Overhang Angle Research Articles

Robust topology optimization of multi-material structures with overhang angle constraints using the material field series-expansion method

This paper presents a novel topology optimization method to enhance the manufacturability and practicality of multi-material structures. Traditional topology optimization techniques excel at generating high-performance designs, but the performance of these designs is often compromised due to the load perturbations encountered in real-world applications or post-processing for additive manufacturing (AM). This work addresses this challenge by incorporating three key features directly into the optimization process. First, the method integrates overhang angle constraints, ensuring designs are inherently manufacturable with AM. Second, it utilizes the material field series-expansion method for a significant reduction in design variables while simultaneously providing a clear and efficient description of material distribution within the optimized designs. Finally, to enhance design robustness under real-world scenarios with uncertain loads, the method employs Monte Carlo simulation, which is decoupled from the optimization process to reduce the computational cost. Numerical examples demonstrate the efficiency and effectiveness of the proposed method in generating robust designs of multi-material structures well-suited for AM. The proposed framework offers a promising pathway for the realization of complex, high-performance composite structures.

Influence of strut angle and radius on the energy absorption and failure mechanisms in 3-strut, 4-strut and 6-strut lattice structures

Abstract 3D-printed truss structures have remarkable potential in the aerospace and weight-critical technologies fields. However, design parameters need to be carefully considered. A low overhang angle or diameter can result in discrepancies. This research presents an approach by examining the effect of strut overhang angle and radius on the mechanical properties of 3-, 4- and 6-strut lattice structures under compressive loading. 1.6- and 2.4-mm diameter struts were designed with 45°, 50°, 55° and 60° overhang angle strut lattices. Experiments were simulated and compared with test results for each parameter. Even if joint regions have little effect on specimens’ density, it has a remarkable effect on mechanical properties of the specimen. To simulate this, many studies were investigated to simulate joint regions. The study’s goal is to deepen the understanding of how design variations in strut lattice structures influence their energy-absorbing characteristic and mechanical behavior, using a combination of static tests and finite element analysis for validation. This insight is crucial for optimizing lattice design to balance weight, strength, and energy-absorbing capacity effectively. The experimental test result and numerical result showed rather good agreement. It is observed that joint regions, overhang angle, and diameters were the main parameters affecting specimens’ mechanical behavior.

Feedrate-preserved motion planning for five-axis directed energy deposition of freeform metal parts

Laser-powder DED (LP-DED) has been investigated extensively for the rapid prototype of complex and customized metallic parts and in-situ repairing tasks. However, unlike the material extrusion type which allows a relatively large overhang angle, the conventional 2.5-axis LP-DED faces a severe overhang issue that deteriorates the printing stability and quality. While five-axis LP-DED is able to effectively resolve the overhang problem, it however introduces new kinematic issues and limited nozzle orientation range due to physical restrictions of DED. The existing computer numerical control systems are mainly designed for machining, where the above issues can be mostly solved by feedrate scheduling, which, however, is not applicable for LP-DED processes, as the feedrate must be preserved as programmed lest deposition height would be altered since in most cases it is not practical to vary the powder flow rate in real-time. In this paper, a feedrate-preserved motion planning method is proposed to optimize the rotational angles of the machine tool in the machine coordinate system (MCS) under the constraints of MCS and workpiece coordinate system (WCS). Given a five-axis DED path as well as its accompanying initial nozzle orientation in WCS, we first map them via inverse kinematics to MCS, which is represented by a cylindrical coordinate system. Then, the motion path in the cylindrical coordinate system is optimized to avoid the singularity. Finally, the physical constraint of nozzle orientation in WCS is introduced into the time-weighted constrained Laplacian smoothing in MCS with the axial speed limits upheld. The experimental results confirm that the actual feedrate is successfully preserved as the theoretical one under the constraints of the axial kinematic limits, while the singularity is avoided.

