Procedia Manufacturing Volume 5, 2016, Pages 974–988 44th Proceedings of the North American Manufacturing Research Institution of SME http://www.sme.org/namrc Geometric Analysis for Concurrent Process Optimization of AM Nazmul Ahsan, Ahasan Habib and Bashir Khoda* Industrial & Manufacturing Engineering Dept North Dakota State University, Fargo, ND 58102, USA *Email: akm.khoda@ndsu.edu Abstract Build orientation and deposition direction are two important AM process parameters which are determined at the pre-processing stage of AM Carefully determined build direction and deposition direction can significantly improve the process and fabrication attributes Either build direction or deposition direction is usually optimized independently considering one or multiple attributes Such approach undermines the hierarchical relationship in the AM process plan and may produce suboptimal solution Besides, both build direction and deposition direction alter the layer topology and tool-path pattern which eventually determine the process and part attributes But, the geometry is not taken into consideration while determining the build and deposition orientation In this paper, an integrated framework is proposed to concurrently determine the optimum build orientation and toolpath/deposition direction using Genetic Algorithm (GA) The proposed methodology is designed on the basis of the layer geometries and the resulting part attributes to ensure manufacturability and minimize fabrication complexity for parts in AM processes The proposed algorithm is implemented on two free form shaped objects and the process converges within a reasonable number of iterations Keywords: Build orientation, deposition direction, genetic algorithm, geometric analysis, additive manufacturing Introduction In additive manufacturing (AM) processes, commonly known as layer manufacturing or 3D printing, physical models are built layer-by-layer The process plan starts with a digitized model and end by stacking the individual printed layers along the build direction creating the 3D physical model However, depending upon the AM technique and the process plan, the fabricated part may require post processing Thus, the AM processes can be divided into three sequential technological steps: preprocessing (virtual), processing (actual printing), and post-processing Activities under each steps directly contributes towards the fabricated part and optimizing one or more steps may improve the 974 Selection and peer-review under responsibility of the Scientific Programme Committee of NAMRI/SME c The Authors Published by Elsevier B.V doi:10.1016/j.promfg.2016.08.085 Geometric analysis for concurrent process optimization of AM Ahsan et al process capabilities However, these activities are directional, i.e., they have a hierarchical relationship and the error accumulates often time amplifies along the downstream activities The pre-planning/pre-processing stage is at the top of the AM hierarchy and can proactively alter the AM strategy into a guided desired outcome (B Khoda, 2014) The pre-processing stage primarily uses computer aided design techniques to guide both the machine motion and material deposition systems This stage starts with design conceptualization and ends by generating the AM process control instructions The outcome of this stage is information, which is fully reversible based on the user requirement Information from this stage is directed towards the processing stage where actual fabrication starts occurring and the process become irreversible Build direction and deposition direction determination are two key tasks in the virtual preprocessing stage of AM fabrication Carefully determined build direction and deposition direction can significantly improve the process and fabrication attributes Xu et al (F Xu, 1999) considered building inaccuracy, surface finish, and manufacturing time and cost as the part attributes to choose optimum building directions for multiple additive manufacturing processes Byun and Lee (H.