A new overhang constraint for topology optimization of self-supporting structures in additive manufacturing

This work falls within the scope of computer-aided optimal design, and aims to integrate the topology optimization procedures and recent additive manufacturing technologies (AM). The elimination of scaffold supports at the topology optimization stage has been recognized and pursued by many authors recently. The present paper focuses on implementing a novel and specific overhang constraint that is introduced inside the topology optimization problem formulation along with the regular volume constraint. The proposed procedure joins the design and manufacturing processes into a integrated workflow where any component can directly be manufactured with no requirement of any sacrificial support material right after the topology optimization process. The overhang constraint presented in this work is defined by the maximum allowable inclination angle, where the inclination of any member is computed by the Smallest Univalue Segment Assimilating Nucleus (SUSAN), an edge detection algorithm developed in the field of image analysis and processing. Numerical results on some benchmark examples, along with the numerical performances of the proposed method, are introduced to demonstrate the capacities of the presented approach.     

Ribbed Support Vaults for 3D Printing of Hollowed Objects

Additive manufacturing techniques form an object by accumulating layers of material on top of one another. Each layer has to be supported by the one below for the fabrication process to succeed. To reduce print time and material usage, especially in the context of prototyping, it is often desirable to fabricate hollow objects. This exacerbates the requirement of support between consecutive layers: standard hollowing produces surfaces in overhang that cannot be directly fabricated anymore. Therefore, these surfaces require internal support structures. These are similar to external supports for overhangs, with the key difference that internal supports remain invisible within the object after fabrication. A fundamental challenge is to generate structures that provide a dense support while using little material. In this paper, we propose a novel type of support inspired by rib structures. Our approach guarantees that any point in a layer is supported by a point below, within a given threshold distance. Despite providing strong guarantees for printability, our supports remain lightweight and reliable to print. We propose a greedy support generation algorithm that creates compact hierarchies of rib-like walls. The walls are progressively eroded away and straightened, eventually merging with the interior object walls. We demonstrate our technique on a variety of models and provide performance figures in the context of fused filament fabrication 3D printing.     

Combined optimization of part topology,support structure layout and build orientation for additive manufacturing

Additive manufacturing (AM) enables the fabrication of parts of unprecedented complexity. Dedicated topology optimization approaches, that account for specific AM restrictions, are instrumental in fully exploiting this capability. In popular powder-bed-based AM processes, the critical overhang angle of downward facing surfaces limits printability of parts. This can be addressed by changing build orientation, part adaptation, or addition of sacrificial support structures. Thus far, each of these measures have been studied separately and applied sequentially, which leads to suboptimal solutions or excessive computation cost. This paper presents and studies, based on 2D test problems, an approach enabling simultaneous optimization of part geometry, support layout and build orientation. This allows designers to find a rational tradeoff between manufacturing cost and part performance. The relative computational cost of the approach is modest, and in numerical tests it consistently obtains high quality solutions.     

An Improved Two-Level Support Structure for Extrusion-Based Additive Manufacturing

Extrusion-Based Additive Manufacturing is one of the most commonly used Additive Manufacturing techniques. However, the technique requires that the overhang features in a model should be provided with supports from below. The added supports contribute to a major source of material waste during the manufacturing process. In order to save support materials, considering 3D printing directions as a constraint of adding supports, we propose a two-level support structure where Level 1 consists of a truncated beam-structure and Level 2 consists of a slim tree-shaped structure. The main contribution of this paper is the modification of the shape of Level 1 support and optimization of the topologies of the tree-supports in Level 2. The approach developed in this paper leads to material savings up to 31.01% and printing time savings up to 13.10% in comparison to the existing literature. Several comparison experiments were conducted on benchmark models to validate the developed approach and have been reported in this paper.     

An additive manufacturing filter for topology optimization of print-ready designs

Additive manufacturing (AM) offers exciting opportunities to manufacture parts of unprecedented complexity. Topology optimization is essential to fully exploit this capability. However, AM processes have specific limitations as well. When these are not considered during design optimization, modifications are generally needed in post-processing, which add costs and reduce the optimized performance. This paper presents a filter that incorporates the main characteristics of a generic AM process, and that can easily be included in conventional density-based topology optimization procedures. Use of this filter ensures that optimized designs comply with typical geometrical AM restrictions. Its performance is illustrated on compliance minimization problems, and a 2D Matlab implementation is provided.     

Measurement designs to improve the computational efficiency of linear system state estimators

A design procedure for the measurement process is proposed to decrease the computational burden of state estimation in linear discrete-time systems. System order reduction is involved, which is achieved by a derived transformation, yielding an alternative system and measurement process representation that includes time delays in both the system and the measurement process. Without loss of filter optimality, measurement designs yielding reductions in the computational requirements of the Kalman filter applied to the reduced order system are derived. A computational comparison is included to show that the proposed method, as opposed to the direct application of the Kalman filter, can yield large reductions in the filter computation time.     

