output 2D layers using a top down process. The subsequent task is an iteration process to find out the internal contour for each layer based on the input boundary and boundaries of its adjacent layers. As the generated internal structures with the outward method are connected to the wall, the wall thickness becomes larger on these layers. Therefore, the outward method can be also called as wall thickening strategy. Two requirements need to be considered in generating the internal contours of each layer, one is that the wall thickness should be guaranteed to meet the strength requirement, and the other is that the inclination angle of internal structures should not go beyond the
maximal self-supporting angle. According to this, the internal contour of each layer is generated with three steps. The first step is to generate an internal contour to satisfy the thickness requirement; and the next step is to obtain another internal contour based on the self-supporting capability; the last step is to unite two internal contours with a Boolean operation. As the wall thickness refers to the nearest distance between the point on internal contours and the exterior surface of the part, the spatial geometric information of the current layer (including the planar geometry and the vertical location) should be involved. Therefore, besides the boundary of the current layer, the boundaries of its adjacent layers should also be considered to obtain the internal contour. The detailed algorithm is illustrated in Fig. 8. Before the implementation, the input boundaries of all the layers are offset inwards by a distance of the required minimal wall thickness T. By doing this, the horizontal thickness can be guaranteed. For a specific layer, the vertical thickness is ensured by considering its above and below layers, these associated layers are termed as influencing layers. The number of influencing layers above the current layer is determined by the required minimal wall thickness T and the layer height t. The total height of all the above influencing layers should be larger than T. So the number of above influencing layer is [T/t] + 1, where [] is the integral symbol. At the same time, the total height of below influencing layers is also larger than T. With the identified influencing layers, an intersection operation is applied on the projections of the offset contours of all the influencing layers to obtain the internal contour of the current layer. Afterwards, the self-supporting capability is adopted to further modify the internal contours. The detailed flowchart is illustrated in Fig. 9. For a given layer Li which has no internal contour Ci1 generated from the last step, it is impossible to generate the internal
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Fig. 9. Flowchart to generate the internal contour based on the self-supporting capability.
Fig. 7. Flowchart to obtain the internal contour with sliced data.
Fig. 10. Demonstration of generating the internal contour Ci 2 according to Ci+ 1 .
Fig. 11. Demonstration of determining the internal contour Ci 2 according to Ci 1 .
Fig. 8. Flowchart of generating the internal contour based on thickness requirement.
contour Ci2 as the solid filling is required on this layer. The generation of another internal contour Ci2 is demonstrated as follows. If the internal contour Ci1 on the current layer Li exists, the next judgment is applied on the internal contour Ci+1 of the directly above layer Li+1 , where Ci+1 is the final internal contour on the layer Li+1 . If Ci+1 does exist, Ci+1 is offset outwards with the offset distance equaling to tan␣*t, where ␣ is the maximal self-supporting angle and t is the layer height. Then the offset contour is projected to Li vertically and the obtainable contour is the internal contour Ci2 of Li . This can be demonstrated in Fig. 10.
By contrast, if Ci+1 does not exist, the situation is completely different because there is no any reference contour on Li+1 for the generation of Ci2 . To address this case, the internal contour Ci2 is obtained by offsetting the Ci1 inwards iteratively taking tan␣*t as the offset distance. The terminate condition for the offsetting process is that the radius of the minimum circumscribed circle of the offset shape is smaller than tan␣*t. This shape is considered as the Ci2 of current layer. This circumstance usually appears among top layers and is demonstrated in Fig. 11. Next, a judgment is conducted to ensure that the thickness of generated internal structures is larger than the required wall thickness T. The judgment is performed by computing the radius of the maximal inscribed circle of each separate area. If the radius of one
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Fig. 12. Illustration of two general path patterns for filling the long and narrow geometry.
area is smaller than T, the contour is offset taking tan␣*t as the offset distance to enlarge this area until the radius of its maximal inscribed circle is larger than T. With the obtained internal contours Ci1 and Ci2 on the current layer Li , the internal contour Ci is generated by uniting these two internal contours. Specifically, the input boundary and Ci1 define one area Si1 , while the input boundary and Ci2 define another area Si2 , the Boolean union is performed on these two areas and the interior contour of the united area Si is Ci . So far, the internal contour of each layer is identified by considering both the wall thickness and the self-support capability, implying that the volume confined by the internal surface (the enveloping surface defined by internal contours of all the layers) and the exterior surface of the part can achieve desirable wall thickness and the maximal self-support ability. Therefore, only this type of volume needs to be filled, resulting in a large volume of materials can be saved accordingly. The subsequent step is to generate the filling paths inside the volume; the boundary of the filled area on each layer is confined by the generated internal contours and the original contour of input geometry.