-S Byun & Lee, 2006) evaluated stair stepping effect, build time, and part cost to determine the optimal build direction of a part for different AM systems They first chose build orientation candidates from the convex hull of a part and then used multi-criterion decision making method to select the best orientation among the candidate orientations Moroni et al (Moroni, Syam, & Petrò, 2014) proposed a model to predict the deviation of an additively manufactured part from its CAD model due to fabrication process They also developed an approach to determine part orientation focusing on the surface quality/accuracy of assembly features (Moroni, Syam, & Petrò, 2015) Volumetric error (Rattanawong, Masood, & Iovenitti, 2001) and layered process error (Lin F, 2001) of additively manufactured parts are also considered to determine build orientation Tool-path planning is another critical task in AM process planning The material deposition path is generated for each layer with a selected raster/deposition angle to fill the interior of the layer The extruder or laser head needs to be guided along the generated tool-path to fabricate the layer Since each fabricated layer is supported by its preceding layer, a 0°-90° raster angle pattern among successive layers is usually used to ensure structural integrity (Ahsan, Habib, & Khoda, 2015) However, other pre-determined layout patterns were also investigated for the structural integrity (EsSaid et al., 2000) Adaptive material laying patterns have recently been proposed by Khoda et al (A K M B Khoda & Koc, 2013) to achieve the desired porosity of the functionally gradient porous internal architecture of additively manufactured tissue scaffolds A multi-directional parametric material deposition orientation (A K M Khoda, Ozbolat, & Koc, 2013) is also demonstrated considering the accessibility and porosity of the internal region of tissue scaffolds Both Build orientation and deposition direction optimizations in AM processes are computationally intensive and multimodal problem Rattanawong et al (Rattanawong, et al., 2001) determined optimum build orientation using exhaustive search method where only one build orientation angle was varied at 15º interval to minimize the volumetric error occurred in additively manufactured parts Ahsan et al (Ahsan, et al., 2015) used a coarse resolution (10º) of two build orientation angles to obtain the optimum orientation and then further explored the neighbor of that orientation with a fine resolution (1º) to find the best build orientation to optimize build height, fabrication resource requirements, and surface quality Part cylindricity error (Paul & Anand, 2011) was minimized to achieve geometric tolerances by incrementally rotating the part with 1º resolutions and thus finding the optimum build orientation Anca˘u and Caizar (Ancău & Caizar, 2010) determined pareto-optimal set of build orientation to optimize surface quality and build time by incrementally rotating the parts with 2º and 5º as well Frank and Fade (Frank & Fadel, 1995) developed an empirical knowledge based expert system using expert questionnaire for the decision matrix which helps select the optimum or near optimum build direction Exhaustive search method was also used in an adaptive mixed tool-path generation algorithm (G Q Jin, Li, & Gao, 2013; G Q Jin, Li, Gao, & Popplewell, 2013) to determine the best zigzag tool-path angle in order to optimize 975 Geometric analysis for concurrent process optimization of AM Ahsan et al build time However, these grid searching processes may require significant computational power and may never reach optimal or near optimal solution Alternatively, Tyagi et al (Tyagi, Ghorpade, Karunakaran, & Tiwari, 2007) used evolutionary stickers-based DNA algorithm to determine optimal build orientation Their heuristic technique uses attributes (i.e volumetric error and build time) to determine the near optimal build orientation with finite number of iteration The effectiveness of their objective function may be restricted to the complex geometry and concave layer contours Build Orientation Algorithms used: ̶ Exhaustive ̶ MCDM ̶ GA Part Attributes Considered: ̶ Surface quality (Ahn, Kim, & Lee, 2007; Alexander, Allen, & Dutta, 1998; Ancău & Caizar, 2010; H.-S Byun & Lee, 2006; H S Byun & Lee, 2005; Canellidis, Giannatsis, & Dedoussis, 2009; Danjou & Koehler, 2009; Moroni, et al., 2015; Nikhil & Kalyanmoy, 2011; Pandey, Thrimurthulu, & Reddy, 2004; Phatak & Pande, 2012; Singhal, Pandey, Pandey, & Nagpal, 2005; Thrimurthulu, Pandey, & Venkata Reddy, 2004; West, Sambu, & Rosen, 2001; Zhang, Bernard, Harik, & Karunakaran, 2015) Surface accuracy (Choi & Samavedam, 2002) Layer process (Tyagi, et al., 2007) and volumetric (Li & Zhang, 2013; Masood, ̶ ̶ Rattanawong, & Iovenitti, 2003; Rattanawong, et al., 2001) errors Support volume (Paul & Anand, 2014; West, et al., 2001; Zhang, et al., 2015) Part Build time (Ancău & Caizar, 2010; H.