Support structure design in additive manufacturing based on topology optimization

A support structure design technique for additive manufacturing (AM) is proposed that minimizes the deformation while using the least amount of support material, minimizes the time required to add the supports, and designs supports that are easily removed. This study presents a repulsion index (RI), which satisfies the easy removal requirement and minimizes the number of artifacts left on the specimen surface, and a weighting function, which quantifies the cost incurred by the time taken to build the supports. A multi-objective topological optimization based on the simple isotropic material with penalization method, continuous approximation of material distribution, and method of moving asymptotes is formulated that includes the proposed RI and cost formulation. Numerical simulations demonstrate that rational support layouts can be determined with the proposed cost-based formulation in the topological optimization, allowing designers to find design solutions with a compromise between specimen surface profile error and support structure costs.     

Support structure constrained topology optimization for additive manufacturing

There is significant interest today in integrating additive manufacturing (AM) and topology optimization (TO). However, TO often leads to designs that are not AM friendly. For example, topologically optimized designs may require significant amount of support structures before they can be additively manufactured, resulting in increased fabrication and clean-up costs.In this paper, we propose a TO methodology that will lead to designs requiring significantly reduced support structures. Towards this end, the concept of ‘support structure topological sensitivity’ is introduced. This is combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints. The robustness and efficiency of the proposed method is demonstrated through numerical experiments, and validated through fused deposition modeling, a popular AM process.     

A knowledge-based process planning framework for wire arc additive manufacturing

Wire arc additive manufacturing (WAAM) provides a rapid and cost-effective solution for fabricating low-to-medium complexity and medium-to-large size metal parts. In WAAM, process settings are well-recognized as fundamental factors that determine the performance of the fabricated parts such as geometry accuracy and microstructure. However, decision-making on process variables for WAAM still heavily relies on knowledge from domain experts. For achieving reliable and automated production, process planning systems that can capture, store, and reuse knowledge are needed. This study proposes a process planning framework by integrating a WAAM knowledge base together with our in-house developed computer-aided tools. The knowledge base is construed with a data-knowledge-service structure to incorporate various data and knowledge including metamodels and planning rules. Process configurations are generated from the knowledge base and then used as inputs to computer-aided tools. Moreover, the process planning system also supports the early-stage design of products in the context of design for additive manufacturing. The proposed framework is demonstrated in a digital workflow of fabricating industrial-grade components with overhang features.     

卡尔曼滤波器及其工程应用

卡尔曼于1960年提出了离散系统线性滤波的递推求解方法即卡尔曼滤波算法。该滤波算法是基于线性最小平方法的、进行有效递推计算的一组数学方程式,算法功能强大,支持对过去、现在和将来状态的估算。本文旨在对离散系统的卡尔曼滤波作应用方面的介绍：包括对基本离散卡尔曼滤波器的描述与讨论;对扩展型卡尔曼滤波的讨论;应用实例进行分析和仿真;讨论卡尔曼滤波在汽车定位与导航工程上的应用。     

Bridging topology optimization and additive manufacturing

Topology optimization is a technique that allows for increasingly efficient designs with minimal a priori decisions. Because of the complexity and intricacy of the solutions obtained, topology optimization was often constrained to research and theoretical studies. Additive manufacturing, a rapidly evolving field, fills the gap between topology optimization and application. Additive manufacturing has minimal limitations on the shape and complexity of the design, and is currently evolving towards new materials, higher precision and larger build sizes. Two topology optimization methods are addressed: the ground structure method and density-based topology optimization. The results obtained from these topology optimization methods require some degree of post-processing before they can be manufactured. A simple procedure is described by which output suitable for additive manufacturing can be generated. In this process, some inherent issues of the optimization technique may be magnified resulting in an unfeasible or bad product. In addition, this work aims to address some of these issues and propose methodologies by which they may be alleviated. The proposed framework has applications in a number of fields, with specific examples given from the fields of health, architecture and engineering. In addition, the generated output allows for simple communication, editing, and combination of the results into more complex designs. For the specific case of three-dimensional density-based topology optimization, a tool suitable for result inspection and generation of additive manufacturing output is also provided.     

Optimal locations of point supports in plates for maximum fundamental frequency

This paper investigates the optimal locations of rigid point supports to maximize the fundamental frequency of free vibration of plates. The computational method uses the Rayleigh-Ritz method for the vibration analysis and the simplex method of Nelder and Mead for the optimization search of support locations. Optimal results have been obtained for various common shapes of plates with a few point supports. The results show that the frequency of the plate is sensitive to the locations of the point supports. Moreover, these new optimal results provide useful information to designers seeking to exploit the position of point supports in their plate designs. It has been found that multiple solutions are a common feature of this plate optimization problem.     

Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design

Additively manufactured components often require temporary support material to prevent the component from collapsing or warping during fabrication. Whether these support materials are removed chemically as in the case of many polymer additive manufacturing processes, or mechanically as in the case of (for example) Direct Metal Laser Sintering, the use of sacrificial material increases total material usage, build time, and time required in post-fabrication treatments. The goal of this work is to embed a minimum allowable self-supporting angle within the topology optimization framework such that designed components and structures may be manufactured without the use of support material. This is achieved through a series of projection operations that combine a local projection to enforce minimum length scale requirements and a support region projection to ensure a feature is adequately supported from below. The magnitude of the self-supporting angle is process dependent and is thus an input variable provided by the manufacturing or design engineer. The algorithm is demonstrated on standard minimum compliance topology optimization problems and solutions are shown to satisfy minimum length scale, overhang angle, and volume constraints, and are shown to be dependent on the allowable magnitudes of these constraints.     

Use of three-dimensional field simulators in the synthesis of waveguide round rod bandpass filters

This paper presents the generalized bandpass filter design method of Levy and Rhodes based on three-dimensional (3D) electromagnetic analysis and discontinuity modeling using commercial software. It shows how to use Levy and Rhodes's famous method for very accurate theoretical designs of waveguide post filters, using modern 3D solvers based on the finite element method, the mode matching method, and the transmission line matrix analysis method. This is the first time that design curves and equations are being presented for constant diameter single and double round rod filters by full electromagnetic modeling. The approach is demonstrated with designs for a number of waveguide round rod filters. This paper also demonstrates the generality of the method. This method can be applied to many other types of coupled resonator waveguide band pass filters. © 1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 484–497, 1998     

多投影机非平面自动几何校正

非平面投影以其高度的沉浸感、多样的表现形式和灵活的场景布局,近年来越来越多地应用在虚拟现实、数字娱乐、展览展示等领域。非平面投影与平面投影相比,由于涉及到投影机位姿标定以及失真图像校正等问题,实现难度较高。目前的投影校正方法虽然可以通过重建或者非重建方法实现非平面屏幕投影的几何校正,但是它们多少都存在成本高昂,步骤复杂,需要人工干预,适用面窄等问题。针对非平面屏幕中最常使用的柱幕面型,提出一种非重建的多投影机投影几何校正方法,此方法可自动实现柱幕环境的几何投影校正,并且可对柱幕在加工中引入的倾斜、表面起伏等外形偏差予以修正,实现了复杂柱幕环境下多投影机高精度、短时间投影几何校正。提出的方法不仅适用于柱幕,还可扩展应用于其他可参数化描述的面型,如球面、双曲面、抛物面等面型的投影环境,具有广泛的适用性。     

Optimization via multimodel simulation

Increasing computational power and the availability of 3D printers provide new tools for the combination of modeling and experimentation. Several simulation tools can be run independently and in parallel, e.g., long running computational fluid dynamics simulations can be accompanied by experiments with 3D printers. Furthermore, results from analytical and data-driven models can be incorporated. However, there are fundamental differences between these modeling approaches: some models, e.g., analytical models, use domain knowledge, whereas data-driven models do not require any information about the underlying processes. At the same time, data-driven models require input and output data, but analytical models do not. The optimization via multimodel simulation (OMMS) approach, which is able to combine results from these different models, is introduced in this paper. We believe that OMMS improves the robustness of the optimization, accelerates the optimization-via-simulation process, and provides a unified approach. Using cyclonic dust separators as a real-world simulation problem, the feasibility of this approach is demonstrated and a proof-of-concept is presented. Cyclones are popular devices used to filter dust from the emitted flue gasses. They are applied as pre-filters in many industrial processes including energy production and grain processing facilities. Pros and cons of this multimodel optimization approach are discussed and experiences from experiments are presented.     

基于2DPCA和支持向量机的人脸检测研究

提出一种基于二维主分量(2DPCA)分析和支持向量机的层叠人脸检测算法,用于复杂背景灰度图像的人脸检测。算法首先采用2DPCA分析方法滤去大量非人脸窗口,之后用支持向量机对通过的窗口进行检测。由于在通过2DPCA分析方法的子空间内训练SVM,降低了分类器的训练难度。并且和传统的PCA方法相比,2DPCA直接采用二维图像矩阵表示人脸,进行特征提取,提高了计算效率。实验对比数据表明该算法大大提高了检测速度,降低了虚警率。     

Topology optimization of structures with manufacturing and unilateral contact constraints by minimizing an adjustable compliance–volume product

In this paper the concept of extended optimality, or hyperoptimality, is adopted. By following this idea, a new compliance–volume product is suggested as objective. The volume appearing in the product is also raised to the power of a new design parameter which can be set to different values. In such manner design concepts with different volume fractions can be generated by using the approach of extended optimality. Both manufacturing constraints and unilateral contact constraints are included in the proposed method. The manufacturing constraints are implemented by adjusting the move limits such that the draw directions are satisfied. Both one draw direction as well as split draw constraints are considered. The contact conditions are modeled by the augmented Lagrangian approach such that the Jacobian in the Newton algorithm as well as in the adjoint equation becomes symmetric. The design parametrization is done by the SIMP model and Sigmund’s filter is utilized when the sensitivities are calculated. The proposed method is very robust and efficient. This is demonstrated by solving problems in both 2D and 3D. The numerical results are also compared to solutions obtained by performing compliance optimization with a constraint on the volume fraction.