协同装配信息集成建模及装配顺序规划研究

研究了装配的参照元素、装配方式、装配关系，并总结出三大装配类型．针对协同装配活动的需求，提出包含设计技术决策和产品社会属性信息在内的广义装配建模思想；在引人装配结和装配链概念的基础上，构建了适合协同装配的装配信息模型．通过搜索模型，容易获得产品装配关系图，再经过界定装配导元属性，依据自定义修剪规则，形成具有装配层次和顺序属性的同心圆图，从而能够有效地获得可行的产品装配顺序．     

Symbolic OBDD representations for mechanical assembly sequences

Assembly sequence planning is one typical combinatorial optimization problem, where the size of parts involved is a significant and often prohibitive difficulty. The compact storage and efficient evaluation of all the feasible assembly sequences is one crucial concern. Ordered binary decision diagram (OBDD) is a canonical form to represent and manipulate the Boolean functions efficiently, and appears to give improved results for large-scale combinatorial optimization problems. In this paper, subassemblies, assembly states and assembly tasks are represented as Boolean characteristic functions, and the symbolic OBDD representation of assembly sequences is proposed. In this framework, the procedures to transform directed graph and AND/OR graph into OBDDs are presented. The great advantage of OBDD-based scheme is that the storage space of OBDD-based representation of all the feasible assembly sequences does not increase with the part count of assembly dramatically so quickly as that of both directed graph and AND/OR graph do. We undertake many experimental tests using Visual C++ and CUDD package. It was shown that the OBDD scheme represented all the feasible assembly sequences correctly and completely, and outperforms either directed graph or AND/OR graph in storage efficiency.     

基于成本和并行装配的装配序列有向图求解

针对虚拟装配中装配序列规划问题,引入了有向图来描述装配过程中的零件以及零件间的装配约束关系。结合装配成本、并行装配、装配经验优化了装配关系有向图的拓扑排序算法。提出了将装配方向变化次数作为衡量装配成本的一项重要指标。提出了将单次可装配的零件数量作为装配优先方向的参考依据。文章最后给出了装配序列生成的具体算法。     

A hierarchical approach on assembly sequence planning and optimal sequences analyzing

Assembly sequence planning (ASP) is a critical technology that bridges product design and realization. Deriving and fulfilling of the assembly precedence relations (APRs) are the essential points in assembly sequences reasoning. In this paper, focusing on APRs reasoning, ASP, and optimizing, a hierarchical ASP approach is proposed and its key technologies are studied systematically. APR inferring and the optimal sequences searching algorithms are designed and realized in an integrated software prototype system. The system can find out the geometric APRs correctly and completely based on the assembly CAD model. Combined with the process APRs, the geometric and engineering feasible assembly sequences can be inferred out automatically. Furthermore, an algorithm is designed by which optimal assembly sequences can be calculated out from the immense geometric and engineering feasible assembly sequences. The case study demonstrates that the approach and its algorithms may provide significant assistance in finding the optimal ASP and improving product assembling.     

The symbolic OBDD scheme for generating mechanical assembly sequences

Assembly sequence planning is one of typical combinatorial optimization problems, where the size of parts involved is a significant and often prohibitive difficulty. The compact storage and efficient evaluation of feasible assembly sequences is one crucial concern. Ordered binary decision diagram (OBDD) is a canonical form to represent and manipulate the Boolean functions efficiently, and appears to give improved results for large-scale combinatorial optimization problems. In this paper, assembly knowledge models of liaison graph and translation function are formulated by OBDDs, and OBDD-based representation of assembly sequences is proposed. A novel OBDD-based procedure was presented to generate all geometrically feasible assembly sequences from the OBDDs of liaison graph and translation relation. This procedure can be used conveniently on the computer and all the feasible sequences can be derived. The great advantage of OBDD-based scheme is that the storage space of OBDD-based representation of feasible assembly sequences does not increase with the part count of assembly dramatically so quickly as that of AND/OR graph does. We developed the prototype tool for generating assembly sequence using Visual C++ and CUDD package, and undertake some experimental tests. It was shown that the OBDD scheme generated feasible assembly sequences correctly and completely.     

