A probabilistic approach to variation propagation control for straight build in mechanical assembly

Random component variations have a significant influence on the quality of assembled products, and variation propagation control is one of the procedures used to improve product quality in the manufacturing assembly process. This paper considers straight-build assemblies composed of axi-symmetric components and proposes a novel variation propagation control method in which individual components are re-orientated on a stage-by-stage basis to optimise the table-axis error for the final component in the assembly. Mathematical modelling methods are developed to predict the statistical variations present in the complete assembly. Three straight-build assembly strategies are considered: (a) direct build, (b) best build and (c) worst build assembly. Analytical expressions are determined for the probability density function of the table-axis error for the final component in the assembly, and comparisons are made against Monte Carlo simulations for the purposes of validation. The results show that the proposed variation propagation control method offers good accuracy and efficiency, compared to the Monte Carlo simulations. The probability density functions are used to calculate the probability that the eccentricity will exceed a particular value and are useful for industrial applications and academic research in tolerance assignment and assembly process design. The proposed method is used to analyse the influence of different component tolerances on the build quality of an example originating in aero-engine sub-assembly.     

Dimensional and geometrical tolerance balancing in concurrent design

In conventional design, tolerancing is divided into two separated sequential stages, i.e., product tolerancing and process tolerancing. In product tolerancing stage, the assembly functional tolerances are allocated to BP component tolerances. In the process tolerancing stage, the obtained BP tolerances are further allocated to the process tolerances in terms of the given process planning. As a result, tolerance design often results in conflict and redesign. An optimal design methodology for both dimensional and geometrical tolerances (DGTs) is presented and validated in a concurrent design environment. We directly allocate the required functional assembly DGTs to the pertinent process DGTs by using the given process planning of the related components. Geometrical tolerances are treated as the equivalent bilateral dimensional tolerances or the additional tolerance constraints according to their functional roles and engineering semantics in manufacturing. When the process sequences of the related components have been determined in the assembly structure design stage, we formulate the concurrent tolerance chains to express the relations between the assembly DGTs and the related component process DGTs by using the integrated tolerance charts. Concurrent tolerancing which simultaneously optimizes the process tolerance based on the constraints of concurrent DGTs and the process accuracy is implemented by a linear programming approach. In the optimization model the objective is to maximize the total weight process DGTs while weight factor is used to evaluate the different manufacturing costs between different means of manufacturing operations corresponding to the same tolerance value. Economical tolerance bounds of related operations are given as constraints. Finally, an example is included to demonstrate the proposed methodology.     

Tolerance evolutionary model and algorithm in product growth design

To guarantee the successful transformation from product functional requirement to geometry constraints and finally to dimension constraints between components in a product, an evolutionary tolerance design strategy is proposed on the basis of automation technology in product structure design. In the first part of this paper, the theory of the growth design and the process of tolerance evolutionary design are introduced. Following the evolution of product structure, product tolerance grows from its initial state, defined by accuracy requirements, to its final state, defined as dimension tolerance and geometric tolerance. In this growing process, the basic units in the product growth design, known as functional surfaces and their nominal features, are used as evolutionary carriers. With the help of these basic units, the method for the construction of a two-layer correlation network is proposed. In the second part, the tolerance assertions to assist tolerance evolutionary design are given, based on which the basic process for an evolutionary design of dimensions chain and geometric tolerance are presented. In order to optimize the allocation of the dimension tolerance, a mathematical model is developed in which a correlated sensitivity function between the cost and the tolerance is created. In the model, the design cost, the manufacturing cost, the usage cost, and the depreciation cost of the product are used as constraints to the tolerance allocation. Considering these costs, a multifactor cost function to express quality loss of the product is developed and is applied into the model. The minimum cost is used as the objective function, and the depreciation cost in the objective function is expressed by the discount rate—terminology in economics. The aim was to achieve a final and ideal balance around assembly, manufacturing, and usage through the control of product precision. In the last part, the successful usage of the proposed tolerance evolutionary strategy in the incremental growth product design is demonstrated through a design example.     

