尹周平
论文题目：面向虚拟原型的产品特征建模和可接近性分析
作者简介：尹周平，男，1972年09月出生，1996年09月师从于华中科技大学熊有伦教授，于2001年01月获博士学位。
摘 要
虚拟原型技术旨在利用产品的CAD信息和虚拟现实技术来构造替代产品物理原型的虚拟原型，以交互分析产品设计的形状、性能和可制造性等。作为数字化制造和快速产品开发的关键技术之一，虚拟原型技术对于缩短产品开发周期，降低产品全生命周期成本，提高产品质量均有着显著意义。然而，有关虚拟原型技术的研究还很不成熟，尚未形成系统理论与实用系统，有许多关键的理论和技术问题有待于进一步研究并解决。
在国家自然科学基金重大项目“支持产品创新的先进制造技术中的若干基础研究”、杰出青年基金项目“虚拟环境下智能4M系统的基础理论与实现”等项目的资助下，本文对产品特征建模、可接近性分析和可制造性分析等虚拟原型关键技术进行了深入系统的研究，定义了一个具有不同几何信息抽象层次和不同应用特征侧面的产品特征模型，提出了基于可视锥的可接近性分析一般方法，实现了面向净成型加工过程的几何可注塑性分析，并初步建立了一个支持快速产品开发的虚拟原型系统。本文的主要研究成果如下：
在基础理论研究方面：1. 定义了可视锥、完全可视锥、部分可视锥和局部可视锥等基本概念，推导出完全可视锥和部分可视锥的一些重要性质，建立可视锥与可视性映射、自由锥等之间的关系。可视锥作为可接近性分析的理论基础和一般工具，既可用于只考虑特征本身阻挡关系的局部可接近性分析，又可用于考虑集合内所有障碍物的全局可接近性分析；2. 提出了基于C空间的可视锥通用计算方法，证明了物体上某一点p的可视锥对应于物体上所有表面片C空间障碍并集的补集，并给出了两类平面片的C空间障碍有效计算方法；3. 提出了基于可视性筛选的可视锥计算算法，利用观察锥筛选、背面筛选和遮挡筛选等可视性筛选方法排除那些对点p不可视的平面片，大大减少了计算C空间障碍平面片的数目，从而有效地提高了算法的计算效率。在可视锥计算的基础上，利用米氏和算子实现了多面体特征的完全可视锥的准确计算；4. 提出了一个包含不同几何抽象层次的产品特征模型，定义了四个几何抽象层次：边界表示B-Rep(M1)、几何抽象集合(M2)、与领域无关的特征(M3)和与领域相关的特征(M4)，应用不同的抽象规则可以得到不同应用领域所需的特征集（如设计特征、加工特征、倒陷特征等）。
在可制造性分析研究方面，将可视锥等几何推理工具应用于倒陷特征识别、分型方向计算和分型线确定，在产品设计阶段实现了对净成型类产品的几何可注塑性分析：
1. 以注塑成型工艺为例，分析了净成型工艺对产品的几何约束，提出了反映产品脱模能力的几何可注塑性概念，定义了产品表面上的形状特征相对于各类成型部件的可脱模性条件。通过定义了一组反映产品制造成本的层次约束，把几何可注塑性分析问题形式化为一个约束满足问题；然后通过几何推理依次确定分型方向、倒陷特征和分型线等设计变量以得到最佳型腔设计方案；最后利用颜色映射把从产品CAD模型中自动获取的几何可注塑性信息可视化反馈给产品设计人员。
2. 提出了一个统一识别包括外部倒陷特征、内部倒陷特征和交倒陷特征(INPUF)在内的所有类型倒陷特征的方法。倒陷特征识别过程分为潜在倒陷特征(PUF)的识别、分型方向的计算和倒陷特征的确定等三个阶段，其中PUF的识别是整个识别过程的重点和难点。在扩展属性邻接图(EAAG)、加工面邻接图(MFAG)和无向阻塞图(NDBG)等基本概念的基础上，本文通过对产品几何信息进行了不同层次的抽象实现了PUF识别：首先根据零件的B-rep模型(M1)构造EAAG(M2)；然后通过删去EAAG中表示凸包面的节点以及与它们相连的弧把EAAG分解为一组MFAG(M3)；最后把每个MFAG映射为一个或多个PUF(M4)。与已有的倒陷特征识别方法相比较，该方法最显著特点在于对不同类型INPUF的有效识别。基于体元分解的INPUF识别方法包括两个主要步骤：体积分解(利用INPUF中所有与凹边相交的面所对应的半空间把INPUF的体积划分为一组最小凸体元)和PUF重构(通过构造体元和零件所组成的装配体的NDBG实现)，能够以较高的计算效率重构所有可能的PUF，并避免了其它基于体元分解的方法经常出现的“组合爆炸”问题。另外，通过在PUF之间按不同的顺序进行布尔差运算来产生INPUF的多种特征解释，并利用启发式规则得到一种可行的特征解释，为生成最优工艺方案创造了条件。