装配规划与方案评价集成系统的研究与开发

为了将装配顺序规划与方案评价有效集成,规划合理的装配顺序,检验装配过程中存在的干涉情况,提出了人机交互定义分层装配顺序主模型与自动生成子装配的两级装配顺序规划方法．该方法适用于大型装配模型的装配顺序规划场合;在原有的研究项目KMCAD3D基础之上,开发了一套实用的装配顺序规划与方案评价原型系统;通过对二级蜗轮减速器实例的装配顺序规划讨论,说明了该方法的可行性．     

An approach to determine geometric feasibility to assembly states by intersection matrices in assembly sequence planning

In this article, an approach is described for the development of a process for the determination of geometric feasibility whose binary vector representation corresponds to assembly states. An assembly consisting of four parts is considered as an example. First, contact matrices generate the assembly's connection graph. The developing connection graph was used to model the example assembly. In the assembly's connection graph, each node corresponds to a part in the assembly, and edges in the graph of connections correspond to connecting every pair of nodes. Moreover, in the connection graph, each connection corresponds to an element in the binary vector representation. In the development of the approach, intersection matrices are used to represent interference among assembling parts during the assembly operation. Intersection matrices are defined to along the Cartesian coordinate system's six main directions. The elements of intersection matrices are constituted to Boolean values. Each element of binary vector representations includes a connection between a pair of parts. First, ordered pairs of parts are established. Then, Cartesian products, which are produced from these established ordered pairs of parts, are applied to Boolean operators. Finally, geometric feasibility of these binary vector representations is determined. In this work, some assembly systems are sampled and examined. Among these examples, six assembly sequences for a four-part packing system; two assembly sequences for a five-part shaft bearing system; 373 assembly sequences for a seven-part clutch system and assembly states have been investigated.     

基于图的子装配识别与装配序列规划

本文基于图建立了装配模型,并提出了一种基于配合关联图的子装配识别和装配序列 规划方法．直接从配合关联图出发识别出围绕箱体、轴和螺纹联接等典型零件所形成的子装 配;对配合关联图进行了简化,完成了基于配合关联图的装配序列规划．     

Nested partitions method for assembly sequences merging

The severe competition in the market has driven enterprises to produce a wider variety of products to meet consumer’s need. However, frequent variation of product specification and more complexity of product cause the assembly sequence planning of product become more and more complicated. As a result, the issue of assembly sequence planning of complex product becomes a problem which is worthy of concern. In this study, a methodology for assembly sequence planning of complex components is presented, which consists of three phases: assembly-based modular design, assembly subsequences generation for each module and assembly sequences merging. Nested partitions (NP) method is used to merge assembly subsequences. Assembly sequences merging can make full use of subsequences information of modules and simplify assembly sequence planning of the complex products. A desk lamp is used as an example for implementation to validate the feasibility of this research.     

基于集成干涉矩阵的蚁群装配序列规划

针对装配序列规划问题,构建了面向装配的蚁群算法。利用有向图进行产品的装配建模,有效地表达了装配零件之间的接触以及优先关系。探讨了装配干涉矩阵的形式和性质,提出了集成干涉矩阵的概念和变换方法,采用集成干涉矩阵以及工具列表矩阵来表达模型的基本装配信息。分析了基于干涉矩阵的可行方向推导过程、装配零件的状态转移概率以及蚁群算法的信息素更新规则。从装配可行方向的改变次数和装配工具的改变次数建立目标优化函数,从而建立面向装配的蚁群算法用于序列的搜索及构造,并给出蚁群算法的伪代码。最后通过实例对算法进行了验证说明。     

A physically based approach with human–machine cooperation concept to generate assembly sequences

Assembly plan is considered one of the important stages to minimize the cost of manufacturer and to ensure the safety of assembly operation, the main problem of assembly sequence planning approach is how to reduce the deviation from the real manufacture conditions. In this paper, we have extensively investigated a novel approach to automatically generate the assembly sequences for industrial field, which is especially applied to other large-scale structures. A physically based assembly representation model includes not only the pre-determined basic assembly information, such as precedence relations between parts or subassemblies, geometric constraints, different assembly types, and also the dynamic real-time physical properties, such as the center position of gravity, the force strength of the part, et al. This representation model considered the influences on optimum sequences by assembly operations will be modified by the feedback from interactive virtual environment. Then, we select the safety, efficiency and complexity as the optimization objectives. A hybrid search approach may be used to find the optimum assembly sequence, which will be integrated into an interactive assembly virtual environment (IAVE). It means that the results of assembly interaction can be provided to update the assembly planning model as a feedback, by which the approach will take advantages of the immune memory for local optimum search. The user can adjust the assembly sequences with obvious good objective by interaction with IAVE to improve the performance of the search algorithm. We describe human–machine cooperation (HMC) method for ASP in this work, by which human also can play a pivotal role instead of pure soft-computing. A series of numerical experiments are done to validate the performance of the physically based approach (PBA) to generate assembly sequence, which shows the efficiency and the operability to guide the assembly work.     