Optimizing FDM 3D Printing of Medical Models

Present paper presents the results on four cases of optimization of FDM 3D printing of medical models used for training on specific medical issues (2 cases) and of personalized patient-specific models used for complex Trauma and Orthopedic surgical procedures planning (2 cases). Depending on optimization criteria (proper combination of model splitting – minimum need of supports/or no supports – minimization of printing time and material consumption, facile support removal and good surface quality), the modification of the Cura slicer recommended settings related to layer thickness and support pattern, support Z distance, support X/Y distance, support overhang angle, and minimum support area, allowed the reduction of 3D printing time with 24% and 33%, very easy support removal, and an assessment of surface accuracy and quality as very good for the purpose, made by end users.

Topological awareness towards collision-free multi-axis curved layer additive manufacturing

We present a topology-aware computational framework that enables global collision-free and support-structure-free material extrusion for curved layer multi-axis printing of a range of high-genus and simply connected models. The nature of multi-axis additive manufacturing facilitates continuous variation of build direction, which paves the way for numerous approaches of geometry-based curved layer design. However, due to unawareness of global topological features, prevention of collision between the printer nozzle and the workpiece can either remain uncertain or demand for exhaustive algorithmic approaches, depending on the topological and geometrical complexity of a given mesh model. In this paper, we present a topological analysis framework that draws inspiration from the concepts of Reeb graph and Morse theory, to distinguish between collision-prone and collision-free regions of mesh models. We provide an exact definition for global collision-inducing features in regions of risk and optimise the nozzle orientation vector field to avoid global collisions whilst adhering to the overhang angle constraints. A new shape analysis method is then proposed to find the model orientation which maximises the manufacturability of bifurcating simply connected models. To validate our algorithmic framework, several high-genus and bifurcating simply connected models are printed using a robotic multi-axis printer. The experimental results demonstrate the feasibility and effectiveness of our framework for minimising global collisions in multi-axis curved layer additive manufacturing for a range of mesh models.

Topology optimization and 3D printing of a unibody quadcopter airframe

The performance of any unmanned aerial vehicle largely depends upon its weight as this characteristic dictates its payload capacity and flight duration. This paper presents a multiphysics simulation method for designing a unibody quadcopter airframe with optimum weight in SolidWorks. By adopting the computer-aided topology optimization concept, the mass of the frame is decreased by 91% (from 1558.44 to 134.738 grams) after getting rid of the unwanted elements, while not compromising its structural rigidity. The efficacy of the model is assessed by finite element analysis and it is found that the stress would remain within the acceptable limit. The optimized structure shows an operating life of 1.6×105 cycles in the fatigue analysis and experiences significantly less drag force in the computational fluid dynamics test than the original airframe for several angles of attack, thus proving the superiority of the optimized frame over the initial model. Finally, additive manufacturing is performed to fabricate the optimized structure using PLA material. 3D printing through the fused deposition modeling technique is chosen since it is ideal for fabricating intricate engineering prototypes compared to orthodox manufacturing processes. While creating the frame, a 45° overhang angle is maintained to ensure the usage of less support material.

Process qualification, additive manufacturing, and postprocessing of a hydrogen peroxide/kerosene 6 kN aerospike breadboard engine

This contribution addresses the complete process chain of an annular aerospike breadboard engine fabricated by laser powder bed fusion using the nickel-based superalloy Inconel® 718. In order to qualify the material and process for this high-temperature application, an extensive material characterization campaign including density and roughness measurements, as well as tensile tests at room temperature, 700, and 900 °C, was conducted. In addition, various geometric features such as triangles, ellipses, and circular shapes were generated to determine the maximum unsupported overhang angle and geometrical accuracy. The results were taken into account in the design maturation of the manifold and the cooling channels of the aerospike breadboard engine. Postprocessing included heat treatment to increase mechanical properties, milling, turning, and eroding of interfaces to fulfill the geometrical tolerances, thermal barrier coating of thermally stressed surfaces for better protection of thermal loads, and laser welding of spike and shroud for the final assembly as well as quality assurance. This contribution goes beyond small density cubes and tensile samples and offers details on the iterations necessary for the successful printing of large complex shaped functional parts. The scientific question is how to verify the additive manufacturing process through tensile testing, simulation, and design iterations for complex geometries and reduce the number of failed prints.