Optimal tolerance design for mechanical assembly considering thermal impact

In this paper, a cost–tolerance model based on neural network methods is proposed in order to provide product designers and process planners with an accurate basis for estimating the manufacturing cost. Tolerance allocation among the assembly components is carried out to ensure that the functionality and design quality are satisfied considering the effect of dimensional and geometric tolerance of various components of the assembly by developing a parametric computer aided design (CAD) model. In addition, deformations of various components of mechanical assembly due to inertia and temperature effects are determined and the same is integrated with tolerance design. The benefits of integrating the results of finite element simulation in the early stages of tolerance design are discussed. The proposed method is explained with an application example of motor assembly, where variations due to both dimensional and geometric tolerances are studied. The results show that the proposed methods are much effective, cost, and time saving than the ones considered in literature.     

生长型设计中公差进化设计方法研究

为实现生长型设计中尺寸链及形位公差项目的自动生成,在产品结构设计自动化技术基础上,研究生长型设计中公差进化设计的策略与原则。指出生长型设计中紧随结构的自顶向下、不断进化,公差进化设计模型也呈现为一种层次式结构;同时由于功能表面及其名义特征所具有的承载功能及几何信息的特点,可作为公差进化演绎的单元载体;在此基础上建立公差进化设计的基本过程模型。提出产品结构进化设计中,构建基于功能表面的装配网络以及基于名义特征的约束网络的双层装配约束网络的基本方法,给出辅助公差进化设计的公差断言;在此基础上,给出基于双层装配约束网络及公差断言的尺寸链及形位公差进化设计的基本过程。以活塞精镗销孔夹具的公差设计为例,说明所提出的公差进化设计方法在生长型设计中的成功应用。     

Modeling method for assembly variation propagation taking account of form error

The propagation of variations, such as fixture errors and datum errors resulting from assembly and machining processes, has been extensively studied. However, only a few studies that focus on form error propagation in assembly systems have been implemented. Machining errors, especially form errors, have great impact on assembly accuracy and accuracy stability of precision mechanical systems. With form errors being the research object, a method for calculating mating variation and specifying mating coordinate is proposed to improve the accuracy of the variation propagation model. Taking into account the form error of mating surfaces, the assembly variation propagation of a precision mechanical system is analyzed, and the brief derivation procedure of the variation propagation model is introduced afterwards. The variation propagation model involves a new concept of mating variation specified by the two mating surfaces. An innovative method, the difference surface search based method, is proposed to calculate the mating variation amongst the mating surfaces. The obtained mating variation is then utilized to specify the mating coordinate in the variation propagation model. Moreover, FEM is employed to simulate the contact state of the two mating surfaces to demonstrate effectiveness of the proposed method. Meanwhile, the mating variation and mating coordinate obtained are incorporated into the assembly variation propagation model, which is then verified by a following case study through a comparison between the calculated results and the experimental results. The comparing results indicate that the established model improves the prediction of assembly accuracy. The developed model enables the investigation of various fundamental issues in variation reduction, including variation analysis, process monitoring, accuracy prediction, and accuracy control.     

基于偏差传递的二维多工位装配夹具系统公差可行稳健设计

提出一种基于偏差传递的二维多工位装配夹具系统公差可行稳健设计方法。分析二维多工位装配尺寸偏差传递关系,建立由定位销和零件定位孔(槽)公差引起夹具定位偏差的偏差流状态空间模型。采用数论网格方法对定位销和零件定位孔(槽)公差进行采样,将得到的公差样本代入夹具定位偏差模型,求得夹具定位偏差样本空间,将夹具定位偏差作为状态空间模型的输入偏差,提出基于状态空间模型的二维多工位装配成功率计算方法。继而应用Taguchi正交试验直观分析方法,分析得到影响装配成功率的主要因素即夹具系统定位销副关键公差,运用回归正交组合设计拟合得到二维多工位装配成功率与夹具系统定位销副关键公差的响应面模型。以定位销、零件定位孔(槽)制造成本所构成的装配成本最小化为目标,二维多工位装配成功率为约束,建立二维多工位装配夹具系统定位销和零件定位孔(槽)公差可行稳健设计模型。以汽车车身地板二维三工位装配为例,建立其公差可行稳健设计模型并对该模型进行计算与分析,结果表明在装配成本增幅较小的情况下,采用稳健约束后可显著提高公差设计的可行稳健性。该方法为二维多工位装配夹具系统公差稳健设计提供了一种新途径。     

