Non-Uniform Offsetting and its Applications in Laser Path Planning of Sterolithography Machine

Laser path planning is an important step in solid freeform fabrication processes such as Stereolithography (SLA). An important consideration in the laser path planning is to compensate the shape of laser beam. Currently the compensation is divided into two steps, Z-compensation and X-Y compensation, and the shape of laser beam is assumed to be uniform for the whole platform. In this research, we present a sampling based non-uniform offsetting method which accounts for the different shapes of laser beam at various locations. We discuss the related steps and algorithms. We demonstrate its effectiveness by using various test cases. Besides improving the accuracy of SLA machine, non-uniform offsetting can also be applied to address other accuracy issues caused by thermal and structural variationsMechanical Engineerin

Design for Additive Manufacturing of Conformal Cooling Channels Using Thermal-Fluid Topology Optimization and Application in Injection Molds

Additive manufacturing allows the fabrication parts and tools of high complexity. This capability challenges traditional guidelines in the design of conformal cooling systems in heat exchangers, injection molds, and other parts and tools. Innovative design methods, such as network-based approaches, lattice structures, and structural topology optimization have been used to generate complex and highly efficient cooling systems; however, methods that incorporate coupled thermal and fluid analysis remain scarce. This paper introduces a coupled thermal-fluid topology optimization algorithm for the design of conformal cooling channels. With this method, the channel position problem is replaced to a material distribution problem. The material distribution directly depends on the effect of flow resistance, heat conduction, as well as forced and natural convection. The problem is formulated based on a coupling of Navier-Stokes equations and convection-diffusion equation. The problem is solved by gradient-based optimization after analytical sensitivity derived using the adjoint method. The algorithm leads a two -dimensional conceptual design having optimal heat transfer and balanced flow. The conceptual design is converted to three-dimensional channels and mapped to a morphological surface conformal to the injected part. The method is applied to design an optimal conformal cooling for a real three dimensional injection mold. The feasibility of the final designs is verified through simulations. The final designs can be exported as both three-dimensional graphic and surface mesh CAD format, bringing the manufacture department the convenience to run the tool path for final fitting

Topology Driven Improvement of FDC Build Parameters

The likeliest failure origin for advanced ceramics parts, prepared by fused deposition, is a void from improper fill. Adequate filling of each cross-section is dependent upon the deposition toolpath. Cross-sectional spaces are conventionally filled with pre-defined parameters. We propose that adaptive build parameters will control variations in geometry and property of a part. Voids, overfilling, incomplete bonding and excess traversing can be suppressed by adjusting the fill parameters for cross-sectional areas. Improved build parameters and toolpath allows for faster build time and components ofj full density. Some implementations are discussed and presented.Mechanical Engineerin

Point-based mathematics for computer-aided manufacture

This thesis demonstrates the feasibility of machining high quality sculptured surfaces directly from a point-based definition. The work is founded on the strategy of using a sparse set of points to characterise shape although it is assumed that an appropriately dense definition can be generated by the use of some unspecified high quality interpolation algorithm. This is in contrast to the conventional CAD/CAM approach where explicit parametric expressions are used to describe the part. The research is founded on the Inverse Offset Method (IOM) proposed by Kishinami; the algorithm is chosen because it possesses a number of desirable properties, most notably its versatility and robustness. The first fundamental contribution is an error analysis of the IOM that has not been published before, the analysis is dependent on the surface and cutter path point spacing, the tool radius and the local surface curvature. The accuracy of the error analysis is corroborated by the machining and measuring of a physical part. Furthermore it is established that the quality of the finished part produced by the IOM compares favourably with that produced by a commercial package for similar tolerances. The principal research achievement is the optimisation of the IOM to exploit the coherence of data ordered into sections. This results in the IOM generating cutter paths in a time period comparable to that of the commercial package without a reduction in the quality of the finished part. The last contribution made in this thesis is a report on the issues concerning the machining of point definitions derived from multi-surfaces. The work presented in this thesis offers an alternative strategy to the design and manufacture of free-form surfaces. The main benefits of adopting this strategy are gained because it removes the need to generate a parametric surface definition

Embodied Interactions for Spatial Design Ideation: Symbolic, Geometric, and Tangible Approaches