-S Byun & Lee, 2006; H S Byun & Lee, ̶ Deposition Direction Algorithm used: ̶ Exhaustive ̶ 2005; Canellidis, et al., 2009; Choi & Samavedam, 2002; Nikhil & Kalyanmoy, 2011; Pandey, et al., 2004; Thrimurthulu, et al., 2004; Tyagi, et al., 2007; West, et al., 2001) Layer build time (G Q Jin, Li, & Gao, 2013) Number of turns in tool-path (Y.-a Jin, He, Fu, Gan, & Lin, 2014) ̶ Tool start-stops (Ding, Pan, Cuiuri, & Li, 2014) ̶ ̶ Figure Different part attributes used to determine build orientation and deposition direction Part attributes such as surface quality (Ahn, et al., 2007; Alexander, et al., 1998; Ancău & Caizar, 2010; H.-S Byun & Lee, 2006; H S Byun & Lee, 2005; Canellidis, et al., 2009; Danjou & Koehler, 2009; Nikhil & Kalyanmoy, 2011; Pandey, et al., 2004; Phatak & Pande, 2012; Singhal, et al., 2005; Thrimurthulu, et al., 2004; West, et al., 2001; Zhang, et al., 2015), accuracy (Choi & Samavedam, 2002), assembly feature surface quality/accuracy (Moroni, et al., 2015), volumetric errors (Li & Zhang, 2013; Masood, et al., 2003; Rattanawong, et al., 2001; Tyagi, et al., 2007), support volume (Paul & Anand, 2014; West, et al., 2001; Zhang, et al., 2015), and build time (Ancău & Caizar, 2010; H.-S Byun & Lee, 2006; H S Byun & Lee, 2005; Canellidis, et al., 2009; Choi & Samavedam, 2002; Nikhil & Kalyanmoy, 2011; Pandey, et al., 2004; Thrimurthulu, et al., 2004; Tyagi, et al., 2007; West, et al., 2001) are often used to determine the optimum build direction Similarly, deposition direction for zig-zag tool path was optimized mostly for layer build time (G Q Jin, Li, & Gao, 2013), the number of turns (Y.-a Jin, et al., 2014), and tool start-stops (Ding, et al., 2014) as shown in Fig Thus far either build direction or deposition direction is optimized independently considering one or multiple attributes in the objective function However, this approach undermines the hierarchical relationship in the AM process plan and may landed upon sub-optimal solution Besides, both build direction and deposition direction alter the layer topology and tool-path pattern which eventually determine the process and part attributes But, the geometry is not taken into consideration while determining the build and deposition orientation In this paper, an integrated framework is proposed to concurrently determine the optimum build orientation and tool-path/deposition direction using Hypothetical Equivalents and Inequivalents Method (HEIM) and Genetic Algorithm (GA) The proposed methodology is designed on the basis of the layer geometries and the resulting part attributes to ensure manufacturability and minimize fabrication complexity for parts in AM processes as shown in fig Exhaustive search method would require extensive computation power even for a coarse resolution/increment of the rotation angles This fact justifies the use of GA to solve the current AM process planning problem The roadmap of our proposed methodology is shown in Fig 976 Geometric analysis for concurrent process optimization of AM Ahsan et al Build Orientation Layer Geometry Part Attributes Deposition Direction Figure Proposed approach to concurrently determining build orientation and deposition direction The rest of the paper is organized as follows Section demonstrates the framework to optimize build orientation and deposition direction concurrently on the basis of a set of geometric attributes of both object and its layers Section illustrates the approach to determining optimum weights assigned to the geometric attributes Genetic algorithm based solution methodology is presented in section The Results obtained by implementing the proposed methodology is discussed in section Finally, section concludes the paper Object features Bounding box Ws Ds Figure Object discretized with parallel planes and bounding box construction for one of the object features Interaction between Process Parameters and Geometric Complexity To quantify the effect of layer topology and tool-path pattern, the 3D object is first discretized into features with a set of parallel planes The planes are generated by analyzing the object geometry and the change in curvatures (Ahsan, et al., 2015) Once discretized, the feature’s attributes are quantified to construct the objective function Seven geometric attributes are measured namely slenderness ratio ( I O ,1 ), depth index ( I O , ), width index ( I O , ), fill factor ( I O , ), contour