3. 提出了确定最佳分型方向和分型线的几何推理方法。利用自由锥、NDBG等确定满足层次约束的最佳分型方向，使零件的倒陷特征数目最少，同时从PUF中找出真正的倒陷特征。利用自由锥分析模具的分型方向，不仅可以考虑一般型芯的平移运动，而且可以推广到特殊型芯(如螺纹成型)所需的旋转或复合运动。在确定分型线和倒陷特征时，提出了一种广义的NDBG方法：利用零件表面片的外法失对单位球进行划分得到球面排列R，使R上每个球面单元唯一对应一组分型线和倒陷特征；然后通过按一定顺序逐步遍历所有的球面单元，在O(ml2)计算复杂性内产生所有可能的型腔设计方案（m和l分别表示表面片和凸表面片的数目）；最后选择满足层次约束的型腔设计方案作为最佳型腔设计方案。上述计算过程利用了中心投影把球面排列映射为平面排列，避免了自由锥的计算，同时把复杂的球面几何计算转换为简单的平面几何计算。
在工程应用研究方面：1. 系统地阐述了虚拟原型的基本概念、体系结构和关键技术，提出了一个面向虚拟原型系统的产品特征模型体系结构，讨论了产品特征模型在分布式虚拟原型系统中的应用，包括框架结构、数据传输和数据维护等问题；2. 利用可视锥计算数控加工（或CMM测量）中刀具（或测头）的可接近方向，定义了加工点（或测量点）相对于不同类型刀具（或测头）的可接近锥，并应用“贪婪方法”解决了数控加工中的工件装夹问题；3. 开发了可接近性分析和几何可注塑性分析等程序模块，初步建立了一个支持净成型类产品快速开发的虚拟原型系统，并对几个不同复杂程度的产品模型进行了仿真分析。仿真结果表明：本文所提出可接近性分析和几何可注塑性分析方法对于实现面向制造的设计与快速产品开发是非常有效的。
可接近性是产品概念设计阶段的一个重要设计特征，本文提出了基于可视锥的可接近性分析理论和方法，可广泛应用于模具分型、数控加工规划、CMM测量规划、装配规划等计算制造问题求解。研究虚拟环境下的可制造性分析方法，对简化模具结构、降低模具制造成本和实现净成型产品的快速开发等均具有重要意义。另外，本研究也为实现不同应用程序之间的数据交换和信息共享，以及建立集成产品开发过程的产品模型提供了理论基础。本文的研究成果作为“发动机类零件快速测量、建摸及面向制造的设计”项目的重要组成部分，已通过湖北省科技厅组织的科技成果鉴定，并初步应用于珠海市中航模具有限公司、中国人民解放军第三六一一工厂、东风汽车公司等企业的产品创新开发，产生了显著的经济效益。
Abstract
Virtual prototyping (VP) aims at using the CAD model of a product in combination with virtual reality tools to replace, at least to some extent, physical prototypes. The result of VP is a virtual prototype that is a realistic computer simulation of a product with the capability of evaluating its shape, functions and manufacturability intuitively. As one of the key technologies for digital manufacturing and rapid product development, VP promises to reduce product design cycle with lower lifetime cost and higher quality. However, there are many problems need to be researched for VP before applying it to the product development process.