Parameter analysis to correlate density with surface roughness and productivity in Powder Bed Fusion – Laser Beam (PBF-LB) of AlSi10Mg

This work investigates the development of manufacturing parameters and correlations of parts manufactured via PBF-LB with AlSi10Mg using Design of Experiments (DoE). The main goal of this research is to gain a comprehensive understanding of the parameter space and find correlations of relative density with surface roughness and productivity by considering laser powers up to 400 W. The influence of different process parameters, combined and represented as the Volumetric Energy Density (VED) is investigated. Here, a density of above 99.5 % could be achieved within a wide VED range of 40 – 188 J/mm³. The measured mean downskin surface roughness ranges from 12 – 68 µm depending on their overhang angle and measurement method, whereas the mean top upskin surface roughness ranges between 4 – 48 µm with different parameter combinations of laser power (P) and layer thickness (LT). The approach developed here enables the efficient development of suitable process parameters and reduces the optimization effort of the PBF-LB process through the rapid characterization of manufactured part quality in terms of density, which directly influences its mechanical strength.

Surface roughness improvement of Ti-6Al-4V alloy overhang structures via process optimization for laser-powder bed fusion

In recent years, additive manufacturing of Ti-6Al-4V alloy components via Laser-Powder Bed Fusion has seen increasing application in the aerospace, military, and medical sectors. However, the high surface roughness of up- and down-skin for overhang structures remains a primary impediment to expanded implementation. This study aims to investigate the effects of the overhang angle and process parameters on the up- and down-skin surface roughness of the overhang structure. In addition, the underlying mechanisms leading to the different roughness of the up- and down-skin of the overhanging structure are comparatively analyzed. Subsequently, a response surface model was generated using the biharmonic spline interpolation (V4) method to optimize the process parameters, aiming to simultaneously improve the roughness of both up- and down-skin. Results demonstrate that the optimized parameters reduced the roughness of up- and down-skin by approximately 50 %.

A design and optimisation framework for cold spray additive manufacturing of lightweight aerospace structural components

Cold spray additive manufacturing (CSAM) is a solid-state deposition process with the potential to produce near-net shape components with complex geometry at a high fabrication rate, making it an attractive alternative to more widely established additive manufacturing (AM) processes. However, CSAM is still in its early stages and requires numerous advancements. The current literature highlights the lack of a design framework for fabricating structural components that encompasses the advantages and constraints of CSAM. This work proposes such a framework to guide product and process engineers, with its novel aspects including (i) accounting for different spray trajectories and their effect on anisotropic mechanical properties, (ii) accounting for the primary constraint for toolpath planning (maximum overhang angle ‘MOA’), and (iii) virtual development and optimisation of a real-world structural component with complex geometry. To exemplify this framework, tensile properties under two spray trajectories were determined experimentally for a common lightweight metal (titanium) supplemented with a ceramic to form a metal matrix composite with improved strength and hardness. Optimisation of the design was conducted via finite element analysis and topology optimisation (TO). Two different TO processes were conducted, namely (i) minimising the strain energy of the structure and reducing the weight by 60% (best stiffness-to-weight ratio) and (ii) minimising the weight by targeting a maximum factor of safety (FoS) value of 1.2. The final design was fabricated via CSAM with relatively little raw material wastage and reasonably close geometric accuracy. Fabrication defects were, however, noticed after making a demonstration component and mitigation measures are discussed within the context of the design framework proposed here.