discontinued area ( I L ,1 ), 977 Geometric analysis for concurrent process optimization of AM Ahsan et al contour slenderness index ( I L , ), and contour fill index ( I L , ) Among them, the first four attributes formulated by the four terms in Eq (1) are measuring the contribution of build orientation for each discretized feature as shown in Fig The rest formulated by the three terms in Eq (2) are measuring the effect of deposition direction contributed by layer features which is shown in Fig V · § W· § T Ã Đ T Ã Đ (1) I O ă1 ă áă ăă1 D ¹ © W T ¹ © D T â V B áạ â AÃ Đ AD Ã Đ L WL Ã Đ (2) ă áă ăă1 AB áạ â A â L â where, I O and I L are the combined geometric attributes corresponding to build orientation and IL deposition direction, respectively V is the volume of a discretized object-feature and D , W , and VB are the depth, width, and volume of the discretized object-feature’s bounding box, respectively, as shown in Fig T is defined as the threshold dimension based on the fabrication process AD and A are the areas of discontinuous layer-feature and the entire layer, respectively L , WL , and AB are the length, width, and area, respectively, of the bounding box of discretized layer feature as shown in Fig Layer features 45º 60º 0º 90º L (a) Build Direction WL (b) Figure Generated layer contours and tool-path for two different build directions (a) deposition discontinuity and (b) continuous deposition path Considering their importance, a normalized weight may be assigned in each of these attributes in Eq (1) and (2) This weight will be determined based on the object functionality and user preference Considering the weight factors, objective function is formulated as f (D , E , J ) wO I O wL I L , which is a function of build orientation angles ( D , E ) and material deposition angle ( J ) A J r H crisscross filling pattern is employed, where tool-path angles for odd numbered layers would be J odd J and for even numbered layers would be J even J H or J even J H The analytical model for determining both optimum build orientation and deposition direction concurrently can be represented by Eq (3) 978 Geometric analysis for concurrent process optimization of AM Min f (D , E , J ) Ahsan et al wO I O wL I L s.t 90 q d D d 270 q 0q d E d 360 q (3) 0q d J d 180 q J odd J J even J rH wO wL This function varies as the object is rotated about Z and Y axes by angles D and E , respectively, and the material deposition direction is rotated about Z axis by angle J in a standard 3D coordinate system Weight Determination In several AM process plan studies, the weights assigned to the respective attributes are chosen arbitrarily (H.-S Byun & Lee, 2006; Canellidis, et al., 2009; Phatak & Pande, 2012; Thrimurthulu, et al., 2004), by experience (Kim & Lee, 2005), or taken as user defined input (Paul & Anand, 2014) However, different sets of weights can result in diverse results This arbitrary assessment of weights is not systematic and is, therefore, the main downside of using any method where the weights are not selected using any strict decision theory principle (See, Gurnani, & Lewis, 2005; Watson & Freeling, 1982) In this paper, the hypothetical equivalents and inequivalents method (HEIM) (See, et al., 2005) is used to determine the appropriate weights assigned to the geometric attributes introduced in the objective function of Eq (3) HEIM is mathematically sound and can determine the actual importance of the attributes using a set of preferences stated by a decision maker rather than choosing weights arbitrarily from experience or intuition In this technique, the user preferences are used to determine the weights of the geometric attributes For each attributes, the weightage become the variable and a set of outcomes are selected as hypothetical alternatives The user provides both equality and inequality preferences among them which are used to determine their optimum values In this paper, hypothetical alternatives are the pairs of hypothetical build orientation and deposition orientation ( D , E , J ) The user preference between two hypothetical alternatives can be used to form a constraint Thus, a set of constraints is formulated from the preference information among all the hypothetical alternatives as shown in Eq (4) The objective function in Eq (4) ensures the summation of all the weight values is unity Solving Eq (4) yields the optimum values of the attributes m n Min [1 ( ¦ wO ,m ¦ wL ,n )] s.t f (D , E , J ) i