Proceedings of the ASME 2014 International Design Engineering Technical Conferences &Computers and Information in Engineering Conference

IDETC/CIE 2014August 17-August 20, 2014, Buffalo, USA

DETC2014-34067

COMPUTATIONAL GEOMETRIC SOLUTIONS FOR EFFICIENT ADDITIVEMANUFACTURING PROCESS PLANNING

Anoop VermaDART Laboratory

Department of Mechanical and Aerospace EngineeringUniversity at BuffaloBuffalo, NY 14260

Email: anoopver@buffalo.edu

Rahul Rai∗DART Laboratory

Department of Mechanical and Aerospace EngineeringUniversity at BuffaloBuffalo, NY 14260

Emai: rahulrai@buffalo.edu

ABSTRACTAdditive manufacturing processes are capable of printing

parts with any shape and complexity. The parts fabricated withadditive manufacturing processes requires minimum human in-tervention. Process planning decisions play an important role inmaking sure the fabricated parts meets the desired specification,including the build time and cost. A quick and unified approachto quantify the manufacturing build time, accuracy, and cost inreal time is lacking. In the present research, a generic and nearreal-time framework for unified additive manufacturing processplanning is presented. We have developed computational geo-metric solutions to estimate tight upper bound of manufacturingprocess planning decisions that can be analyzed in almost realtime. Results of developed computational approach are com-pared against the optimized process plans to ensure its applica-bility. Case studies comprising of numerous parts with varyingshape, and application area is also outlined.Keywords: Voxelization, process planning, selective laser sinter-ing, slicing, curve fitting

NOMENCLATUREα Part orientation along x axis.β Part orientation along y axis.ζ Part scaling factor.

∗Address all correspondence to this author.

1. INTRODUCTIONAdditive manufacturing (AM) refers to set of techniques

through which a part is built additively in a layer-by-layer fash-ion. Selective laser sintering (SLS), digital light printing (DLP),Direct metal laser sintering (DMLS), Fused deposition modeling(FDM), Laminated object manufacturing (LOM), Direct write(DW) are some of the well-known AM techniques used in widearray of application areas such as aerospace, medical, sports, andarts etc.

Over the fast few years, a tremendous growth in additivemanufacturing research has been witnessed. Such technical ad-vancement has lead to the development of novel AM machines.The key attributes of additive manufacturing processes namelythe .stl file input (a form of solid CAD model), and process au-tomation (similar to a normal paper printing) makes it much suit-able for remote printing. Thus it is possible to model a part inone location and to get the desired part fabricated in another lo-cation. Such aspects makes the 3D printing easier and afford-able. Manufacturing firms now provide remote printing optionsfor such customers who in turn upload their design and get theparts shipped to their address. A typical operation of such remoteprinting option is obtaining a manufacturing quote. Manufactur-ing quote comprises of (1) Realization of materials to be used, (2)Associated processes to be used in part fabrication, and (3) theoverall cost assessment. In current setting, the process of gen-erating manufacturing quotations of parts appears to be lengthy(2-3 days or more) and usually contains very little information

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about the criteria influencing the service purchase. Figure 1 dis-play one such remote printing options of a 3D printing companythat provide the manufacturing quote in 2-3 days. Even thoughthe information provided at the end of 2-3 days is accurate, anapproximate real time information about the part is customary.2-3 days time is long enough to change the customers’ purchas-ing decision. Moreover, as the customers’ are becoming environ-mentally conscious, sustainability criteria such as material waste,and energy consumption also play an important role in customerservice purchasing decision. A real time assessment of such cri-teria is lacking. In the present research, a generalized frameworkfor generating the manufacturing quotes of 3D parts in near realtime is developed. A selective laser sintering (SLS) machine hasbeen considered for the analysis due to its widespread applicabil-ity. However, the approach developed here is generic enough tobe applicable to other additive manufacturing process with littleor no modifications.

FIGURE 1. Remote 3D printing options: A typical scenario

The remainder of the paper is organized as follows. In Sec-tion 2, a detailed description of the related literature is provided.Section 3 presents the developed framework as its constituents.The results obtained from the developed approach is presentedand discussed in section 4. The conclusion and future researchtopics are provided in Section 5.