An integrated method of topological optimization and path design for 3D concrete printing

As an advanced construction technology, 3D concrete printing (3DCP) has the advantage of high manufacturing freedom for various freeform structures. The digital design of 3D printing using topology optimization contributes to obtaining the maximum performance potential from manufactured structures. However, most digitally designed structures obtained by topology optimization cannot be directly manufactured using 3DCP owing to various manufacturing constraints that have not yet been considered in the design process. This paper presents an integrated design method for 3DCP by incorporating extrusion-based manufacturing characteristics into the topology optimization algorithm. Topological optimization is based on the solid isotropic material with penalization (SIMP) method owing to its ease of adaptation to multiple constraints. During the optimization iteration, the manufacturing characteristics of nozzle size and path continuity are considered as the design requirements of 3D printed structures to achieve high-quality manufacturing by using intermittent interruption of topology optimization to modify the design variables. Meanwhile, the anisotropic behaviors of material constraints and the volume and Tsai-Wu criterion of design constraints are introduced to obtain the desired mechanical performance with lightweight designs. Moreover, the number of closed regions and overhang angle controls are incorporated to ensure the global path continuity and stable stacking of optimized 3D structures. A concrete arch structure is 3D printed to validate the proposed integrated method, and the removal of breakpoints and short paths and complete filling rate are demonstrated. The integrated method facilitates the engineering application of 3DCP in a high-efficiency and high-quality manner.

Selective laser melting of GH3536 superalloy: microstructure, mechanical properties, and hydrocyclone manufacturing

The effect of scanning strategy on the microstructure and properties of GH3536 Ni-based superalloy prepared by Laser Powder Bed Fusion was investigated, for the purpose of building high quality hydrocyclone part. The results show that the strength of Z67° (a zone with 67° hatch angle strategy) specimen is the highest among the four scanning strategies (0°, 67°, 90°and Z67°), with yield strength and tensile strength of 681 ​MPa and 837 ​MPa, respectively. Selective orientation of crystals occurs during the forming process because the longitudinal section of the specimen exhibits a high texture strength in (001). As the stretching proceeds, the plastic deformation mechanism of the specimen gradually changes from slip to twin-dominated, a substantial amount of twinning is observed in the region where the deformation of the specimen reaches 80%. The additive manufacturing simulation suite: Ansys Additive is used to simulate the stress and deformation of the part during the process, and the displacement results are consistent with the experimental phenomena. According to the simulation results, the structure design is optimized and the surface quality of the part is improved. The results show that the support of the part is more reasonable when the overhang angle is 45°.

Downskin Surface Roughness Prediction with Machine Learning for As-Built CM247LC Fabricated Via Powder Bed Fusion with a Laser Beam.

Powder bed fusion with a laser beam (PBF-LB) is a widely used metal additive manufacturing method for fabricating complex three-dimensional components with a variety of metallic powders. However, metal parts fabricated by PBF-LB often present surface quality problems because of the layer-wise building process and the occurrence of partially unmelted powder particles. To reduce the surface roughness, surface post-processing is required, which incurs additional time and cost. In particular, the downskin surface generally has the worst surface roughness among the fabricated components. The rough surface reduces the lifetime and quality of the holed part owing to cracks, corrosion, and wear. In this study, for fast and efficient improvement of the downskin surface roughness of CM247LC fabricated by PBF-LB, machine learning algorithms, namely support vector regression (SVR), random forest (RF), and multilayer perceptron (MLP), were introduced to predict downskin surface roughness in the process parameter selection step. Three PBF-LB process parameters (laser power, scanning speed, and hatching distance) and the overhang angle were selected as the input variables for the machine learning models for predicting downskin surface roughness. Test samples were prepared and used for training and evaluation of the proposed machine learning algorithms, with RF showing the most promising results. Early results were confirmed when model predictions were compared to the actual measured roughness of a fabricated vane part, with average deviations of 13.7%, 4.3%, and 22.5% observed for SVR, RF, and MLP, respectively. The results showed that the proposed machine learning models could accurately predict the downskin surface roughness in the process parameter selection step without the use of any sensor, with RF showing the highest prediction accuracy.