f (D , E , J ) j d G ; i, j d wO ,m d 1; m d wL ,n d 1; n 1,2, ! , a and i z j Here, f (D , E , J ) i and f (D , E , J ) j are the values of i th and j th (4) hypothetical alternatives, respectively These values can be determined using the objective function of Eq (3) The constraints 979 Geometric analysis for concurrent process optimization of AM Ahsan et al th are formulated given that i th hypothetical alternative is preferred to j hypothetical alternative G is a small positive number which is used to ensure the inequality between two hypothetical alternatives A set of hypothetical build orientation and deposition direction pairs {Pi (D , E , J ) i } are created using a 27–3 fractional factorial experimental design (Montgomery, 2012) as there are seven attributes and each attribute is assumed to have two levels, high (1) and low (0) Table shows the corresponding attribute levels and the overall values of the hypothetical build orientation and deposition direction pairs Table Attribute levels and overall values of the hypothetical alternatives Hypothetical alternatives I O ,1 Geometric attributes I O,2 I O ,3 I O,4 I L ,1 I L,2 I L ,3 Values P1 0 0 0 0 P2 0 1 wO ,1 I O ,1 wL ,1 I L ,1 wL , I L , P3 0 1 wO , I O , wL ,1 I L ,1 wL , I L , P4 1 0 1 wO ,1 I O ,1 wO , I O , wL , I L , wL , I L , P5 0 1 1 wO , I O , wL ,1 I L ,1 wL , I L , wL , I L , P6 1 0 wO ,1 I O ,1 wO , I O , wL , I L , P7 1 0 wO , I O , wO , I O , wL , I L , P8 1 1 0 wO ,1 I O ,1 wO , I O , wO , I O , wL ,1 I L ,1 P9 0 1 wO , I O , wL , I L , wL , I L , P10 0 1 wO ,1 I O ,1 wO , I O , wL ,1 I L ,1 wL , I L , P11 1 1 wO , I O , wO , I O , wL ,1 I L ,1 wL , I L , P12 1 0 wO ,1 I O ,1 wO , I O , wO , I O , P13 0 1 0 wO , I O , wO , I O , wL ,1 I L ,1 P14 1 0 wO ,1 I O ,1 wO , I O , wO , I O , wL , I L , P15 1 1 wO , I O , wO , I O , wO , I O , wL , I L , P16 1 1 1 wO ,1 I O ,1 wO , I O , wO , I O , wO , I O , wL ,1 I L ,1 wL , I L , wL , I L , In Table 1, all the geometric attribute values of hypothetical alternative P1 are zero indicating that P1 is highly preferable as the objective is to minimize all the geometric attribute values If the slenderness ratio, contour discontinued area, and contour fill index are most important to the user, then the user would prefer P3 to P2 Hence, the user preference among P1 , P2 , and P3 can be represented 980 Geometric analysis for concurrent process optimization of AM Ahsan et al as P1 E P3 E P2 , where the symbol ‘ E ’ stands for ‘preferred to’ From this preference information, three constraints f ( P1 ) f ( P ) d G , f ( P1 ) f ( P ) d G , and f ( P ) f ( P ) d G can be constructed Similarly, using the preference information among all other alternatives, the rest of the constraints of Eq, (4) are formulated Finally, the optimum values of the attribute weights are determined by solving the Eq (4) Optimization with Genetic Algorithm In an optimization process, classical exhaustive methods usually suffice for small solution spaces However, for lager solution spaces, evolutionary heuristic methods can efficiently provide optimal or near optimal solutions Genetic Algorithm is an efficient stochastic evolutionary search technique which is extensively used to solve complex optimization problems GA imitates the process of natural evolution and improves a randomly generated population of potential solutions by applying genetic operations, i.e, crossover and mutation (Goldberg, 1989; Michalewicz, 1996) In this paper, GA is used to determine optimal build orientation and deposition direction to minimize the geometric attribute values of an object Thus, build orientation and deposition direction are the decision variables of this problem Both of the variables have infinite solutions within their respective solution spaces Furthermore, if the decision variables for an object are determined concurrently, the size of the solution space would grow in an exponent manner This fact justifies the use of an efficient heuristic optimization method such as genetic algorithm to solve this complex AM process plan optimization problem modeled in Eq (3) Details of the main steps of GA are illustrated in the following sections In this paper, the build orientation is represented by two rotation angles ( D and E ) of the object about Z and Y axes in a standard 3D coordinate system By changing the magnitudes of these two angles, any orientation in the 3D space can be achieved Similarly, the material deposition direction is