2. LITERATURE SURVEYAdditve manufacturing has witnessed significant amount of

growth in past few years. The technology initially started for partprototyping is quickly transforming into mainstream manufactur-ing. Research in additive manufacturing can be broadly divided

into (1) machine design [1, 2], and (2) process planning and op-timization [3, 4, 5]. The machine design aspects of the additivemanufacturing aims to improve the current devices or to developnovel additive manufacturing techniques. Research in this areahas resulted in some novel manufacturing techniques includingarea based sintering, i.e. digital light processing (DLP) [6], hy-brid additive manufacturing such as shape deposition manufac-turing (SDM) [7]. The research in additive manufacturing pro-cess planning is however very broad as numerous approaches toidentify optimal build direction [8, 9], laser scanning [10, 11],part slicing [12, 13, 14, 15, 16], and 3D packing [17, 18] has beendeveloped. Numerous such studies have shown the relative ad-vantages of optimized process over traditional rule based processplanning.

The limitation of laser sintering capability and the complex3D shapes however makes the optimization process lenghty andcomputationaly challenging. Off-the-self additive manufactur-ing devices thus rely on set of rules for fabricating a given part.These set of rules includes (1) fixed/limited part orientation alongx,y or z axis, (2) dense/sparse slicing, and (3) fixed tool pathmovement and fabricates part which are usually not optimal frombuild time or accuracy point of view. However, the ongoing ad-vancement in computing resources, an optimal process plan willlikely to be generated in near real time. In current setting, gener-ating a manufacturing quote using such optimized process planis a far cry. A real time assessment of manufacturing quotesis essential to aid customers’ printing decisions. Research insuch aspects of 3D printing process is lacking. In the presentresearch, we develop an efficient approach to generate manufac-turing quotes attributes in near real time which are quite simi-lar to the one obtained using the time-intenstive optimized pro-cess. In the present research, the analysis is based on selectivelaser sintering (SLS) machine which selectively sinters a matar-ial power to create a 3D model in a layer-by-layer fashion (seeFigure 2. Apart from the given part, and input material at hand,machine attributes such as laser power, beam spot size, roller andpiston movement contribute greatly to the manufacturing quoteattributes namely build time and energy consumption.

In next sextion, the developed framework is discussed.

FIGURE 2. Selective laser sintering process

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3. DEVELOPED COMPUTATIONAL GEOMETRIC (CG)FRAMEWORK

In this section, details of developed CG framework is pro-vided. The aim of proposed framework is to provide an esti-mate of manufacturing quote attributes such as manufacturingtime, and energy consumption of a given part in near real time.Obtaining estimation of such attributes aids customers’ on-lineremote printing purchasing decisions. The objective is to pro-vide a tighter upper bound of optimal process planning parame-ters that lead to calculation of the manufatcuring quote attributes.The developed framework utilizes the part abstraction process toquantify additive manufacturing process criteria such as manu-facturing build time, process energy consumption, and part buildaccuracy (see Figure 3). The results obtained from the developedapproach is then compared against the time-intensive optimiza-tion process to make a real time assessment of manufacturingobjectives. The developed approach utilizes computational ge-ometric solutions including voxelization, part specific geometryinformation such as facet angle along build directions etc. Therepresentative sub-parts (very few in numbers) are then extractedand optimized individually for estimating the process objectivesof whole 3D model. Salient features of developed framework arediscussed next.

3.1.Part orientation optimizationBeing a layer-wise fabrication process, the orientation of in-

put part plays an important role in governing the accuracy, sur-face finish, and build cost/time of the fabricated part. In the de-veloped research, objectives related with part material waste andsurface roughness are considered while optimizing the part orien-tation for fabrication. Material wastage in SLS reflects the unsin-tered powder laid on each sintering pass. A fraction of unsineterdpowder becomes waste due to its loss in properties upon exposedto the laser. A great deal of savings in material is possible by (1)optimizing the part orientation, and (2) printing multiple partstogether. In the present research, part orientation is optimizedwhile minimizing material waste. Parts fabricated with smallerheight along build direction can certainly minimize the materialwaste, however, the resultant fabricated model may have poorsurface roughness. In the proposed research, a balancing objec-tive namely minimization of surface roughness is also included.A mathematical model of the underlying part orientation opti-mization problem is provided in equation 1.

Min. f (α,β ) =w1×ξ +w2×Raavg

w1 +w2,s.t.,0 <= α,β <= π (1)

In equation (1), α,β , are the part rotation angles in x,y directionswhich are varied in the range (0−π), w1, and w2 are the weightsassociated with the objective functions namely material waste ξ

and surface roughness Raavg. The material waste depends on

the effective build volume and the waste fraction (ψ), given inequation 2. Waste fraction typically depends on the input rawmaterial. For the present analysis, a waste fraction of 56% isassumed. Whereas, the average surface roughness is based onpart facet angles (FAi∀F) along build direction (equation 3).