Supported by the NSFC grand project “research on some fundamental of advanced manufacturing technology supporting product innovation” and the National Distinguished Youth Scientific Fund project “the theory foundation and realization of the intelligent 4M system in virtual environment”, this thesis investigates some key technologies on VP, such as feature-based product modeling, accessibility analysis and manufacturability analysis. A feature-based product model consisting of different geometric abstraction levels and multiple application views is firstly presented. Then, a general method for accessibility analysis is proposed based on visibility cones (VCs), which have been applied to geometric manufacturability analysis for near-net-shaped products. Finally, a VP prototype system for rapid product development has been implemented.
The research contributions on fundamental theories achieved in this dissertation include:
1. Extending the concept of VC of a point, three kinds of visibility of a feature, namely, complete visibility cone (CVC), partial visibility cone (PVC) and local visibility cone (LVC), are defined. These VCs (i.e. CVC, PVC, LVC) in combination with some deduced important properties constitute the basic theory for accessibility analysis in the thesis. Moreover, the relationships between VCs and the other accessibility analyzing methods, such as visibility map and freedom cone, are established. As a general tool for accessibility analysis, VCs can be applied to both local accessibility analysis, where only the feature itself is considered as the potential obstacle, and global accessibility analysis, where all obstacles in the set are considered.
2. A general method to computing VC is proposed based on the concept of C-space. Let rp(d) represents a ray or a half-line originated at the point p on an object S and traveling along a direction d. It has been proved that the VC of p corresponds to the free space of the ray rp(d), which can be obtained by subtracting from its C-Space (i.e. the unit sphere) the union of C-Obstacles of all composed face in S. Moreover, two kinds of methods for computing these C-Obstacles are also proposed.
3. An efficient algorithm for computing VC has been implemented by making use of visibility culling. Using three kinds of visibility culling techniques (i.e. view-frustum culling, back-face culling, and occlusion culling), a large number of invisible faces can be detected and removed as early as possible so that much expensive computation involved in computing C-Obstacles and performing Boolean operations for them can be avoided. As a result, the VC can be obtained efficiently by computing the C-Obstacles of a small number of visible faces. In addition, the CVC of a polyhedral feature can be obtained accurately by computing the VC of the origin with the Minkowski sum operation.
4. A feature-based product model with several geometrical abstract levels is presented, to meet the requirement that different application programs in VP may input different levels of geometric information. Four levels of geometric information abstraction are defined as follows: (1) boundary representation (B-Rep) (M1), (2) aggregate geometric abstractions (M2), (3) domain independent features (M3), and (4) domain dependent features (M4). Different feature sets (e.g. design features, machining features, and undercut features) required by different application domains can be extracted by different abstraction rules.
Another research contribution is on manufacturability analysis, where VCs are applied to recognize undercut features, to compute parting directions, and to determine part lines, i.e.
1. A VP approach for geometric mouldability analysis of near-net-shape manufactured parts is presented. The geometric mouldability of a part, which depends on the geometry of the part, is defined as the ability of the part to clear out of the mold core and cavity when the mold opens. With the definition of a constraint hierarchy to minimize manufacturing costs, the geometric mouldability analyzing problem can be formulated as a constraint satisfaction problem, which has been resolved by sequentially determining the undercut features, the parting directions and the parting lines according to the constraint hierarchy. Using the concept of color map, the geometric mouldability of a part automatically extracted from its CAD model is visualized as a feedback to part designers.