represented by a rotation angle J about the vertical Z axis Hence, the three independent decision variables D , E , and J would constitute a chromosome/individual of the GA population Binary string is used to encode these three variables as shown in Fig Each chromosome consists of 34 bits where the first 11 bits encode D in the range of 90º–270º, the next 12 bits encode E in the range of 0º–360º, and the last 11 bits encode J in the range of 0º–180º Every single bit in a chromosome is called a gene For the initial population of a specified size N , each of its chromosomes is randomly generated in this bitwise fashion Chromosome: D E J 1 1 1 1 1 0 1 0 1 1 0 1 Figure A binary encoded chromosome A single-point crossover operator is used to exchange the genes between the parents at the crossover position in order to generate offspring as shown in Fig In mutation operation, multiple genes of every offspring are randomly selected with a given probability of mutation and then altered as shown in Fig 981 Geometric analysis for concurrent process optimization of AM Ahsan et al Crossover point Parent 1: 1 1 1 1 1 0 1 0 1 1 0 1 Parent 2: 1 1 0 1 1 1 0 0 1 1 1 1 0 Crossover Offspring 1: 1 1 0 1 1 1 0 1 0 1 1 0 1 Offspring 2: 1 1 1 1 1 0 0 1 1 1 1 0 Figure Single point crossover operation Selected genes for mutation Chromosome: 1 1 0 1 1 1 0 1 0 1 1 0 1 Mutation Mutated Chromosome: 1 1 0 1 1 0 0 0 1 0 1 1 0 1 Figure Mutation operation Implementation The proposed methodology described is implemented on two 3D example objects using a Visual Basic based script All the computations are performed on a core i7 @3.6 GHz CPU with GB RAM The proposed methodology is utilized for extrusion based AM technique to determine the optimum build orientation and deposition direction for the two distinct objects Constrained nonlinear minimization routine provided in MATLAB package is used to determine the optimum attribute weights (HEIM) To ensure the inequality between two alternatives is assumed to have a magnitude of 0.01 It took about seconds to compute the optimum weight The time required to implement the methodology on example and example are approximately 15 and seconds per objective function evaluation, respectively The GA input parameters defined by the user are population size, crossover probability, mutation probability, and generation limit The maximum number of generation is used as the termination condition for GA The GA parameter values used for both examples are listed in Table The layer thickness is assumed 0.254 mm and in equation (3) for crisscross tool-path is considered 90° for both objects Example 1, which is used to demonstrate the proposed methodology, is shown in Fig 8(a) The object has a volume of 23319 cubic mm For Eq (3), the following weight values of the geometric attributes are determined using HEIM which is discussed in Section 3: Fig 10(a) wO ,1 0.073 , wO , 0.175 , wO , 0.15, wO , 0.25, wL ,1 0.1, wL , 0.08, and wL , 0.172 illustrates the convergence of the optimization procedure after 15 generations for diamond (example 982 Geometric analysis for concurrent process optimization of AM Ahsan et al 1) Since the fitness value is the evaluation measure of a chromosome (build orientation and tool-path angle), the build orientation and tool-path angle with the minimum fitness value in each generation is the best solution of that generation Table GA parameters Example and Population size: 60 crossover probability: 0.6 mutation probability: 0.01 Z 60 Build Direction Maximum number of generation: Y X D 0q, E 0q D* 90 q, E * (a) 236 22 q (b) Figure (a) Example at reference orientation ( D orientation ( D * 0q, E 90 q, E * 0q ) and (b) Example at the optimal build 236 22 q ) 12th Layer 5th Layer Y X (a) J (b) * odd 45 02 q * J even 135 02 q Figure Optimum deposition directions for odd and even numbered layers of example at its optimum build orientation 983 Geometric analysis for concurrent process optimization of AM Ahsan et al The optimum build orientation and tool-path angle obtained using our algorithm for the Example are D * 90 q , E * 236 22 q , and J * 45 02 q as shown in Fig 8(b) and The real values of the angles obtained from GA are rounded to two decimal places As H 90 q , optimum tool-path angle for * * 45 02 q and J even 135 02 q , respectively odd numbered layers and even numbered layers are J odd 0.230 (a) 0.214 Best Fitness value 0.212 Best Fitness value (b) 0.225 0.210 0.208 0.206 0.204 0.202 