2.3. Path planning For a specific layer, the areas to be filled are confined by the exterior boundary and the generated internal contours from last section, and commonly have long and narrow geometrical property. To fill shapes with such type of geometry, general filling path patterns cannot achieve desirable filling quality or long build time is required. As illustrated in Fig. 12, the general contour path would bring in several overfill issues when the distance between adjacent path elements is smaller than the expected path gap. This issue is very common in filling long and narrow geometry with contour parallel path patterns. One of typical direction parallel path patterns, zigzag path, would avoid the overfill issue, but long build time is required due to many sharp turns along the filling paths. In order to address the above mentioned issues, a new path planning method is proposed to fill shapes with long and narrow geometry exclusively; the flowchart is illustrated in Fig. 13. Note that the analyzing unit here is the shape that just has one exterior boundary and several internal contours because it can be easily extend to arbitrary shapes with any number of exterior boundaries. For demonstrative purpose, a shape shown in Fig. 13 (a) is adopted to explain the path generation method step by step.
Step 1: Generate the initial contour parallel paths based on the desired path space w and the input polygon. The input connected region is comprised of one exterior boundary and several internal contours. Generally, the exterior boundary is defined by a large number of line segments in counter-clockwise (CCW), while the internal contour is in clockwise (CW) for distinction. Then the contour parallel paths are generated by repeated offsetting with the distance of path space w as the offset distance. The offset distance of the first contours is half of the path space w for accurate deposition of the first loop. The contour paths are shown in Fig. 13 (b). Step 2: Analyze the potential overfilling and underfilling cases. Based on the parent/child relationship between contours, a tree representing the mutual relation between them can be built [26]. In the relation tree, one parent contour may have more than one children contour, and vice versa. The input exterior boundary and the internal contours are on the top of the established tree. As shown in Fig. 13 (c), the offset contours are indexed based on the information from the offsetting operations. The input contours are named as B1, B2,. . .Bi and their subsequent child contours are named as Bi-1, Bi-2,. . .Bi-j until one child contour has several children, the names are changed to Bi-j-1, Bi-j-2. . . Bi-j-k, etc. If one contour is obtained by offsetting two input contours Bm and Bn, its name is Bmn-1. The corresponding relationship tree is built up as shown in Fig. 13 (d) and the color of each node is the same as that in Fig. 13 (c) for easy visualization. All of the potential overfilling and underfilling cases can be analyzed based on the relationship tree and the geometry of offset contours. To analyze the path gap accurately, the medial axis transform (MAT) is adopted in this work. Medial axis transform (MAT) of a 2D shape can be used to concisely represent the domain shape and is very useful for analyzing the complex domain. The MAT is based on the medial axis, which geometrically bisects the domain and becomes the shape skeleton [27]. So the medial axis is also called as the skeleton. Two examples are shown in Fig. 14; the medial axis is bounded by the planar curve and is the set of the locus of centers of locally maximal circles that are tangent to the curve in two or more points. The red dot lines are the medial axis of the input geometry. The medial axis of a simple polygon can be visually described as a tree whose leaves are the vertices of the polygon, while the edges are either straight segments or arcs of parabolas [28]. From the definition of medial axis, the distance between two adjacent path segments can be approximately represented by the diameter of locally maximal inscribed circles. So it can be judged
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Fig. 13. Flowchart of the proposed path planning method.
from these circles whether overfill or underfill would appear or not. In the implementation, points are sampled on the obtained medial axis based on a predefined period length firstly. Then the diameters of corresponding maximal inscribed circles are computed. If the diameter of one circle is out of a certain range, like [0.8w, 1.25w], the distance between two associated paths at the center of this circle is considered beyond its proper range. If there are a certain
number of consecutive sampling points all satisfying this condition, the segment of medial axis containing these samples is recorded for the subsequent modification. Two cases may occur on the recorded segments of medial axis after the computation and selection. One case is that the diameter is smaller than the defined range, and the other case is that the diameter is larger than the defined range. These two cases are illus-
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Fig. 14. Demonstration of medial axis of shapes with (a) single contour and (b) multi-contours.