ξ = ((ARbed×Hpart)−Vpart)×ψ (2)

Raavg =∑

Fi=1 Rai×Ai

∑Fi=1 Ai

(3)

Mathematically, the surface roughness of a facet can be calcu-lated as:

Rai =

{(2cosφsinφ ×937+3.5φ +48)×0.0254, if 0 <= φ <= π/2(2cos(π−φ)sin(π−φ)×937+3.5φ +48)×0.0254,else

(4)In equation (4), Rai is the surface roughness of ith facet, φ is theangle between facets surface normal and build direction.

A simulated annealing with re-annealing (to escape from lo-cal minima) is used to perform part orientation optimization. SAis selected due to its fast convergence ability and popularity issolving such optimization problems [19,20]. A matlab optimiza-tion routine namely ‘simulatedbnd’ is used to solve the above-mentioned optimization problem. Figure 4 display a sample partwith initial, optimal orientation and the iterative improvement inthe material waste. Overall 76% of improvement in the materialwaste is achieved.

FIGURE 4. Part orientation optimization: sample part

3.2. Part abstractionPart abstraction relates with the removal of finer details from

the actual model to get a generalized model. Such model can thusbe defined as a set of recognized sub-components. In the presentresearch, part abstraction based on 3D voxelization is used.

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FIGURE 3. Developed framework for efficient process planning

3.2.1. Lego based uniform part voxelization Quitesimilar to the normal voxelization, the input part is fitted witha series of lego studs. A standard lego studs consists of threesquare bricks and a cylindrical disc stacked on top of each other.Each brick is of 8 mm× 8 mm dimension, whereas, the cylindri-cal disc is of 1.6 mm height and 4.8 mm diameter. One such legostud is shown in Figure 5 where the units are displayed in LDrawformat (LDU). One LDU being 0.4 mm. Lego studs of samedimension based on optimized ray casting through the faces ofpolygonal objects are used in the voxelization. The process in-volved two steps namely (1) space partitioning of the part faces,and (2) optimized ray casting. Figure 6 display a sample 3Dmodel and associated parameters to create the voxelized part us-ing standard lego studs. The voxelized part contains uniformstuds oriented along six possible directions. A finer resolution ofvoxelization is used to minimize the volume difference betweenoriginal and voxelized part. For detailed description, interestedreaders can refer [21, 22, 23].

FIGURE 5. A standard lego stud

3.3. Representative sub-part/feature extractionOnce the input part is voxelized, the representative

features/sub-parts are extracted. As the process performs uni-form voxelization, the information related with the number ofstuds, and their orientation is sufficient for estimating the pro-

FIGURE 6. Input part (left) and voxelized part using lego studs(right). The parameter for the voxelization is shown in middle

cess objectives of the whole part. In the present research, suchinformation is extracted from the lsculpt file. Lsculpt file for-mat is widely used in lego community which includes the rele-vant information about each lego studs used to approximate thegiven 3D model. Figure 7 display the snapshot of the samplelsculpt file and its components. Given the pre-fixed dimensionof standard lego studs, the input model is usually upscaled forbetter voxelization. The header of lsculpt file given in Figure 7display a up-scaling of 3230.07 of given part. For the examplepart given in Figure 6, a total of 3629 uniform lego studs wereobtained. A total of six possible orientation pattern ({α = 0◦,β = 90◦}, {α = 0◦, β = 270◦},{α = 90◦, β = 0◦},{α = 270◦,β = 0◦},{α = 0◦, β = 0◦},{α = 0◦, β = 180◦} ) was obtainedfor the given voxelized part (see Figure 8). For the ease of visu-alization, the lego studs with different orientations are shown indifferent color.

3.4. Process optimization of lego studsIn this section, optimal process plan for representative lego

studs is generated. For 3D printing as the parts are fabricatedalong build direction (z axis presumably), only two represen-tative orientation ({α = 0◦, β = 90◦}, {α = 0◦, β = 0◦} aresufficient to estimate the overall process objectives. In case ofabstraction using lego studs, unique studs (studs with varyingorientation) are extracted and individually optimized for fabri-cation.The optimization tasks here includes part adaptive slicingand laser scanning path optimization. The approach is based on

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FIGURE 7. lsculpt file format of a sample part

FIGURE 8. Sample part with possible orientation (left), stud transfor-mation pattern and associated orientation angles α,β (right)

our previous work (see Ref. [24])Performing uniform slicing on studs with orientation 0◦ and

90◦ resulted in part build time 434.0316 s and 380.67 sec respec-tively. Figure 9 display various objectives of the representativestuds. The results obtained from the optimization based algo-rithm are compared against traditional sparse and dense slicingconsisting of uniform thickness values of maximum and mini-mum allowable thicknesses. The term accuracy here means thepart build error (see Ref. [24]). The developed optimization algo-rithms outperforms traditional uniform slicing (dense and sparse)approaches and provides a better trade off between build time,energy consumption and part build accuracy. In next section,the present approach is compared against the optimized solutionwhich is validated on a set of 3D models.