0.220 0.215 0.210 0.205 0.200 10 20 30 40 50 60 10 20 Generation 30 40 50 60 Generation Z Y D Z Y X 0q, E 0q D* 91 67 q, E * X 269 45 q Build Direction Figure 10 Convergence plot of the optimization procedure for (a) Example 1, and (b) Example (b) (a) Figure 11 (a) Example (earbud) at reference orientation ( D the optimal build orientation ( D * 0q, E 91 67 q, E * 0q ) and (b) Example (earbud) at 269 45 q ) The second example shown in Fig 11 (a) is an earbud which has a volume of 3287 mm Like example 1, the same weight values of the geometric attributes are used for the earbud The optimum build orientation and tool-path angle obtained for the earbud are D * 91 67 q , E * 269 45 q , and J* 75 8q Therefore, the optimum tool-path angle for odd numbered layers and even numbered * * layers are J odd 75 8q and J even 165 8q , respectively as shown in Fig 12 The convergence of the optimization procedure for the earbud (example 2) within 37 generation as shown in Fig 10 (b) The * part oriented through D * and E in the standard coordinate system is shown in Fig 11(b) The 984 Geometric analysis for concurrent process optimization of AM Ahsan et al optimum build orientation results in minimum number of concave layer contours and the optimum tool-path angle further minimizes the overall contour discontinued area to approximately 3%, thereby reducing the undesired interruptions in tool movement On the other hand, the reference orientation and tool-path angle (D 0q, E 0q, J 0q) experience concave contours with almost 12.4% overall discontinued area index Y X (a) 15th Layer * J odd 75 8q 16th Layer * 165 8q even (b) J Figure 12.Optimum deposition directions for odd and even numbered layers of the earbud at its optimum build orientation To further assess the effectiveness of the proposed algorithm in terms of build time, the total build times of both example parts are estimated for their optimum build orientation and tool-path angle using a build time estimation model (Ahasan, 2015) The total build time of each part for an arbitrarily selected build orientation and tool-path angle (D 0q, E 0q, J 20q for example and D 0q, E 180 q, J 0q for example 2) is also estimated using the same build time estimation model Then all these estimated build times listed in Table are compared with the build times provided by a commercial FDM 3D printing software named Cura 14.09 developed by Ultimaker For both parts, the optimum build orientation and tool-path angle yields minimum build time However, compared to example 1, the build time of example corresponding to the optimum solution significantly improves, because example has higher contour geometric complexity Table Build time comparison between optimum and arbitrary process plans Time (sec) Object Example Example Build Direction Toolpath Angle Time Model Commercial Software Optimum Optimum 3600 NA Optimum Arbitrary 3798 5040 Arbitrary Optimum 3780 NA Arbitrary Arbitrary 3810 5700 Optimum Optimum 420 NA Optimum Arbitrary 444 900 Arbitrary Arbitrary Optimum Arbitrary 587 578 NA 1080 985 Geometric analysis for concurrent process optimization of AM Ahsan et al Conclusion Build orientation and deposition direction are two important AM process parameters which are determined at the pre-processing stage of AM Exhaustive search method would require extensive computation power even for a coarse resolution/increment of the rotation angles This fact justifies the use of GA to solve the current AM process planning problem In this paper, a frame work is developed for optimizing both build orientation and deposition direction simultaneously by analyzing the 3D part geometry as well as the corresponding layer contours in order to minimize fabrication complexity Incorporating support structure and multi-material heterogeneous object in this model will be the future direction of this work References Ahasan, H., Nazmul, A., Bashir, K., (2015) Optimization Material Deposition Direction for Functional Internal Architecture in Additive Manufacturing Processes Paper 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Optimum deposition directions for odd and even numbered layers of example at its optimum build orientation 983 Geometric analysis for concurrent process optimization of AM Ahsan et al The optimum... 578 NA 1080 985 Geometric analysis for concurrent process optimization of AM Ahsan et al Conclusion Build orientation and deposition direction are two important AM process parameters which are