一种设计和工序公差计算机辅助并行设计方法的研究

提出一种计算机辅助设计公差和工序公差并行设计的数学模型，以成本公差函数作为目标函数，以装配功能要求、加工方法、加工余量、工序制造公差范围作为约束条件，并用蒙特卡洛法模拟尺寸装配、模拟退火算法用于优化求解，实现了设计公差和工序公差并行设计，缩短了设计周期。     

Unified dimension and tolerance modeling for mechanical precision predicting

Precision predicting is significant for quality qualification of complicated product, and it is one of the fundamental applications for virtual assembly system. For most predicting methodologies, functional precision is propagated by both dimension and geometric tolerance; however, dimension and geometric tolerance have different manifestation patterns that relay on traditional GD&T standard, and it brings difficulty in considering dimension and geometric tolerance simultaneously; hence, a uniform model called maximum compatible constraint model (MCCM) is proposed. Dimension and geometric tolerance are clustered into three types: deterministic constraint, micro-degree constraint, and release constraint. The MCCM model explains these multiform constraints with unified constraint matrix, dimension torsor (D _mT ), and deviation torsor (D _vT ). D _mT is introduced to record the ideal position of functional geometry referring to geometry coordinate system. D _vT and micro-degree variational zone are discussed for explaining variational information of precision; in addition, topological structure related to functional and datum surfaces are extracted. By compatible structure, MCCM is not only adaptable for explaining dimension and geometric tolerance, but also for modeling geometric and assembly constraints that are meaningful for variation propagation during assembly process. With all constraints, dimension and tolerances are modeled, and then MCCM set is attained. Within the MCCM set, dimension cumulative, variation, and error propagation are facilitated by constraint and direction discussion, and precision predicting is conducted more specifically.     

STEP-NC compliant process planning of additive manufacturing: remanufacturing

Additive manufacturing is becoming one of the key methods for reproducing repair sections in remanufacturing processes. The major advantage of using additive processes is to minimize production time and waste. However, the surface quality and shape accuracy are usually insufficient for the final product because the approximated representation format causes the accumulation of the error during the geometric operations of the process planning. This limitation is a barrier to utilize additive processes as finishing processes, such as general metal cutting. There is need to improve the final quality of parts obtained with additive manufacturing. In this paper, STEP-based numerical control (STEP-NC)-based process planning is applied to the additive manufacturing. ISO 14649 (STEP-NC) describes part programs with geometric data directly and also contains the information necessary for the intelligent process planning. This paper proposes the STEP-NC-based representation method of additive manufacturing and the series of geometric reasoning to automate the derivation of the repair section. The proposed representation has the benefits to provide a high accuracy for the final surface and to describe multiple materials. Topological data maintain low error during the series of process planning through the CAD-CAM-CNC chain. The proposed platform supports consideration of the process tolerance and comparison of the selected plan with alternative processes. In order to show the practical advantages, an analysis of the remanufacturing process is carried out. The case study of remanufacturing a pocket part is presented in order to validate the proposed process plan. The result of the case study shows the improvement in terms of automatic process planning and surface quality accuracy.     

多工位装配过程夹具系统公差和维护综合优化设计

提出一种面向二维多工位装配过程、综合考虑装配夹具系统全寿命周期成本、产品零件孔制造成本和产品质量损失成本的公差和维护综合优化方法。分析多工位装配尺寸偏差传递关系,建立多工位装配过程产品质量损失模型。然后根据4-2-1夹具定位原则,构建考虑夹具磨损过程损失的夹具定位销副偏差统计数字特征模型。继而发展了以夹具系统全寿命周期成本、零件孔制造成本和和产品质量损失成本为装配总成本最小化的定位销公差、零件孔公差与更换周期优化模型。以汽车侧围装配过程为例,分别研究定位销公差、零件孔公差、定位销更换周期、配合间隙、平均磨损率和磨损率方差对装配总成本的影响,并优化设计定位销公差、零件孔公差和定位销更换周期。所提出的综合优化设计方法比采用定位销等公差设计、零件孔等公差设计、定位销与零件孔等公差设计和定周期更换设计的装配总成本分别减少了16.25%、11.31%、39.93%和13.54%。该方法为产品装配夹具系统高质量低成本设计提供了一种新的途径。     