trated in Fig. 15. Corresponding methods are presented to generate the paths under these two circumstances in the next step. Besides the area confined by one contour and its child/parent contours, some areas confined by two adjacent contours that do not have containing/contained relationship also need to be analyzed to compute the diameter of the maximally inscribed circles. Specifically, if a contour has more than one parents and several brothers, all of these contours are required to be analyzed together. For
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example, in the relationship tree as shown in Fig. 13(d), the parents of contour B12-1 are B1-2 and B2-2, and it also has a brother contour B12-2, so the area confined by B1-2, B2-2, B12-1 and B122 requires the further geometrical analysis. The same situation appears on B12-1, B3-3, B123-1 and B123-2. Step 3: Generate a skeleton-based path. The subsequent step is to use a skeleton-based path to replace the associated contour path segments for the case where the diameter of maximally inscribed circles is smaller, or to insert into the areas where the diameter of maximally inscribed circles is larger. Fig. 16 illustrates the steps of the skeleton-based path generation for the former case. Step 3.1: The first step is to identify the segment of the medial axis selected from Step 2 based on the diameter of maximally inscribed circles. As the segment in Step 2 is selected according to a given range, it should be extended (or shortened) from two ends to enable the diameter of the maximally inscribed circle to equal to a proper limit value, like w. However, there are two exceptional situations. The first is that if the selected segment is closed, it is impossible to extend it and unnecessary to shorten it. Another exception is that the end of segment may extend to the whole medial axis to identify the end points if the diameters of all maximal inscribed circles within this contour are all smaller than the limit value. Fig. 16(a) shows the original ends and the extended ends and Fig. 16(b) shows the exceptions. Step 3.2: The next step is to get the corresponding tangent points on the contours by considering the maximally inscribed circles taking the end points as centers and tangent to the contours, as illustrated in Fig. 16(c); Step 3.3: Delete the segment of the original contour between two tangent points and connect the adjacent end points of the contour with a Hermite curve which can ensure smooth transition between them;
Fig. 15. Demonstration of two cases where the distance between paths is out of defined range.
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Fig. 16. Illustration of the wavy path generation process.
Step 3.4: Generate a new path based on the medial axis and the distance between the end point and the contour path is w/2, so it is called the skeleton-based path, as show in Fig. 16(d). As the medial axis transform is a complete shape descriptor and can be used to reconstruct the shape of the original domain[29], the geometric information of MAT allows the generation of path inside the domain to be very effective and feasible. Actually, there are some similar researches on the combination of skeleton-based path and contour parallel-based path in the traditional machining and these can be effectively adjusted to fit the path generation for additive manufacturing [30,31]. With the present method, the modified path for the shape in Fig. 12 is shown in Fig. 17. 3. Demonstration and discussion In this section, two 3D objects are used to validate the proposed process planning methodology. In the case studies, mainly two aspects are emphasized: one is the implementation of the optimized internal filling from the sliced file; another is the difference on the material consumption before and after optimization. In the evaluation of consumed materials, the length of generated paths, as well as the weight of printed parts is used for calculation. Fig. 17. Optimized filling path for long and narrow geometry.
3.1. Case study 1 In the first case, the proposed internal optimization strategy is applied to a non-rotational part. The selected part is symmetrical and has three roofs and two inclined surfaces that require additional supports for fabrication. The dimensions of the object along three axes are 112.3 mm, 50 mm and 70 mm respectively and the volume is 182278.058 cubic millimeter, as shown in Fig. 18(a). The layer height for slicing is 0.2 mm and there are totally 350 slices shown in Fig. 18(b). In the generation of internal contours, the maximal self-supporting angle is set as 45◦ and the desired wall thickness is set as 4 mm to determine the internal contour of the underneath layer based on the internal contour of the current layer,
this process is illustrated in Fig. 18(d). After all the layers are processed, the sliced model is shown in Fig. 18(c). The red polygons are the generated internal contours of each layer. To further demonstrate the self-supporting strategy, the cross section of the sliced modal in the front view is shown in Fig. 18(e). We can see that the maximal self-supporting angle can be reflected from the cross section and the part can be deposited smoothly with the consideration of the self-supporting capability. With the modified sliced data, including the input boundary and the generated internal contour, the next step is to generate the deposition path to fill areas for each layer. The path space is 0.55 mm here to generate the dense filling and the density for the
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Fig. 18. Demonstration of a non-rotational part (a) 3D part; (b) sliced data of the model; (c) generation of internal contours based on the sliced data; (d) internal contour generation; (e) cross section of (c).
Fig. 19. Comparison of filling path at different layers in the case study I.
sparse filling is 40%. For comparison purpose, three layers (20th, 100th and 302th) at different heights are chosen. As illustrated in Fig. 19, the first row shows the paths without optimization, while the second row is the layers with optimized internal structure. It can be observed that some areas which are filled in the former do not need to be filled in the latter and the deposition material can be saved accordingly.