A complexity model for sequence planning in mixed-model assembly lines

Sequence planning is an important problem in assembly line design. It is to determine the order of assembly tasks to be performed sequentially. Significant research has been done to find good sequences based on various criteria, such as process time, investment cost, and product quality. This paper discusses the selection of optimal sequences based on complexity induced by product variety in mixed-model assembly line. The complexity was defined as operator choice complexity, which indirectly measures the human performance in making choices, such as selecting parts, tools, fixtures, and assembly procedures in a multi-product, multi-stage, manual assembly environment. The complexity measure and its model for assembly lines have been developed in an earlier paper by the authors. According to the complexity models developed, assembly sequence determines the directions in which complexity flows. Thus proper assembly sequence planning can reduce complexity. However, due to the difficulty of handling the directions of complexity flows in optimization, a transformed network flow model is formulated and solved based on dynamic programming. Methodologies developed in this paper extend the previous work on modeling complexity, and provide solution strategies for assembly sequence planning to minimize complexity.     

Analysis of assembly operations’ difficulty using enhanced expert high-level colored fuzzy Petri net model

Majority of the products can be assembled in several ways that means the same final product can be realized by different sequences of assembly operations. Different degree of difficulty is associated with each sequence of assembly operation and such difficulties are caused by the different mechanical constraints forced by the different sequences of operations. In the past, few notable attempts have been made to represent and enumerate the degree of difficulty associated with an assembly sequence (in the form of triangular fuzzy number) by using the concept of assembly graph. However, such representation schemes do not possess the capabilities to model the user's reasoning and preferences. In this research, an intelligent Petri net model that combines the abilities of modelling, planning and performance evaluation for assembly operation is presented. This modelling tool can represent the issues concerning degree of difficulty associated with assembly sequences. The proposed mechanism is enhanced expert high-level colored fuzzy Petri net (EEHLCFPN) that is a hybrid of knowledge-based system and colored Petri net. An example encompassing assembly of subassemblies is considered to efficiently delineate the modelling capabilities of proposed hybrid petri net model.     

基于图论的飞机典型装配工艺数据挖掘方法

为实现飞机装配指令编制的快速化、智能化,提出基于图论的飞机典型装配工艺数据挖掘方法。该方法将停用词表和分隔数组两个约束引入语义分词法完成装配工艺指令的分词处理,并以装配工艺特征向量结构化地表达分词后的装配工艺指令。将装配工艺特征向量映射为单向有序链,以此构建装配工艺图。通过定义装配工艺图的节点支持度和边支持度,给出了典型装配工艺挖掘方法。以某型飞机的平尾装配工艺为例,在多个支持度下验证了方法的有效性。     

Geometric skeleton computation enabling concurrent product engineering and assembly sequence planning

This paper introduces a novel modelling approach to geometric skeleton computation enabling concurrent product engineering and assembly sequence planning. Current engineering vision has recently moved towards new modelling and management paradigms to maintain competitive edges all along the product lifecycle. Consistent with concurrent engineering and design for X stakes, this recent shift promotes cross-X and knowledge-intensive philosophies in the product development process, principally focused on lifecycle engineering.The main objective of this research is to integrate assembly process engineering information and knowledge in the early phases of the product development process in a top-down and proactive manner, in order to provide a geometric skeleton-based assembly context for designers. The definition of the product and its related assembly sequence requires both the enhancement and the entire understanding of product relationships between the various product components, and its related assembly rationale. As a consequence, this new modelling approach highlights the need to integrate various stakeholders’ viewpoints involved in the beginning of the product lifecycle. In such a context, earlier work has achieved the early generation of an optimal assembly sequence in the product development process, before the product geometry is completely defined. As a result, previous research has made possible to control and bind the product modelling phase through an assembly oriented product structure.The aim of the proposed approach is to compute and define a geometric skeleton model based on product relational information and the early-defined assembly sequence. The proposed approach–called SKeLeton geometry-based Assembly Context Definition (SKL-ACD)–enables the control of the product modelling phase by introducing skeleton entities consistent with product relationships and assembly sequence planning information. A prototype application within a CAD tool has been developed for aiding geometric skeleton computation and generation. Lastly, an industrial case study is introduced to highlight the feasibility and the relevance of the proposed modelling approach.     

