Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

3D objects, modeled using Computer Aided Geometric Design tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physical analysis, in isogeometric analysis (IGA) in specific, necessitates a volumetric parametrization of the interior of the object. IGA is performed directly by integrating over the spline spaces of the volumetric spline representation of the object. Typically, tensor-product B-spline trivariates are used to parameterize the volumetric domain. A general 3D object, that can be modeled in contemporary B-rep CAD tools, is typically represented using trimmed B-spline surfaces. In order to capture the generality of the contemporary B-rep modeling space, while supporting IGA needs, Massarwi and Elber (2016) proposed the use of trimmed trivariates volumetric elements. However, the use of trimmed geometry makes the integration process more difficult since integration over trimmed B-spline basis functions is a highly challenging task. In this work, we propose an algorithm that precisely decomposes a trimmed B-spline trivariate into a set of (singular only on the boundary) tensor-product B-spline trivariates, that can be utilized to simplify the integration process in IGA. The trimmed B-spline trivariate is first subdivided into a set of trimmed B\'ezier trivariates, at all its internal knots. Then, each trimmed B\'ezier trivariate, is decomposed into a set of mutually exclusive tensor-product B-spline trivariates, that precisely cover the entire trimmed domain. This process, denoted untrimming, can be performed in either the Euclidean space or the parametric space of the trivariate. We present examples on complex trimmed trivariates' based geometry, and we demonstrate the effectiveness of the method by applying IGA over the (untrimmed) results.Comment: 18 pages, 32 figures. Contribution accepted in International Conference on Geometric Modeling and Processing (GMP 2019

Manufacturability analysis for non-feature-based objects

This dissertation presents a general methodology for evaluating key manufacturability indicators using an approach that does not require feature recognition, or feature-based design input. The contributions involve methods for computing three manufacturability indicators that can be applied in a hierarchical manner. The analysis begins with the computation of visibility, which determines the potential manufacturability of a part using material removal processes such as CNC machining. This manufacturability indicator is purely based on accessibility, without considering the actual machine setup and tooling. Then, the analysis becomes more specific by analyzing the complexity in setup planning for the part; i.e. how the part geometry can be oriented to a cutting tool in an accessible manner. This indicator establishes if the part geometry is accessible about an axis of rotation, namely, whether it can be manufactured on a 4th-axis indexed machining system. The third indicator is geometric machinability, which is computed for each machining operation to indicate the actual manufacturability when employing a cutting tool with specific shape and size. The three manufacturability indicators presented in this dissertation are usable as steps in a process; however they can be executed alone or hierarchically in order to render manufacturability information. At the end of this dissertation, a Multi-Layered Visibility Map is proposed, which would serve as a re-design mechanism that can guide a part design toward increased manufacturability

Multi axis slicing for rapid prototyping

With multi-axis capability, direct laser deposition process can produce a metal part without the usage of support structures. In order to fully utilize such a capability, a slicing method for multi-axis metal deposition process is discussed. Using the geometry information of adjacent layers, the slicing direction and layer thickness can be changed as needed. A hierarchy structure is designed to manage the topological information which is used to determine the slicing sequence. The parallel slicing process is studied to build hollow type structure. With such a character, the hole like feature can be deposited directly to save the required machining operation and material cost, which improves the efficiency of the metal deposition process. Combined with direct 3D layer deposition technique, the multi-axis slicing method is implemented --Abstract, page iii

Computer aided process planning for multi-axis CNC machining using feature free polygonal CAD models

This dissertation provides new methods for the general area of Computer Aided Process Planning, often referred to as CAPP. It specifically focuses on 3 challenging problems in the area of multi-axis CNC machining process using feature free polygonal CAD models. The first research problem involves a new method for the rapid machining of Multi-Surface Parts. These types of parts typically have different requirements for each surface, for example, surface finish, accuracy, or functionality. The CAPP algorithms developed for this problem ensure the complete rapid machining of multi surface parts by providing better setup orientations to machine each surface. The second research problem is related to a new method for discrete multi-axis CNC machining of part models using feature free polygonal CAD models. This problem specifically considers a generic 3-axis CNC machining process for which CAPP algorithms are developed. These algorithms allow the rapid machining of a wide variety of parts with higher geometric accuracy by enabling access to visible surfaces through the choice of appropriate machine tool configurations (i.e. number of axes). The third research problem addresses challenges with geometric singularities that can occur when 2D slice models are used in process planning. The conversion from CAD to slice model results in the loss of model surface information, the consequence of which could be suboptimal or incorrect process planning. The algorithms developed here facilitate transfer of complete surface geometry information from CAD to slice models. The work of this dissertation will aid in developing the next generation of CAPP tools and result in lower cost and more accurately machined components

