Overhang Region Research Articles

Build orientation optimization considering thermal distortion in additive manufacturing

Additive manufacturing (AM) technology enables the fabrication of three-dimensional objects with complex shapes and has been extensively applied in various industries. AM is a layer-wise fabrication process where a variety of factors affect manufacturing performance and product quality. One of the most important factor is the thermal distortion, which is caused by the high temperature gradients in the fabrication process. The thermal distortion is also influenced by the support structure of the printing object, and this distortion varies depending on the chosen build orientation. Additionally, for the overhang regions, extra supports are required for printing and will be removed in the post-processing. For the 3D printing process, the thermal distortion and support requirements are interconnected and linked to build orientation. To investigate suitable build orientation, the thermal distortion and support are quantified, and a multi-objective build orientation optimization method is proposed to obtain representative orientations. Based on the proposed method, 9 typical 3D shapes are evaluated. In addition, the single-objective build orientation optimization problem is studied and compared, and the influence of slicing layers per stage on the simulation accuracy and efficiency is discussed. The effectiveness and applicability of the method are verified, and representative directions can be obtained for different fabrication purposes.

Understanding coaxial photodiode-based multispectral pyrometer measurements at the overhang regions in laser powder bed fusion for part qualification

Coaxial photodiode monitoring sensors provide a digital signature at the melt pool level in laser powder bed fusion (L-PBF), facilitating faster part qualification. However, current signatures are plagued by significant noise and signal variation and show counterintuitive trends such as a decrease in measured temperature near overhang surfaces. This paper investigates the behavior of coaxial photodiode-based melt pool monitoring (PD-MPM) thermal measurements at overhang regions by conducting a combination of experiments and multiphysics simulations. High-speed in situ synchrotron X-ray imaging is coupled with a coaxial photodiode system to enable comparison of the observed melt pool phenomena and monitoring signals during double-track AlSi10Mg experiments. A multiphysics model is developed to simulate the melt pool dynamics and concurrent sensor signals throughout the process. We propose a surrogate model that clarifies the correlation between sensor signals and melt pool temperature. Both experimental and simulation results emphasize the significant impacts of laser energy and keyhole formation on solid-liquid interface discontinuities and PD-MPM signals. Results reveal that a boiling region with a relatively smaller projected area, as near an overhang, can lead to a decrease in the measured melt pool temperature, even when the true peak temperature remains constant, meaning that PD-MPM temperature measurements cannot be used to estimate absolute melt pool temperature. Consequently, in overhang regions, interaction between the melt pool and underlying powder results in an abruptly deforming melt pool and a pronounced decrease in both individual photodiode intensities and overall measured melt pool temperature. This work illustrates how to correctly interpret the coaxial photodiode monitoring signals in L-PBF by uncovering the intricate dynamics within the melt pool, particularly in challenging overhang regions, and pave the foundation for data-driven part qualification.

Topology Optimization of Self-supporting Structures for Additive Manufacturing via Implicit B-spline Representations

Owing to the rapid development in additive manufacturing, the potential to fabricate intricate structures has become a reality, emphasizing the importance of designing structures conducive to additive manufacturing processes. A crucial consideration is the ability to design structures requiring no additional support during manufacturing. This paper employs implicit B-spline representations for self-supporting structure design by integrating a topology optimization model with self-supporting constraints derived analytically from the implicit representation. This analytical derivation for detecting overhang regions enables accurate and efficient calculation of constraints, outperforming other B-spline-based methods. Compared to the traditional voxel-based methods, the implicit B-spline representation significantly expedites the optimization process by reducing the number of design variables. Additionally, several acceleration techniques are implemented to enhance the efficiency of our method, allowing simulations of 3D models with millions of finite elements to be completed within one and half an hour, excelling other B-spline-based methods and voxel-based methods. Various numerical experiments validate its excellent performance, confirming the effectiveness and efficiency of the proposed algorithm.

