Optimization of Tool Path for Uniform Scallop-Height in Ultra-precision Grinding of Free-form Surfaces

Free-form surfaces have been widely used in complex optical devices to improve the functional performance of imaging and illumination quality and reduce sizes. Ultra-precision grinding is a kind of ultra-precision machining technology for fabricating free-form surfaces with high form accuracy and good surface finish. However, the complexity and variation of curvature of the free-form surface impose a lot of challenges to make the process more predictable. Tool path as a critical factor directly determines the form error and surface quality in ultra-precision grinding of free-form surfaces. In conventional tool path planning, the constant angle method is widely used in machining free-form surfaces, which resulted in non-uniform scallop-height and degraded surface quality of the machined surfaces. In this paper, a theoretical scallop-height model is developed to relate the residual height and diverse curvature radius. Hence, a novel tool-path generation method is developed to achieve uniform scallop-height in ultra-precision grinding of free-form surfaces. Moreover, the iterative closest-point matching method, which is a well-known algorithm to register two surfaces, is exploited to make the two surfaces match closely through rotation and translation. The deviation of corresponding points between the theoretical and the measured surfaces is determined. Hence, an optimized tool-path generator is developed that is experimentally verified through a series of grinding experiments conducted on annular sinusoidal surface and single sinusoidal surface, which allows the realization of the achievement of uniform scallop-height in ultra-precision grinding of free-form surfaces

Intelligent Automation Technologies for Machine Tool Industry

Chapter Two, Automation Door Planning Book, Executive Yuan Secretary Ministry of Science and Engineering, China, 201

Precision sculptured surface CNC machining using cutter location data

Industrial parts with sculptured surfaces are typically, manufactured with the use of CNC machining technology and CAM software to generate surface tool paths. To assess tool paths computed for 3-and 5-axis machining, the machining error is evaluated in advance referring to the parameter controlling the linearization of high-order curves, as well as the scallop yielded as a function of radial cutting engagement parameter. The two parameters responsible for the machining error are modeled and corresponding cutter location data for tool paths are utilized to compare actual trajectories with theoretical curves on a sculptured surface assessing thus the deviation when virtual tools are employed to maintain low cost; whilst ensuring high precision cutting. This operation is supported by applying a flexible automation code capable of computing the tool path; extracting its CL data; importing them to the CAD part and finally projecting them onto the part’s surface. For a given tolerance, heights from projected instances are computed for tool paths created by changing the parameters under a cutting strategy, towards the identification of the optimum tool path. To represent a global solution rough machining is also discussed prior to finish machining where the new proposals are mainly applied.</jats:p

Automated Digital Machining for Parallel Processors

When a process engineer creates a tool path a number of fixed decisions are made that inevitably produce sub-optimal results. This is because it is impossible to process all of the tradeoffs before generating the tool path. The research presents a methodology to support a process engineers attempt to generate optimal tool paths by performing automated digital machining and analysis. This methodology automatically generates and evaluates tool paths based on parallel processing of digital part models and generalized cutting geometry. Digital part models are created by voxelizing STL files and the resulting digital part surfaces are obtained based on casting rays into the part model. Tool paths are generated based on a general path template and updated based on generalized tool geometry and part surface information. The material removed by the generalized cutter as it follows the path is used to obtain path metrics. The paths are evaluated based on the path metrics of material removal rate, machining time, and amount of scallop. This methodology is a parallel processing accelerated framework suitable for generating tool paths in parallel enabling the process engineer to rank and select the best tool path for the job

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

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

Automatic Feature Recognition and Tool Path Generation Integrated with Process Planning

The simulation and implementation of Automatic recognition of features from Boundary representation solid models and tool path generation for precision machining of features with free form surfaces is presented in this thesis. A new approach for extracting machining features from a CAD model is developed for a wide range of application domains. Feature-based representation is a technology for integrating geometric modeling and engineering analysis for the life cycle. The concept of feature incorporates the association of a specific engineering meaning to a part of the model. The overall goal of feature-based representations is to convert low level geometrical information into high level description in terms of form, functional, manufacturing or assembly features. Using the boundary representation technique, the information required for manufacturing process can be directly extracted from the CAD model. It also consists of a parameterization strategy to extract user-defined parameters from the recognized features. The extracted parameters from the individual features are used to generate the tool path for machining operations regardless of the intersection of one or more features. The tool path generation is carried out in two phases such as roughing and finishing. Various types of tool paths such as one-way, zig-zag, contour parallel are generated according to the type of the feature for the roughing operation. The algorithm automatically plans the sequence of machining operation with respect to the feature location, and also selects the type of tool and tool path to be used according to the feature. The finishing operation uses the tool path generation strategy in the same manner as used in roughing operation. The algorithm is implemented using the Solid works API library and verified with CNC milling simulator. The results of the work proved the efficiency of this approach and it demonstrate the applicability

Automated Process Planning for Five-Axis Point Milling of Sculptured Surfaces

Ph.DDOCTOR OF PHILOSOPH