3.4.1. Scaling effect As the voxelization process in-volves scaling up of 3D models to better fit lego studs, an effectof sub-part scaling on the process objectives is assessed. Thegiven sub-part is upscaled and downscaled at various level to ob-tain a parametric estimation of the objectives. Build time and

FIGURE 9. Optimized representative sub-parts of 3D models

process energy consumption of lego studs at scaling factor of0.1,0.25,0.5,5,10 and 25 is analyzed. A multiplier metric forbuild time and process energy is estimated from the calculatedbuild time and energy at different scaling factor. The resultantvalue is regressed against the scaling factor to get a parametricmodel. Based on the trend of process objectives, a 3rd degreepolynomial is used for estimation. Figure 10, and 11 display the3rd degree polynomial fit and the associated parameters.

4. COMPUTATIONAL RESULTSIn this section, numerous example parts are analyzed. The

comparison is made with the optimized parts reported in [24,25].A total of seven parts with varying complexity are considered.Figure 12 display the attributes of the considered voxelized parts.The complexity of the parts can be assessed with the total num-ber of associated sub-parts. In the Figure, column 3-6 displaythe number of lego studs used, whereas, the last column in thefigure provides the overall scaling factor of the voxelized part.The build time and energy consumption multiplier of the scalingfactors is obtained through polynomial equations given in Figure10, 11.

Table 1 display the comparison of present approach with theoptimized process plan of seven representative models. It can beseen from the results that the build time and process energy esti-mates of the parts are very close to the one shown in Ref. [24,25].The results are even closer when the part size is smaller. Thebuild time and process energy is always higher than the opti-mized one as the volume of the voxelized part is always higherthan the corresponding 3D part. The analysis shown here pro-vides a better and tighter bound to the optimized process plan.Compared with the computationally intensive optimization pro-cess, the approach developed here can estimate the process ob-jectives in almost real time. Such attribute of proposed approachmakes it suitable for remote printing as the interested customerscan estimate the process build time and energy consumption oftheir upload design in almost no time and therefore can decide

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FIGURE 12. The attributes of voxelized parts

accordingly about the service purchasing options.

5. CONCLUSIONS AND FUTURE RESEARCHIn this paper, a systematic approach to quantify additive

manufacturing quote attributes namely process build time andenergy consumption was presented. The results obtained fromthe developed approach were found to be very close to the opti-mized process from our previous work. The results thus providea very tight upper bound of the optimized process plan and there-fore can be used for generating manufacturing quotes. More-over, compared with the time intensive optimization process, the

results using the present were obtained in almost real time andtherefore very suitable for assisting customer’s in their on-lineprinting decisions.

In the present work, manufacturing quotes attributes namelybuild time and energy consumption were presented. Future workincludes incorporating estimating of overall part accuracy usingthe developed approach. An on-line interface displaying suchattributes will also be developed to extend the present researchscope. Considering the role of process planning parameters suchas number of layers, laser scan movement, layer thickness inthe manufacturing quotes, present work will also be extended toquickly estimate such attributes.

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FIGURE 10. The third degree polynomial and its associated parame-ters for stud orientation {0,0} and {180,0}

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FIGURE 11. The third degree polynomial and its associated parame-ters for stud orientation {0,90}, {0,270} {270,0} and {90,0}

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TABLE 1. Comparison of present approach with the optimized pro-cess planning in [24, 25]

Sl. No Build Time (sec) Process Energy (W)

Ref. [24-25] Present Ref. [24-25] Present

Part1 38.23 45.89 99.56 106.91

Part2 178.66 195.63 94316.23 95514.32

Part3 35.52 43.96 120.35 140.55

Part4 39.55 48.85 23.52 30.98

Part5 43.46 52.65 100.0 118.65

Part6 24.68 28.98 39.68 45.68

Part7 578.35 610.63 780000 785606

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