How to Make a Single-Layer Pouch Cell That Matches the Performance of a Commercial Li-Ion Cell

As lithium-ion batteries (LIBs) have exploded in popularity due to the consumer electronics and electric vehicle industries, many resources are poured into research. While the simplest cell format requiring the least amount of active material to make in a research laboratory to study various aspects of the cell is usually the coin cell, it is far from the most representative of commercial LIBs. Oftentimes, coin cells are made with a large negative electrode overhang to reduce the risk from positive/negative electrode misalignment, but the overhang region can cause Li+ to become effectively trapped at higher C-rates1. While this is a necessary trade-off in today’s commercial LIB manufacturing, the overhang area is normally a much smaller fraction of the total negative electrode area in a commercial cell than in a laboratory coin cell, which can lead to discrepancies in cycle testing. Moreover, during assembly of commercial stacked or wound cells, there is always a region in which one side of a double-sided coating, typically the negative, is not needed and thus a single-sided electrode should be used. However, not all manufacturers eliminate the outward-facing second side and elect to simply use double-sided coatings throughout. Therefore, studying the effects of excess electrode in single-layer pouch cells will be explored in this presentation. In this presentation, cells made in various formats (coin and stacked pouch) will be compared to single-layer pouch cells made with and without negative electrode overhang. Single-layer pouch cells are the easiest format for assembling full cells without overhang because they are neither too small nor too big for positive/negative electrode alignment to be difficult. Moreover, single-layer pouch cells made with double-sided coatings (without overhang) and cycled using Ultra-High Precision Coulometry (UHPC) will be shown to have poor cycling. This is for two reasons: 1) for a double-sided negative, the outward-facing coating of the electrode can trap Li+ just like the overhang on the inward-facing coating; and 2) the outward-facing positive can be deintercalated and provide more capacity than desired2, possibly even surpassing the negative/positive areal capacity ratio. Single-layer pouch cells with no overhang are shown in Figure 1a to outperform all other cell formats tested, retaining 90% of their original capacity after 500 cycles at C/3 and 40 °C, and have the lowest difference in capacity between typical C/3 and C/20 checkup cycles as shown in Figure 1b. The stacked pouch cells in Figure 1 are composed of 3 positive and 4 negative electrodes that are all double-sided, meaning there are two outward-facing negative electrode coatings that can trap Li+, possibly resulting in the much poorer capacity fade to 80% after 500 cycles illustrated in Figure 1a. Thus, single-layer pouch cells without overhang give the most realistic cycling results for the tested electrode materials. Figure 1. C/3 cycling of full cells of various formats denoted in the legend. Plotted in (a) is the normalized discharge capacity and (b) is the difference in areal discharge capacity between the C/20 checkup cycle and preceding C/3 cycle. REFERENCES Gyenes, B., Stevens, D.A., Chevrier, V.L., and Dahn, J.R. (2015). Understanding Anomalous Behavior in Coulombic Efficiency Measurements on Li-Ion Batteries. J Electrochem Soc 162, A278–A283. 10.1149/2.0191503jes.Smith, A., Stüble, P., Leuthner, L., Hofmann, A., Jeschull, F., and Mereacre, L. (2023). Potential and Limitations of Research Battery Cell Types for Electrochemical Data Acquisition. Batter Supercaps e202300080. doi.org/10.1002/batt.202300080. Figure 1

Terminal bridging of siRNA duplex at the ribose 2′ position controls strand bias and target sequence preference

Small interfering RNA (siRNA) and short hairpin RNA (shRNA) are widely used as RNA interference (RNAi) reagents. Recently, truncated shRNAs that trigger RNAi in a Dicer-independent manner have been developed. We generated a novel class of RNAi reagent, designated enforced strand bias (ESB) RNA, in which an siRNA duplex was chemically bridged between the 3' terminal overhang region of the guide strand and the 5' terminal nucleotide of the passenger strand. ESB RNA, which is chemically bridged at the 2' positions of ribose (2'-2' ESB RNA), functions in a Dicer-independent manner and was highly effective at triggering RNAi without the passenger strand-derived off-target effect. In addition, the 2'-2' ESB RNA exhibited a unique target sequence preference that differs from siRNA and silenced target sequences that could not be effectively suppressed by siRNA. Our results indicate that ESB RNA has the potential to be an effective RNAi reagent even when the target sequence is not suitable for siRNA.