Computer interfaces are evolving from mere aids for number crunching into active partners in creative processes such as art and design. This is, to a great extent, the result of mass availability of new interaction technology such as depth sensing, sensor integration in mobile devices, and increasing computational power. We are now witnessing the emergence of maker culture that can elevate art and design beyond the purview of enterprises and professionals such as trained engineers and artists. Materializing this transformation is not trivial; everyone has ideas but only a select few can bring them to reality. The challenge is the recognition and the subsequent interpretation of human actions into design intent

Design and Production of Complex Architectural Forms with Ceramic Elements

This paper describes a studio experiment developed with the aim of exploring the design and fabrication of complex architectural forms using ceramic elements. History has examples of double-sided curved forms built in ceramics. Such examples would not fulfill contemporary functional and aesthetic principles, neither would they be feasible or cost-effective considering current construction standards. There are recent examples of such forms built in other materials. These examples are difficult to emulate when ceramics is concerned, as they imply the fabrication of unique parts and sophisticated assembly techniques. Creating a double-curved surface in ceramics thus seems a difficult task. There are, however, advantages to such a formulation of design problems. They prompt the questioning of traditional wisdom, the rejection of accepted types, and the raising of interesting questions. What are the design strategies that should be followed when creating ceramic free-forms? What is the design media required to design them? And what are the techniques needed to fabricate and construct them? These are the questions investigated in the design project pursued jointly by students at an American and a Portuguese school, in collaboration with a professional research center and a ceramics factory. The students tested various possibilities, and in the process learned about state-of-art design and production techniques. The final projects are very expressive of their investigations and include a twisted glass tunnel, large-scale ceramic ‘bubbles,’ a rotated-tile wall, and a load-bearing wall

Investigation into adaptive slicing methodologies for additive manufacturing

Adaptive slicing is a methodology used to optimise the trade-off between build-time reduction and geometric accuracy improvement in additive manufacturing (AM). It works by varying decreasing layer thickness in sections of high curvature. However, current adaptive slicing methodologies all face the difficulty of adjusting layer thickness precisely according to the variations of the model’s geometry, thereby limiting the geometric accuracy improvement. This thesis tackles this difficulty by indicating the geometric variations of the model by evaluating the ratio of the volume of each sliced layer’s geometric deviation to the volume of its corresponding region in the digital model. This indication is accomplished because all the topological information of the corresponding region is considered in assessing the geometric deviation (volume) between each sliced layer and its corresponding region. Through having this precise indication to modify each layer thickness, this thesis aims to develop an adaptive slicing that can mitigate geometric inaccuracies (e.g. staircase effect and dimensional deviation) while balancing the build time. This slicing is evaluated using six different test models, compared with three current slicing methodologies (voxelisation-based, cusp height-based, and uniform slicing), and validated through computation and manufacturing. These validations all demonstrate that volume deviation-based slicing optimises the trade-off between build-time reduction and geometric accuracy improvement better than the other existing slicing methodologies. For example, it can reduce the build time by nearly half compared to other existing slicing methodologies assuming a similar degree of printed parts’ geometric accuracy. The improved trade-off optimised by volume deviation-based slicing can directly benefit the AM applications in the aerospace and medical industries. This is because current research has shown geometric inaccuracies are the primary cause of reducing energy efficiency (e.g. turbine blade and wind tunnel testing models) and having failed implants (e.g. hip and cranial implants, dental prostheses). In addition to improving the geometric accuracy of AM-constructed parts, volume deviation-based slicing may also be incorporated with non-planar layer slicing. Non-planar layer slicing is designed to mitigate the mechanical anisotropy of printed parts by using curved-sliced layers. By integrating volume deviation-based slicing with non-planar layer slicing, the thickness of each curved-sliced layer can be adjusted according to the model’s geometric variations and, therefore, has a possibility of reducing the geometric inaccuracies and mechanical anisotropy simultaneously.Open Acces