运用有向联接件知识求解装配序列规划

在分析联接件特征的基础上，提出了有向联接件的概念，建立基于联接件知识的零件表达式；运用有向联接件知识求解装配序列规划，实现了知识推理算法和几何约束推理算法的有机结合，有效地降低了装配规划的计算复杂度，保证规划所得装配序列的合理性和实用性．此外，还建立了装配体的自由空间图，可以解决非单调装配序列规划问题。     

Assembly Coplanner: co-operative assembly planner based on subassembly extraction

The distribution of assembly workstations enables assembly operations to be done in parallel, while the multiple routing of parts in flexible assembly systems allows the opportunistic scheduling of assembly operations. This paper presents an assembly planning system, called the Assembly Coplanner, which automatically constructs an assembly partial order and generates a set of assembly instructions from a liaison graph representation of an assembly based on the extraction of preferred subassemblies. Assembly planning in Coplanner is carried out by the co-operation of multiple planning agents, such as the geometric reasoner, the physical reasoner, the resource manager and the plan coordinator, under the constraints of finding a cost-effective assembly plan in a flexible assembly system. The Coplanner identifies spatial parallelism in assembly as a means of constructing temporal parallelism among assembly operations. This is achieved in the following way: (1) the selection of a set of tentative subassemblies by decomposing a liaison graph into a set of subgraphs based on feasibility and difficulty of disassembly; (2) the evaluation of each of the tentative subassemblies in terms of assembly cost represented by subassembly selection indices; and (3) the construction of a hierarchical partial order graph (HPOG) as an assembly plan. A case study applying the Coplanner to a mechanical assembly is illustrated in this paper.     

An New Approach to Represent Assembly Sequences

How to identify all feasible assembly sequences and compactly represent them is very important and necessary to computer-aided assembly sequence planning. An approach to get precedence relationships between components directly from assembly modeling is proposed in this paper. A representation method called disassembly sequence graph (DSG) is also presented in this paper. An example has been provided to illustrate the proposed approach.     

虚拟环境下面向装配的设计系统的研究

虚拟环境下面向装配的设计,是一种集成虚拟现实技术和装配性评价的交叉学科研究,文中提出了一个虚拟环境下面 向装配的设计系统VirDFA(Virtual Design For Assembly)的体系结构,首先描述了虚拟人工实时拆卸的过程,着重研究在实现虚拟人工拆卸过程中,需要解决的装配体物性建模、虚拟环境下装配约束的动态管理及装配序列/路径的自动记录等关键技术,其次,从面向产品结构和装配工艺过程两方面的再设计角度,构建了装配性评价体系,提出了定量的装配效率模型和装配复杂度指标模型。并从装配成本的角度来评价产品的装配性优劣,为产品和装配工艺规划的再设计提供了依据。     

Assembly sequence planning of rigid and flexible parts

Assembly sequence planning (ASP) is the process of computing a sequence of assembly motions for constituent parts of an assembled final product. ASP is proven to be NP-hard and thus its effective and efficient solution has been a challenge for the researchers in the field. Despite the fact that most assembled products like ships, aircrafts and automobiles are composed of rigid and flexible parts, no work exists for assembly/disassembly sequence planning of flexible parts. This paper lays out a theoretical ground for modeling the deformability of flexible assembly parts by introducing the concept of Assembly stress matrix (ASM) to describe interference relations between parts of an assembly and the amount of compressive stress needed for assembling flexible parts. Also, the Scatter Search (SS) optimization algorithm is customized for this problem to produce high-quality solutions by simultaneously minimizing both the maximum applied stress exerted for performing assembly operations and the number of assembly direction changes. The parameters of this algorithm are tuned by a TOPSIS-Taguchi based tuning method. A number of ASP problems with rigid and flexible parts were solved by the presented SS and other algorithms like Genetic and Memetic algorithms, Simulated Annealing, Breakout Local Search, Iterated Local Search, and Multistart Local Search, and the results and their in-depth statistical analyses showed that the SS outperformed other algorithms by producing the best-known or optimal solutions with highest success rates.