Hybridization-based CpG methylation level detection using methyl-CpG-binding domain–fused luciferase

Hypermethylation of tumor-suppressor genes and global hypomethylation, which is related to methylation level at the retroelement, have been recognized as features of the cancer genome. In this study, we developed a hybridization-based CpG methylation level detection method using methyl-CpG-binding domain-fused firefly luciferase (MBD-Fluc). In this method, methylated probe oligonucleotides were used to capture target oligonucleotides. Fully methylated and hemimethylated double-stranded DNA (dsDNA) was formed by hybridization of the methylated captured oligonucleotides with methylated or unmethylated target oligonucleotides, respectively. MBD-Fluc specifically binds to fully methylated dsDNA but not to hemimethylated dsDNA; therefore, methylated target oligonucleotides can be detected by measuring the luciferase activity of the bound MBD-Fluc. Using the corresponding methylated probe oligonucleotides, the CpG methylation levels of SEPT9, BRCA1, and long interspersed nuclear element-1 (LINE-1) oligonucleotides were quantified. Moreover, we demonstrated that the emission detection signal was not affected by the methylation state of the overhang region of the target oligonucleotide, which was not hybridized to the probe oligonucleotide, indicating that methylated CpG of the target region could be accurately detected. Unmethylated-CpG-binding domain-fused luciferases and 5-hydroxymethyl-CpG-binding domain-fused luciferases have been constructed, suggesting that other modified bases can be detected by the same platform.

Inhibited complete folding of consecutive human telomeric G-quadruplexes.

Noncanonical DNA structures, termed G-quadruplexes, are present in human genomic DNA and are important elements in many DNA metabolic processes. Multiple sites in the human genome have G-rich DNA stretches able to support formation of several consecutive G-quadruplexes. One of those sites is the telomeric overhang region that has multiple repeats of TTAGGG and is tightly associated with both cancer and aging. We investigated the folding of consecutive G-quadruplexes in both potassium- and sodium-containing solutions using single-molecule FRET spectroscopy, circular dichroism, thermal melting and molecular dynamics simulations. Our observations show coexistence of partially and fully folded DNA, the latter consisting of consecutive G-quadruplexes. Following the folding process over hours in sodium-containing buffers revealed fast G-quadruplex folding but slow establishment of thermodynamic equilibrium. We find that full consecutive G-quadruplex formation is inhibited by the many DNA structures randomly nucleating on the DNA, some of which are off-path conformations that need to unfold to allow full folding. Our study allows describing consecutive G-quadruplex formation in both nonequilibrium and equilibrium conditions by a unified picture, where, due to the many possible DNA conformations, full folding with consecutive G-quadruplexes as beads on a string is not necessarily achieved.

Lightweight design of two-level supports for extrusion-based additive manufacturing based on metaheuristic algorithms

PurposeTwo-level support with Level 1 consisting of a set of beams and Level 2 consisting of a tree-like structure is an efficient support structure for extrusion-based additive manufacturing (EBAM). However, the literature for finding a slim two-level support is rare. The purpose of this paper is to design a lightweight two-level support structure for EBAM.Design/methodology/approachTo efficiently solve the problem, the lightweight design problem is split into two subproblems: finding a slim Level 1 support and a slim Level 2 support. To solve these two subproblems, this paper develops three efficient metaheuristic algorithms, i.e. genetic algorithm (GA), genetic programming (GP) and particle swarm optimization (PSO). They are problem-independent and are powerful in global search. For the first subproblem, considering the path direction is a critical factor influencing the layout of Level 1 support, this paper solves it by splitting the overhang region into a set of subregions, and determining the path direction (vertical or horizontal) in each subregion using GA. For the second subproblem, a hybrid of two metaheuristic algorithms is proposed: the GP manipulates the topologies of the tree support, while the PSO optimizes the position of nodes and the diameter of tree branches. In particular, each chromosome is encoded as a single virtual tree for GP to make it easy to manipulate Crossover and Mutation. Furthermore, a local strategy of geometric search is designed to help the hybrid algorithm reach a better result.FindingsSimulation results show that the proposed method is preferred over the existing method: it saves the materials of the two-level support up to 26.34%, the materials of the Level 1 support up to 6.62% and the materials of the Level 2 support up to 37.93%. The proposed local strategy of geometric search can further improve the hybrid algorithm, saving up to 17.88% of Level 2 support materials.Research limitations/implicationsThe proposed approach for sliming Level 1 support requires the overhanging region to be a rectilinear polygon and the path direction in a subregion to be vertical or horizontal. This limitation limits the further material savings of the Level 1 support. In future research, the proposed approach can be extended to handle an arbitrary overhang region, each with several choices of path directions.Practical implicationsThe details of how to integrate the proposed algorithm into the open-source program CuraEngine 4.13.0 is presented. This is helpful for the designers and manufacturers to practice on their own 3D printers.Originality/valueThe path planning of the overhang is a critical factor influencing the distribution of supporting points and will thus influence the shape of the support structure. Different from existing approaches that use single path directions, the proposed method optimizes the volume of the support structure by planning hybrid paths of the overhangs.