오프셋 곡선 및 곡면의 자가 교차 검출 및 제거

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 김명수.Offset curves and surfaces have many applications in computer-aided design and manufacturing, but the self-intersections and redundancies must be trimmed away for their practical use. We present a new method for offset curve and surface trimming that detects the self-intersections and eliminates the redundant parts of an offset curve and surface that are closer than the offset distance to the original curve and surface. We first propose an offset trimming method based on constructing geometric constraint equations. We formulate the constraint equations of the self-intersections of an offset curve and surface in the parameter domain of the original curve and surface. Numerical computations based on the regularity and intrinsic properties of the given input curve and surface is carried out to compute the solution of the constraint equations. The method deals with numerical instability around near-singular regions of an offset surface by using osculating tori that can be constructed in a highly stable way, i.e., by offsetting the osculating torii of the given input regular surface. We reveal the branching structure and the terminal points from the complete self-intersection curves of the offset surface. From the observation that the trimming method based on the multivariate equation solving is computationally expensive, we also propose an acceleration technique to trim an offset curve and surface. The alternative method constructs a bounding volume hierarchy specially designed to enclose the offset curve and surface and detects the self-collision of the bounding volumes instead. In the case of an offset surface, the thickness of the bounding volumes is indirectly determined based on the maximum deviations of the positions and the normals between the given input surface patches and their osculating tori. For further acceleration, the bounding volumes are pruned as much as possible during self-collision detection using various geometric constraints imposed on the offset surface. We demonstrate the effectiveness of the new trimming method using several non-trivial test examples of offset trimming. Lastly, we investigate the problem of computing the Voronoi diagram of a freeform surface using the offset trimming technique for surfaces. By trimming the offset surface with a gradually changing offset radius, we compute the boundary of the Voronoi cells that appear in the concave side of the given input surface. In particular, we interpret the singular and branching points of the self-intersection curves of the trimmed offset surfaces in terms of the boundary elements of the Voronoi diagram.오프셋 곡선 및 곡면은 computer-aided design (CAD)와 computer-aided manufacturing (CAM)에서 널리 이용되는 연산들 중 하나이다. 하지만 실용적인 활용을 위해서는 오프셋 곡선 및 곡면에서 생기는 자가 교차를 찾고 이를 기준으로 오프셋 곡선 및 곡면에서 원래의 곡선 및 곡면에 가까운 불필요한 영역을 제거하여야한다. 본 논문에서는 오프셋 곡선 및 곡면에서 생기는 자가 교차를 계산하고, 오프셋 곡선 및 곡면에서 생기는 불필요한 영역을 제거하는 알고리즘을 제안한다. 본 논문은 우선 오프셋 곡선 및 곡면의 자가 교차점들과 그 교차점들이 기인한 원래 곡선 및 곡면의 점들이 이루는 평면 이등변 삼각형 관계로부터 오프셋 곡선 및 곡면의 자가 교차점의 제약 조건을 만족시키는 방정식들을 세운다. 이 제약식들은 원래 곡선 및 곡면의 변수 공간에서 표현되며, 이 방정식들의 해는 다변수 방정식의 해를 구하는 solver를 이용하여 구한다. 오프셋 곡면의 경우, 원래 곡면의 주곡률 중 하나가 오프셋 반지름의 역수와 같을 때 오프셋 곡면의 법선이 정의가 되지 않는 특이점이 생기는데, 오프셋 곡면의 자가 교차 곡선이 이 부근을 지날 때는 자가 교차 곡선의 계산이 불안정해진다. 따라서 자가 교차 곡선이 오프셋 곡면의 특이점 부근을 지날 때는 오프셋 곡면을 접촉 토러스로 치환하여 더 안정된 방법으로 자가 교차 곡선을 구한다. 계산된 오프셋 곡면의 자가 교차 곡선으로부터 교차 곡선의 $xyz$-공간에서의 말단 점, 가지 구조 등을 밝힌다. 본 논문은 또한 바운딩 볼륨 기반의 오프셋 곡선 및 곡면의 자가 교차 곡선 검출을 가속화하는 방법을 제시한다. 바운딩 볼륨은 기저 곡선 및 곡면을 단순한 기하로 감싸고 기하 연산을 수행함으로써 가속화에 기여한다. 오프셋 곡면의 자가 교차 곡선을 구하기 위하여, 본 논문은 오프셋 곡면의 바운딩 볼륨 구조를 기저 곡면의 바운딩 볼륨과 기저 곡면의 법선 곡면의 바운딩 볼륨의 구조로부터 계산하며 이때 각 바운딩 볼륨의 두께를 계산한다. 또한, 바운딩 볼륨 중에서 실제 오프셋 곡선 및 곡면의 자가 교차에 기여하지 않는 부분을 깊은 재귀 전에 찾아서 제거하는 여러 조건들을 나열한다. 한편, 자가 교차가 제거된 오프셋 곡선 및 곡면은 기저 곡선 및 곡면의 보로노이 구조와 깊은 관련이 있는 것이 알려져 있다. 본 논문에서는 자유 곡면의 연속된 오프셋 곡면들로부터 자유 곡면의 보로노이 구조를 유추하는 방법을 제시한다. 특히, 오프셋 곡면의 자가 교차 곡선 상에서 나타나는 가지 점이나 말단 점과 같은 특이점들이 자유 곡면의 보로노이 구조에서 어떻게 해석되는지 제시한다.1. Introduction 1 1.1 Background and Motivation 1 1.2 Research Objectives and Approach 7 1.3 Contributions and Thesis Organization 11 2. Preliminaries 14 2.1 Curve and Surface Representation 14 2.1.1 Bezier Representation 14 2.1.2 B-spline Representation 17 2.2 Differential Geometry of Curves and Surfaces 19 2.2.1 Differential Geometry of Curves 19 2.2.2 Differential Geometry of Surfaces 21 3. Previous Work 23 3.1 Offset Curves 24 3.2 Offset Surfaces 27 3.3 Offset Curves on Surfaces 29 4. Trimming Offset Curve Self-intersections 32 4.1 Experimental Results 35 5. Trimming Offset Surface Self-intersections 38 5.1 Constraint Equations for Offset Self-Intersections 38 5.1.1 Coplanarity Constraint 39 5.1.2 Equi-angle Constraint 40 5.2 Removing Trivial Solutions 40 5.3 Removing Normal Flips 41 5.4 Multivariate Solver for Constraints 43 5.A Derivation of f(u,v) 46 5.B Relationship between f(u,v) and Curvatures 47 5.3 Trimming Offset Surfaces 50 5.4 Experimental Results 53 5.5 Summary 57 6. Acceleration of trimming offset curves and surfaces 62 6.1 Motivation 62 6.2 Basic Approach 67 6.3 Trimming an Offset Curve using the BVH 70 6.4 Trimming an Offset Surface using the BVH 75 6.4.1 Offset Surface BVH 75 6.4.2 Finding Self-intersections in Offset Surface Using BVH 87 6.4.3 Tracing Self-intersection Curves 98 6.5 Experimental Results 100 6.6 Summary 106 7. Application of Trimming Offset Surfaces: 3D Voronoi Diagram 107 7.1 Background 107 7.2 Approach 110 7.3 Experimental Results 112 7.4 Summary 114 8. Conclusion 119 Bibliography iDocto