2. After giving the definition and classification of undercut features, a new volume-based feature recognition method is presented to recognize both isolated and interacting undercut features in a uniform way. This method consists of three main stages: recognizing potential undercut features (PUFs), determining parting directions, and identifying undercut features, where the most difficult step of the whole process is to recognize PUFs. Based on the concepts of Extended Attributed Adjacent Graph (EAAG), Manufacturing Face Adjacent Graph (MFAG), and Non-Directional Blocking Graph (NDBG), PUFs are recognized by building several levels of geometric abstraction from the part’s CAD model. At first, an EAAG (M2) is constructed from the part’s B-rep model (M1). Then, the EAAG is decomposed into a set of MFAGs (M3) by deleting nodes representing convex faces and arcs between these nodes in the EAAG. Finally, each MFAG is mapped into one or more PUFs (M4). Compared with other undercut feature recognition methods, the main advantage of the proposed method lies in the recognition of interacting undercuts. In the method, the interacting features are recognized by two steps: volume decomposition, in which the volume to be recognized is decomposed into convex cells by intersecting it with half spaces of its faces having concave edges; and reconstruction of features, in which potential features are reconstructed through systematically connecting the small cells using NDBG of the cells and the part. In this way, all possible potential features for an interacting feature can be reconstructed efficiently, which avoids the combinatorial explosion problem occurred in other volume-based feature recognition methods. In additions, multiple interpretations of an interacting feature can be easily generated by subtracting PUFs from each other in different orders. Moreover, one or several desirable interpretations can be generated using a set of heuristic rules defined in the thesis, which are used to generate the optimal process plan of the part.
3. After recognizing the potential undercut features from the given part, a method based on geometric reasoning is proposed to determine the optimal combination of a parting direction and a parting line, which is sure to satisfy the constraint hierarchy defined above. As a result, the true undercut features are identified from PUFs with minimal number of undercuts. Using the freedom cone in 6D screw space, not only common undercuts, which are formed by side cores performing translation motion, but also undercut features, which require side cores performing screw motion or rotation motion (e.g. tap holes), can be recognized. The proposed parting method has been implemented using an extended NDBG, which proceeds as follows: a spherical arrangement is constructed firstly by partitioning the unit direction sphere using outward normals of the part's surfaces with the property that each cell in this arrangement has a unique parting line and undercut feature set, and then all possible cavity design schemes can be identified in O(ml2) time by visiting the cells in a certain order and updating the parting line and undercut feature set incrementally, where m and l are the number of the part's overall and convex surfaces respectively. Lastly, the optimal cavity design scheme is selected to be one satisfying the constraint hierarchy. To avoid the computation of freedom cones, central projection has been used to map the spherical arrangement into a planar one so that efficient planar algorithms instead of spherical algorithms are applied to our method.
The research contributions on engineering applications include:
1. After formulating the basic concept, system structure and key technologies of VP, the feature-based product model proposed above has been used to recognize undercut features. Further, applications of the product model in distribute VP systems are explored by discussing the problems of system framework, data transmission, and data maintenance.
2. In NC machining (or CMM measuring), different accessibility cones, which are sets of motion directions of different kinds of tools (or probes) for a machining (or measuring) point, are calculated with VCs. Making use of these accessibility cones, the workpiece setup problem in NC machining has been resolved efficiently by employing a greedy approach.
3. The proposed algorithms have been programmed in C++ on a Pentium™ Ⅱ PC-compatible and integrated with the solid modeler Eureka™, and a VP prototype system for the rapid product development of near-net-shape manufactured parts has been implemented using currently available virtual reality technologies. Various parts with different complex geometries have been chosen to test the prototype system, and the simulation results obtained have proved the correctness and efficiency of the proposed theory and methods.
Accessibility is one of the primary design features in product concept design stage. The theory and methodology for accessibility analysis based on VCs can be applied to many manufacturing processes such as mold parting, NC machining, CMM measuring, and assembly planning. The research achievement on manufacturability analysis is very important to simplify mold structure, to reduce mold-manufacturing cost, and to realize rapid product development. Further, this research also provides an efficient way for information share and exchange between different application programs, which is the basis to develop a complete product model integrating the whole product development process. The contributions achieved in the dissertation are an important part of the project “Rapid measurement, modeling & DFM for a kind of parts with complex cavities”, which has been accredited by Hubei provincial science and technology department. The project achievements have been applied to the innovative product development of ZhuHai ZhongHang Mold co., No. 3611 Works of the People’s Liberation Army of China, and DongFeng Automobile Co. with remarkable economic benefits.