Minimum-Loss Assembly Tolerance Allocation by Considering Product Degradation and Time Value of Money

In the optimisation of tolerance allocation for a mechanical assembly, much work has concentrated on the minimum cost– tolerance allocation without considering the quality of the final assembly. Cheng and Maghsoodloo combined the cost– tolerance function and quality loss function, to determine the optimal tolerances for individual components, so that the total assembly cost (including both tolerance cost and quality loss) might be minimised. The objective of this paper is to propose a model for optimal tolerance allocation by considering both tolerance cost and the present worth of quality loss such that the total assembly cost/loss is minimised. The proposed model takes into account the time value of money for quality loss and product degradation over time, and includes two new parameters: the planning horizon and the product user’s discount rate. From the result of this study, a longer planning horizon results in an increase in both tolerance cost and quality loss; however, a larger value of discount rate yields a decrease in both tolerance cost and quality loss.     

Accuracy analysis and design of A3 parallel spindle head

As functional components of machine tools, parallel mechanisms are widely used in high efficiency machining of aviation components, and accuracy is one of the critical technical indexes. Lots of researchers have focused on the accuracy problem of parallel mechanisms, but in terms of controlling the errors and improving the accuracy in the stage of design and manufacturing, further efforts are required. Aiming at the accuracy design of a 3-DOF parallel spindle head(A3 head), its error model, sensitivity analysis and tolerance allocation are investigated. Based on the inverse kinematic analysis, the error model of A3 head is established by using the first-order perturbation theory and vector chain method. According to the mapping property of motion and constraint Jacobian matrix, the compensatable and uncompensatable error sources which affect the accuracy in the end-effector are separated. Furthermore, sensitivity analysis is performed on the uncompensatable error sources. The sensitivity probabilistic model is established and the global sensitivity index is proposed to analyze the influence of the uncompensatable error sources on the accuracy in the end-effector of the mechanism. The results show that orientation error sources have bigger effect on the accuracy in the end-effector. Based upon the sensitivity analysis results, the tolerance design is converted into the issue of nonlinearly constrained optimization with the manufacturing cost minimum being the optimization objective. By utilizing the genetic algorithm, the allocation of the tolerances on each component is finally determined. According to the tolerance allocation results, the tolerance ranges of ten kinds of geometric error sources are obtained. These research achievements can provide fundamental guidelines for component manufacturing and assembly of this kind of parallel mechanisms.     

机械装配偏差源及其偏差传递机理分析

产品装配偏差源和偏差传递机理分析,是装配精度预测的前项工作。综合影响装配功能的尺寸和形位精度、装夹定位精度信息,将刚性零件装配的偏差源分为几何位置偏差、几何形状偏差和装配位置偏差三类;进一步建立面向三类偏差源统一表达和评价的多元统计学模型,及其相对装配功能的正负累积性判断方法。基于偏差源统一表达,分析偏差在零件间、零件内两特征间的偏差传递和相互作用,提出偏差传递的三种偏差流;根据装配过程中是否存在装配间隙,将偏差流分为连续流和断续流两种。基于偏差有向图,对三种偏差流和配合偏差流进行表达;并建立面向整个产品偏差传递及装配功能表达的装配偏差有向图模型。结合某航天器装配为例,验证偏差源表达和偏差传递模型的有效性。     

Design automation and optimization of assembly sequences for complex mechanical systems