Development of a simple and rapid fluorescent aptasensor based on DNA tweezer

AbstractUtilizing the flexible spatial structure and dynamic conformational change of DNA tweezer (DT), a simple and fast fluorescent aptasensor based on fluorescence resonance energy transfer (FRET) was designed. The hinge region and the overhang region were optimized to obtain the satisfied flexibility and controllably conformational change. Using ochratoxin A (OTA) as a simulation target, the established aptasensor showed a simple and time‐saving procedure, higher sensitivity, good selectivity, and good stability with a detection limit of 0.024 ng/ml. Besides, the aptasensor exhibited favorable accuracy with recoveries of 95–103% for spiked cereal samples. The proposed fluorescent aptasensor has a promising potential for the rapid and reliable detection of targets.

Thermal history and high-speed optical imaging of overhang structures during laser powder bed fusion: A computational and experimental analysis

Laser powder bed fusion (LPBF) is a powerful tool for additive manufacturing (AM) of metal components. However, fabricating components with overhanging features using LPBF remains a challenge. Overhangs suffer from dimensional inaccuracies, high surface roughness, and agglomerated material or dross. These parts often do not meet engineering requirements and are discarded and reprinted until requirements are met, or redesigned to avoid overhangs. Printing a flat overhang is especially challenging due to the long, unsupported powder bed that fosters material agglomeration and inhibits heat flux. Commercial LPBF machines use distinct laser parameters for the downskin layers in overhang regions. Downskin parameters for a given material are often selected by trial and error: printing many parts, changing the laser power and velocity parameters, as well as the number of layers to apply them. The impact of changing the laser parameters on the thermal history of a given layer and multiple layers is not well characterized or understood. This research uses thermal simulations, infrared (IR) imaging, and high-speed optical imaging to study the fabrication of flat overhang structures in 316L stainless steel. The thermal evolution of different downskin strategies on multiple layers is simulated with high fidelity thermal simulations and experimentally measured as the part is printed with carefully calibrated forward looking infrared (FLIR) imaging. Emissivity measurements are performed in a custom chamber under a range of conditions to accurately convert FLIR measurements to temperatures. The layer construction is also recorded with high-speed video to observe the powder bed, melt pool formation, and effects of material agglomeration. Parameter strategies that minimize layer-to-layer variations of the peak temperature, heating rate, and cooling rate are investigated to inform print conditions for overhang features.

Stress Grading Performance Analysis of Stator Coil Considering the Manufacturing Method and the Insulation Design

In rotating machines, the approach of applying nonlinear conductive stress grading tape (SGT) has been applied to reduce the electric field stress in the coil’s overhang region. To characterize and verify the electric field grading effect of SGT in electric machines, electric field analysis using the nonlinear conductivity of SGT as a boundary condition must be considered. However, previous studies have shown limitations in the characterization and application of SGT materials in insulation system design for various reasons, such as lack of conductivity measurement standards for nonlinear materials or not considering possible changes in material properties during the manufacturing procedure. In this study, the nonlinear conductivity of SGT was measured by considering the rotating machine’s manufacturing procedure. A finite element method (FEM) electric field analysis was performed using the measured nonlinear conductivity. Based on the improved conductivity measurement method of SGT and FEM analysis, the effects of changing several insulation design parameters in the field grading performance were studied on a 13.8 kV stator coil. Moreover, the effect of preheating on the SGT conductivity was also examined. Based on analysis results, we realized the possibility of more precise insulation design of the stator coil. Our findings supplement the insufficient insulation design guide on the SGT part and contribute to establishing a systematic approach for insulation design. Furthermore, the proposed methods enable design optimization and detection of the cause of insulation failure.

Roughness and Near-Surface Porosity of Unsupported Overhangs Produced by High-Speed Laser Powder Bed Fusion.