Material Behavior of High-Strength Low-Alloy Steel (HSLA) WAAM Walls in Construction

Additive manufacturing with steel offers new opportunities for the construction sector. In particular, direct energy deposition (DED) processes such as Wire Arc Additive Manufacturing (WAAM or DED-Arc), are able to create large structures with a high degree of geometric freedom, like force-flow-optimized steel nodes and frameworks, as well as truss structures. By using high-strength steel, manufacturing times can be shortened because less material has to be applied. In order to enable the usage of WAAM components in the construction industry, profound knowledge of the material behavior is necessary. Based on reliable process parameters, extensive experimental and numerical investigations are carried out to characterize the influence of layer orientation and overhang angle on the mechanical parameters of WAAM high-strength low-alloy steel (HSLA) walls. The results have been compared to HSLA steel sheet material. It is shown that comparable characteristics exist for Young’s modulus E, yield strength Rp,0.2 and tensile strength Rm with regard to civil engineering applications. The influence of the loading direction on the material level is similar. Only the yield strength shows a slight dependence on the layer orientation for WAAM walls (difference 4.5%). The overhang angle has no influence on the material parameters.

Feasibility study and material selection for powder-bed fusion process in printing of denture clasps

Background and objectiveThe retention of selective laser melting (SLM)-built denture clasps is inferior to that of cast cobalt-chromium (Co–Cr) clasps engaging 0.01-in undercuts, which are commonly used in clinical practice. Either the clasps engage in excessively deep undercuts or inappropriate printing process parameters are applied. With appropriate undercut engagement and levels of process parameters, the retention of SLM-built clasps (including Co–Cr, commercially pure titanium [CP Ti], and Ti alloy [Ti–6Al–4V] ones) may be comparable to that of cast Co–Cr clasps. Therefore, this feasibility study aimed to evaluate their retention to guide dentists during material selection for the powder-bed fusion process during the printing of denture clasps. MethodsWe engaged the clasp arm at an appropriate undercut depth (0.01 or 0.02 in), built clasps at the orientation of their longitudinal axes approximately parallel to the build platform, generated square prism support structures at a critical overhang angle of 30°, applied optimized laser parameters (laser power, scan speed, and hatch space), and adopted annealing treatment for Co–Cr, CP Ti, and Ti–6Al–4V clasps. After postprocessing and accuracy measurement, an insertion/removal test of the clasps for 15,000 cycles was performed to simulate 10 years of clinical use, and the retentive force was recorded every 1500 cycles. Permanent deformation of the retentive arms of the clasps was measured. Cast Co–Cr clasps engaging 0.01-in undercuts were designated the control group. ResultsThe initial retentive forces of the SLM-built Co–Cr clasps engaging 0.01-in undercuts and CP Ti and Ti–6Al–4V clasps engaging 0.02-in undercuts were comparable to those of the control group. SLM-built Co–Cr clasps engaging 0.01-in undercuts and Ti–6Al–4V clasps engaging 0.02-in undercuts had similar final retentive force and less permanent deformation compared with those of the control group; SLM-built CP Ti clasps engaging 0.02-in undercuts had lower final retentive force and greater permanent deformation. ConclusionsConsidering the long-term retention and permanent deformation of the retentive arms, Co–Cr and Ti–6Al–4V alloys, except CP Ti, are recommended for printing denture clasps. SLM-built Co–Cr clasps should engage 0.01-in undercuts, and Ti–6Al–4V clasps should engage 0.02-in undercuts.

Stress-based topology optimization of thermoelastic structures considering self-support constraints

A thermoelastic topology optimization method considering stress and manufacturing constraints is developed for engineering structures under thermo-mechanical coupled field in this paper. A design dependent non-uniform temperature field is considered for the heat conduction and the thermoelastic analysis during the topology optimization. Based on the solid isotropic material with penalization (SIMP), a topology optimization model is formulated to minimize the structural compliance under stress and overhang angle constraints. The overhang angle constraint to achieve the self-support property in additive manufacturing is established by connecting the elemental density values between the printing element and the corresponding support elements in the lower layer. The stress aggregation function is built to approximate the maximum stress value and an improved adaptive normalization scheme is applied to deal with the highly nonlinearity of the optimization. The sensitivity of the objective function and constraints with respect to the design variables are derived by the adjoint method, and the design variables are updated by the gradient-based optimization method. Moreover, a robustness scheme is proposed for the thermoelastic topology optimization to eliminate possible manufacturing issues such as “single node connection” and “thin rod” phenomena. Several typical numerical examples are provided to demonstrate the effectiveness of the proposed method in stress value reduction and overhang angle control. Meanwhile, the topology optimization with robustness scheme is also proved to result in more robust designs for manufacturing.