Assembly sequence design for a mechanical system can have significant impact on manufacturing cost and product quality. Traditionally, such a design process is largely based on experience and best practices, often ineffective and non-optimal as the system becomes complex. This paper proposes a new, systematic method for automatic assembly sequence design and optimization. Key elements include assembly modeling, sequence planning, locating scheme optimization, dimensional quality evaluation, and optimization. First, a directed graph and an assembly matrix are employed to describe the assembly relation of a system. Then, the feasible assembly sequences are generated through layered subassembly detection of adjacency matrices, filtered by engineering constraints. To evaluate quickly the assembly quality and compare the influences of different locating point schemes, a linear 3D variation propagation analysis model with deterministic locating principle is introduced. The optimal locating scheme is then selected using a genetic algorithm with the least variation propagation. Finally, the assembly dimensional quality for different sequences is evaluated and the optimal assembly sequences are achieved through genetic algorithms. A case of automotive body side assembly is presented to illustrate the whole methodology.     

Tolerance design of mechanical assembly using NSGA II and finite element analysis

The technological and financial limitations in the manufacturing process are the reason for non-achievability of nominal dimension. Therefore, tolerance allocation is of significant importance for assembly. Conventional tolerance allocation methods are limited by an assumption that all parts are rigid. Every mechanical assembly consists of at least one or more flexible parts which undergo significant deformation due to inertia effect. Finite element analysis is used to determine the deformation of components in an assembly. Therefore, integration of statistical tolerance design with finite element analysis will guarantee that the optimal tolerance values of various components of the assembly obtained as end product of the tolerance design will remain within tolerance variation. Then the product can function as intended under a wide range of operating conditions for the duration of its life. In this paper, tolerance design of a piston cylinder assembly is done to demonstrate the proposed methodology.     

几何增强的装配工艺本体建模

包含产品几何与非几何信息的产品装配要求是装配工艺设计的主要依据,对装配工艺设计决策结果具有决定性的影响。在装配工艺模型中描述产品的几何相关信息能够更好地表达如装配顺序,装配路径等内容,同时可以更好地辅助装配工艺决策,提高决策的自动化水平。提出一种几何增强的装配工艺本体模型,利用语义本体技术,建立产品几何信息在装配工艺中的描述方法,数据结构与关系描述。并以该模型为基础,建立基于几何增强装配工艺本体的装配工艺决策框架。该框架分为两部分：一是采用几何增强的装配工艺本体模型描述产品几何信息和装配工艺信息的数据结构和相互关系;二是为了让几何信息与装配工艺信息之间存在的丰富的隐含关系显性化,对语义本体推理机制进行增强,提出推理单元的概念,使决策框架具有从产品几何信息中推理装配工艺相关信息的能力,有效地支持装配工艺决策。以针对某传动器产品装配顺序决策的过程,验证所提出的几何增强装配工艺本体模型与框架的有效性。     

Particle swarm optimization algorithm to maximize assembly efficiency

The demands on assembly accuracy require accurate operations both in machining and assembly in order to achieve the high performance of products. Although advanced machining technologies can be used to satisfy most of the demands on precision assembly, the corresponding manufacturing cost will also be increased. Selective assembly provides an effective way for producing high-precision assembly from relatively low-precision components. The accuracy of selective assembly is mainly based on the number of groups and the range of the group (allocated equally on the design tolerance). However, there are often surplus parts in some groups due to the imbalance of mating parts, especially in the cases of undesired dimensional distributions, which makes the methods developed and reported in the literature often not suitable for practice. In this work, a particle swarm optimization (PSO) algorithm is proposed by applying batch selective assembly method to a complex assembly with three mating components (as in ball bearing: an inner race, ball and outer race), to minimize the surplus parts and thereby maximizing the assembly efficiency. Due to the continuous nature of particle swarm optimization algorithm, standard PSO equations cannot be used to generate discrete combination of mating parts. An effective encoding scheme is developed to make the combination of mating parts feasible. The evolution performance of the PSO algorithm with different control parameter values is also analysed.     

轿车功能约束对总装配工艺规划的影响分析

在分析轿车功能系统特点的基础上 ,建立功能连接与几何连接相复合的装配关系模型 ;分别探讨了功能约束对作业内容设计、序列生成和作业分配等工艺规划过程的影响作用 ,为在计算机辅助总装配工艺规划中定量化处理功能约束提供了解决途径。以底盘电气系统中音响子系统的总装配序列规划为例进行了实例分析