Laser powder bed fusion (LPBF) is a promising technology that requires further work to improve productivity to be adopted more widely. One possible approach is to increase the laser power and scan speed. A customized high-speed and high-power LPBF system has been developed for this purpose. The current study investigated the surface roughness and near-surface porosity as a result of unsupported overhangs at varying inclination angles and orientations during the manufacturing of Ti6Al4V parts with this custom high-speed and high-power LPBF system. It is known that surface roughness and porosity are among the main drawbacks for parts manufactured by LPBF, and that supports are required for overhang regions with low inclination angles relative to the powder bed, typically in commercial LPBF systems requiring supports for regions with inclination angles less than 45°. However, the appropriate inclination angles for this custom system with high power and speed requires investigation. In this article, a simple benchmark test artefact with different inclination angles was manufactured in different orientations on the build platform and characterized by X-ray tomography, touch probe roughness meter, optical microscopy, and scanning electron microscopy. The analysis of surface roughness and near-surface porosity at upskin and downskin regions was performed as a function of inclination angle. The results indicate that the high-speed LPBF process produces relatively high roughness in all cases, with different porosity distributions at upskin and downskin areas. Both roughness and porosity vary as a function of inclination angle. Significant warping was observed, depending on build orientation relative to laser scanning direction. These are the first reported results of the detailed surface roughness and porosity characterization of part quality from such a high-speed, high-power LPBF process.

Experimental and numerical investigation of the origin of surface roughness in laser powder bed fused overhang regions

ABSTRACT Surface roughness of laser powder bed fusion (L-PBF) printed overhang regions is a major contributor to deteriorated shape accuracy/surface quality. This study investigates the mechanisms behind the evolution of surface roughness (Ra) in overhang regions. The evolution of surface morphology is the result of a combination of border track contour, powder adhesion, warp deformation, and dross formation, which is strongly related to the overhang angle (θ). When 0° ≤ θ ≤ 15°, the overhang angle does not affect Ra significantly since only a small area of the melt pool boundaries contacts the powder bed resulting in slight powder adhesion. When 15° < θ ≤ 50°, powder adhesion is enhanced by the melt pool sinking and the increased contact area between the melt pool boundary and powder bed. When θ > 50°, large waviness of the overhang contour, adhesion of powder clusters, severe warp deformation and dross formation increase Ra sharply.

Using Lithium-ion Differential Thermal Analysis to Probe Tortuosity of Negative Electrodes in Lithium-Ion Cells

If the positive electrode of a lithium-ion cell faces a surface with no opposing negative electrode, Li+ ions can plate on the nearest edge of the negative electrode current collector. This poses considerable danger to the battery, and so modern Li-ion cells have a negative electrode that is both wider and longer than the positive electrode. In this work, we present evidence using Li-ion cell differential thermal analysis that this overhang causes the formation of long lived electrolyte concentration gradients after discharge or charge due to the long times needed for the lithium content in the overhang region of the negative electrode to equilibrate with the lithium content in the bulk of the negative electrode. Several cases are shown, as well as a comparison to a commercial cell, and an estimation of the type and magnitude of the electrolyte concentration gradient is given. Finally, it is shown that this phenomenon can be applied to easily distinguish between graphite electrodes with high and low tortuosity using differential thermal analysis.

Layer-wise control of selective laser melting by means of inline melt pool area measurements

Industrial selective laser melting (SLM) systems commonly employ a fixed set of process parameters throughout the build of the same component. The process parameters are generally found by experimental studies carried out on simple geometries which achieve high density. A common issue is related to the fact that the single set of parameters can be inadequate for small sections and overhang regions where thermal accumulation can occur. An online adaptation of process parameters is required for avoiding such issues and defects that commonly arise, such as the swelling phenomenon. A real-time control strategy would be desirable. However, the real-time control requires fast acquisition and reaction in the order of microseconds. Another approach is to provide corrective actions in a layer-wise fashion by elaborating the monitoring data collected during the previous layer. Therefore, this work proposes a layer-wise control strategy based on coaxial melt pool monitoring. For this purpose, an open SLM platform is employed, fitted with a complementary metal-oxide semiconductor camera, to view the process emission in the near infrared region. Initially, the nominal level of the melt pool area is defined on a simple geometry. Then, the melt pool area is monitored on more complex shapes. The melt pool area measured on each scan vector of a given layer is used to compensate the energy density of the same scan vector at the next layer. The results show an effective reduction of swelling defects on small geometries with fine details.