Contour parallel milling tool path generation for arbitrary pocket shape using a fast marching method

Contour parallel tool paths are among the most widely used tool paths for planer milling operations. A number of exact as well as approximate methods are available for offsetting a closed boundary in order to generate a contour parallel tool path; however, the applicability of various offsetting methods is restricted because of limitations in dealing with pocket geometry with and without islands, the high computational costs, and numerical errors. Generation of cusps, segmentation of rarefied corners, and self-intersection during the offsetting operations and finding a unique offsetting solution for pocket with islands are among the associated problems in contour tool path generation. Most of methods are inherently incapable of dealing with such problems and use complex computational routines to identify and rectify these problems. Also, these rectifying techniques are heavily dependent on the type of geometry, and hence, the application of these techniques for arbitrary boundary conditions is limited and prone to errors. In this paper, a new mathematical method for generation of contour parallel tool paths is proposed which is inherently capable of dealing with the aforementioned problems. The method is based on a boundary value formulation of the offsetting problem and a fast marching method based solution for tool path generation. This method handles the topological changes during offsetting naturally and deals with the generation of discontinuities in the slopes by including an "entropy condition” in its numerical implementation. The appropriate modifications are carried out to achieve higher accuracy for milling operations. A number of examples are presented, and computational issues are discussed for tool path generatio