Facet Connectivity-Based Estimation Algorithm for Manufacturability of Supportless Parts Fabricated via LPBF.

Recent advances in additive manufacturing have provided more freedom in the design of metal parts; hence, the prototyping of fluid machines featuring extremely complex geometries has been investigated extensively. The fabrication of fluid machines via additive manufacturing requires significant attention to part stability; however, studies that predict regions with a high risk of collapse are few. Therefore, a novel algorithm that can detect collapse regions precisely is proposed herein. The algorithm reflects the support span over the faceted surface via propagation and invalidates overestimated collapse regions based on the overhang angle. A heat exchanger model with an extremely complex internal space is adopted to validate the algorithm. Three samples from the model are extracted and their prototypes are fabricated via laser powder bed fusion. The results yielded by the fabricated samples and algorithm with respect to the sample domain are compared. Regions of visible collapse identified on the surface of the fabricated samples are predicted precisely by the algorithm. Thus, the supporting span reflected by the algorithm provides an extremely precise prediction of collapse.

Stress-based form-finding of gridshells for Wire-and-Arc Additive Manufacturing considering overhang constraints

The design of spatial truss networks for fabrication using Wire-and-Arc Additive Manufacturing (WAAM) is addressed, combining funicular analysis and optimization. At first, a characterization of the structural behavior of the printed bars is provided based on available experimental tests. Interpolation laws are given both for the yielding stress and the critical stress in compression, depending on the printing direction. Then, dealing with networks with fixed plan projection, a minimization problem is formulated in terms of any independent subset of the force densities and of the height of the restrained nodes. The maximum value of the ratio of the axial force in each branch of the network to the relevant yielding/critical force is adopted as objective function. Local enforcements are prescribed to set lower and upper bounds for the vertical coordinates of the nodes and to control the overhang angle with respect to the vertical direction in the AM process. Gridshells retrieved by the proposed approach are presented and compared to those found when seeking for spatial networks with minimum horizontal reactions, disregarding or considering overhang constraints. Peculiar features of the achieved layouts are pointed out.

Self-support topology optimization considering distortion for metal additive manufacturing

This paper proposes a self-support topology optimization method that considers distortion to improve the manufacturability of additive manufacturing. First, a self-support constraint is proposed that combines an overhang angle constraint with an adjustable degree of the downward convex shapes and a thermal constraint for heat dissipation in the building process. Next, we introduce a mechanical model based on the inherent strain method in the building process and propose a constraint that can suppress distortion. An optimization problem is formulated to satisfy all constraints, and an optimization algorithm based on level-set-based topology optimization is constructed. Finally, two- and three-dimensional optimization examples are presented to validate the effectiveness of the proposed topology optimization method.

Self-Supporting Structures Produced through Laser Powder Bed Fusion of AlSi10Mg Alloy: Surface Quality and Hole Circularity Tolerance Assessment

In the context of the Design for Additive Manufacturing (DfAM), the elimination and/or reduction of support structures for the parts is a key issue for process optimization in terms of sustainability and surface quality. In this work, the assessment of the surface quality of overhanging thin walls and unsupported holes with different diameters (4, 6, 8 mm) was carried out through confocal microscopy, SEM-EDS analysis and CMM measurements. To this aim, two different types of AlSi10Mg alloy parts were produced with the L-PBF technology, having self-supporting features such as thin walls and holes with different overhang angles. The results showed that (i) unsupported, down-facing surfaces can be printed consecutively without supports up to a 30° overhang angle and with a surface roughness (Sa) ranging from 3 to 40 µm; (ii) unsupported holes can be produced as well, having a mean circularity tolerance ranging from 0.03 to 0.55 mm, regardless of the diameter value; (iii) density and microstructure analysis both revealed that the parts’ integrity was not affected by the design choices.