Topology optimization of easy-removal support structures for additive manufacturing

This paper presents a density-based topology optimization approach to design easy-removal support structures for additive manufacturing (AM). First, a multi-field structural parameterization is proposed for topology optimization by considering AM filtering technique that ensures the physical design being self-support. An easy-removal constraint is developed to generate porous structural patterns in the contact region between the support structures and its surroundings. An improved formulation is further proposed to prevent obtaining impractical solutions which contain one-node connection in the structural members. Besides, an overhang constraint and a design-dependent self-weight load are considered. As a result, the optimized support structures are self-support, able to support the overhang regions of the given prototype and possesses excellent mechanical properties to bear the self-weight of the entire AM part. It can be easily removed from both the prototype and the baseplate. Numerical examples and discussions are given to demonstrate its effectiveness and applicability.

A hairpin probe-mediated isothermal amplification method to detect target nucleic acid

We herein describe Hairpin probe-mediated Isothermal Amplification (HIAmp), a novel isothermal method to detect a target nucleic acid. This method employs a hairpin probe (HP) designed to be opened through binding to the target nucleic acid. Upon opening of the HP, the primer binds to the free stem of the opened HP followed by its extension by DNA polymerase, consequently displacing and recycling the target nucleic acid to open another HP and producing an intermediate product (IP) containing a nicking site. The IP then continuously produces a trigger probe (TP), which subsequently initiates the isothermal amplification cycles in two separate ways by binding to either the intact HP or the overhang region of the IP. Through the following well-designed interconnected pathways, a large amount of final double-stranded DNA products (FPs) is produced and a high fluorescent signal is generated from the duplex-specific fluorescent dye, SYBR Green I. By employing this isothermal strategy, target DNA was very sensitively detected down to 64 zmol with the capability to discriminate the target DNA against non-specific DNAs. This work would provide remarkable insight into the design of a new DNA network enabling isothermal amplification.

The influence of the anode overhang effect on the capacity of lithium-ion cells – a 0D-modeling approach

Abstract In this work, the behavior of the anode overhang effect in lithium-ion cells is experimentally investigated and simulated for experimental three electrode cells. An empirical method is presented to transfer the simple 0D-model from the experimental cell level to pouch cells. An anode overhang model will help to correctly interpret cyclic and calendaric aging experiments e.g. in terms of a more reliable and detailed separation of reversible and irreversible capacity losses as well as evaluating the actual state of health of a lithium-ion battery. For the three electrode cells different cathode diameters are used to modulate different sized anode overhang areas. Moreover, the influence of different state of charges on the reversible capacity effect is investigated. To examine the influence of the separator on the evolution of usable cell capacity different separator thicknesses are applied. It is found that the properties of the separator significantly influence the rate at which balancing processes between overhang and active region take place. The results show good accordance of the experimental results to the simulation.

An investigation upon overhang zones by using finite element modelling and in-situ monitoring systems

The characteristic of heat transfer in direct metal laser sintering is a key point in terms of overall material properties. Thus, this research focuses on the temperature distribution in overhang zones of Inconel 625 by employing finite element modelling and in-situ monitoring systems. The larger fluctuations in radiation signals are observed during solidification of melt pools. Furthermore, optical tomography confirms that overheating caused by lack of heat transfer between melt pool and powder occurs in overhang regions. This phenomenon is explained by finite element modelling based on thermal behavior of melt pool with powder, and surface characterization.

Printing Direction Optimization Through Slice Number and Support Minimization

One major drawback of 3D printing technologies is the low printing efficiency. In general, it takes 8-12 hours to print a normal 3D model. 3D printing technologies manufacture objects layer by layer where each layer is composed of one or more closed 2D polygons (named as slices in this work). As a result, the number of slices will directly affects the printing time. In addition, most 3D printing technologies need extra supporting structures to support overhang regions during printing, such as Fused Deposition Modeling (FDM), which will largely increase manufacturing time. We observe that both the slicing number and the amount of supporting structures are affected by printing direction. In this work, a novel printing direction optimization algorithm is proposed based on the amount of slices and overhang areas. In the proposed method, Genetic Algorithm is used to obtain optimal printing direction where the fitness function is designed as the weighted slice number and overhang areas. Experimental results show that the proposed algorithm is able to obtain an optimal printing direction to reduce the number of slices and overhang areas.