Automatic tool path generation for multi-axis machining

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (leaves 67-72).We present a novel approach to CAD/CAM integration for multi-axis machining. Instead of redefining the workpiece in terms of machining features, we generate tool paths directly by analyzing the accessibility of the surface of the part. This eliminates the problem of feature extraction. We envision this as the core strategy of a new direct and seamless CAD/ CAM system. We perform the accessibility analysis in two stages. First, we triangulate the surface of the workpiece and perform a visibility analysis from a discrete set of orientations arranged on the Gaussian Sphere. This analysis is performed in object space to ensure reliability. For each triangle, a discrete set approximation of the accessibility cone is then constructed. Next, a minimum set cover algorithm like the Quine-McCluskey Algorithm is used to select the minimum set of orientations from which the entire workpiece can be accessed. These set of orientations correspond to the setups in the machining plan, and also dictate the orientation in which the designed part will be embedded in the stock. In particular, we bias the search for setups in favor of directions from which most of the part can be accessed i.e, the parallel and perpendicular directions of the faces in the workpiece. For each setup, we select a set of tools for optimal removal of material. Our tool-path generation strategy is based on two general steps: global roughing and facebased finishing. In global roughing, we represent the workpiece and stock in a voxelized format. We perform a waterline analysis and slice the stock into material removal slabs. In each slab, we generate zig-zag tool paths for removing bulk of the material. After gross material removal in global roughing, we finish the faces of the component in face-based finishing. Here, instead of assembling faces into features, we generate tool paths directly and independently for each face. The accessibility cones are used to help ensure interference- free cuts. After the tool paths have been generated, we optimize the plan to ensure that commonalities between adjacent faces are exploited.by Laxmiprasad Putta.S.M

Computing tool accessibility of polyhedral models for toolpath planning in multi-axis machining

This dissertation focuses on three new methods for calculating visibility and accessibility, which contribute directly to the precise planning of setup and toolpaths in a Computer Numerical Control (CNC) machining process. They include 1) an approximate visibility determination method; 2) an approximate accessibility determination method and 3) a hybrid visibility determination method with an innovative computation time reduction strategy. All three methods are intended for polyhedral models. First, visibility defines the directions of rays from which a surface of a 3D model is visible. Such can be used to guide machine tools that reach part surfaces in material removal processes. In this work, we present a new method that calculates visibility based on 2D slices of a polyhedron. Then we show how visibility results determine a set of feasible axes of rotation for a part. This method effectively reduces a 3D problem to a 2D one and is embarrassingly parallelizable in nature. It is an approximate method with controllable accuracy and resolution. The method’s time complexity is linear to both the number of polyhedron’s facets and number of slices. Lastly, due to representing visibility as geodesics, this method enables a quick visible region identification technique which can be used to locate the rough boundary of true visibility. Second, tool accessibility defines the directions of rays from which a surface of a 3D model is accessible by a machine tool (a tool’s body is included for collision avoidance). In this work, we present a method that computes a ball-end tool’s accessibility as visibility on the offset surface. The results contain all feasible orientations for a surface instead of a Boolean answer. Such visibility-to-accessibility conversion is also compatible with various kinds of facet-based visibility methods. Third, we introduce a hybrid method for near-exact visibility. It incorporates an exact visibility method and an approximate visibility method aiming to balance computation time and accuracy. The approximate method is used to divide the visibility space into three subspaces; the visibility of two of them are fully determined. The exact method is then used to determine the exact visibility boundary in the subspace whose visibility is undetermined. Since the exact method can be used alone to determine visibility, this method can be viewed as an efficiency improvement for it. Essentially, this method reduces the processing time for exact computation at the cost of introducing approximate computation overhead. It also provides control over the ratio of exact-approximate computation