3.2. Case study 2 The purpose of the second case study is to demonstrate the application of the proposed method to a rotational part which has pagoda-like geometry in the illustrated example. The part has
a volume of 284858.55 cubic millimeter with the dimensions in three axes are 107 mm, 107 mm and 76.346 mm respectively, as illustrated in Fig. 20(a). The layer thickness is 0.2 mm and there are totally 382 layers as shown in Fig. 20(b). The maximal selfsupporting angle is considered as 45◦ and the wall thickness is 4 mm in the generation of internal contours, as illustrated in Fig. 20(d). After the internal contours of all the layers have been generated, the sliced model is shown in Fig. 20(c). The interior red polygons are the generated internal contours. As the object can be obtained by rotating a cross section around a vertical axis, the self-supporting property can be observed from one of its cross sections, as illustrated in Fig. 20(e).
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Fig. 20. Demonstration of a rotational part (a) 3D part; (b) sliced data of the model; (c) generation of internal contours based on the sliced data; (d) internal contour generation; (e) cross section of (c).
Likewise, the subsequent step is to plan the deposition path to fill areas which is confined by the exterior boundaries and the generated internal contours for each layer. The path space is also set as 0.55 mm for the dense filling and the density for the sparse filling is 40%. Three layers (80th, 200th and 320th) belonging to different height ranges are selected and their deposition paths are generated based on the determined parameters. From Fig. 21, it can be observed that some filled areas in the former case remain as unfilled areas in the latter case, while the part can be build successfully, so materials can be saved in the practical deposition process using the proposed methodology.
3.3. Discussion To evaluate the material consumption, the length of generated path is firstly used to approximately represent the volume of consumed materials. In the extrusion-based AM, the volume of consumed materials can be obtained from the path length and the cross-sectional area of the deposited filament. In the first case study, the path length for depositing the non-optimization model is 644.14m, while it is reduced to 513.43 mm with the optimized internal topology. In this case, material saving can reach 20%. In the second case study, the path length is changed from 882.72 m to 574.26 m after using the proposed method. The comparison of the
Fig. 21. Comparison of filling path at different layers in case study II.
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due to the internal optimization. One main reason for the gap is the appearance of sharp edge in the internal surface where there are stress concentrations. This can be verified by the fact that the failure began from these zones during the experiments. In theory, this issue can be alleviated by rounding these edges, which can also be achieved using sliced data. Therefore, the slight reduction of the mechanical properties is reasonable and acceptable. Based on the above analysis, it appears that the proposed strategy can reduce the material consumption to additively fabricate parts without much compromise in the part’s mechanical performance. The reduction of the material consumption mainly owns to the optimization of internal topology which can be implemented with the sliced data and fabricated with layer-based manufacturing paradigm.
Fig. 22. Comparison of filling path length before and after optimization in two case studies.
material consumption before and after the optimization is shown in Fig. 22. To investigate the influence on the mechanical strength of fabricated parts brought by the internal optimization, the part in the case study I is additively fabricated using a Lulzbot TAZ3 FDM machine. The sliced files of the part before and after optimization are shown in Fig. 23(a) and the corresponding fabricated parts are shown in Fig. 23(b). The measured weight of the part without internal optimization is 80.7 g while the weight of the part after optimization is 64.5 g. Then, the compressive strength of fabricated parts is measured as illustrated in Fig. 23(c) and the load versus displacement data is collected as shown in Fig. 23(d) respectively. First failure is observed at 18.576 and 16.364 kN for part I and part II respectively. The second failure can be found at 11.834 and 10.92 kN from the stress-strain curve generated from the load displacement data as given in the figure. From the result, it is observed that the compressive strength and compressive stiffness are slightly decreased
4. Conclusion An AM process planning approach emphasizing on the internal optimization and the path planning has been developed in this paper to reduce the material consumption of additively fabricated parts, particularly for large and solid objects. The developed framework proposes an optimal internal topology considering the requirement of minimal wall thickness and the self-supporting capability. The optimal internal topology minimizes the total consumed materials by reducing the volume of the whole part to be filled, and thus saves the build time. Instead of the input CAD file itself, its sliced data is adopted in the internal optimization to reduce the computational cost and avoid errors in addressing 3D geometric operations. Meanwhile, the filling quality is enhanced by utilizing a skeleton-based method for evaluation and path optimization. Two case studies are demonstrated to validate the feasibility and effectiveness of the proposed methodology with acceptable mechanical strength and integrity. The proposed process planning method can help different AM technologies to be more environmental friendly and suitable manufacturing methods with less environmental impacts.
Fig. 23. Investigation of the influence on the mechanical strength of the proposed internal optimization method.
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