Optimum tolerance synthesis for complex assembly with alternative process selection using Lagrange multiplier method

Any part cannot be manufactured to the required nominal dimensions due to inherent variations in workmanship, material, and machine. The specification of tolerance on part dimensions plays a major role on performance, quality, and cost of the product. Distribution of tolerance among the components of an assembly is known as tolerance allocation. The selection of alternative processes for tolerance allocation also plays a vital role in reducing manufacturing cost. Near-optimal allocated tolerances are obtained using nontraditional optimization techniques in which the solutions are achieved randomly. Also, there is a chance for omitting the better process for allocation. The results of successive run of the program based on these techniques will not yield consistent results. An attempt has been made in this work to solve the above problem using Lagrange multiplier method for complex assemblies with univariate search method. The methodology has been demonstrated on wheel mounting assembly. The example product after implementing the proposed method would yield 1.4% savings in manufacturing cost as compared with the cost obtained by Singh.     

Multi-objective optimization for optimum tolerance synthesis with process and machine selection using a genetic algorithm

This paper presents a new approach to the tolerance synthesis of the component parts of assemblies by simultaneously optimizing three manufacturing parameters: manufacturing cost, including tolerance cost and quality loss cost; machining time; and machine overhead/idle time cost. A methodology has been developed using the genetic algorithm technique to solve this multi-objective optimization problem. The effectiveness of the proposed methodology has been demonstrated by solving a wheel mounting assembly problem consisting of five components, two subassemblies, two critical dimensions, two functional tolerances, and eight operations. Significant cost saving can be achieved by employing this methodology.     

Fuzzy-small degrees of freedom representation of linear and angular variations in mechanical assemblies for tolerance analysis and allocation

Tolerances naturally generate an uncertain environment for design and manufacturing. In this paper, a novel fuzzy based tolerance representation approach for modeling the variations of geometric features due to dimensional tolerances is presented. The two concepts of fuzzy theory and small degrees of freedom are combined to introduce the fuzzy-small degrees of freedom model (F-SDOF). This model is suitable for tolerance analysis of mechanical assemblies with linear and angular tolerances. Based on the fuzzy concept, a new index (called the assemblability index) is introduced which signifies the fitting quality of parts in the assembly. Graphical and numerical representations of tolerance allocation by this method are presented. The goal of tolerance allocation is to adjust the tolerances assigned at the design stage so as to meet a functional requirement at the assembly stage. The presented method is compatible with the current dimensioning and tolerancing standards. The application of the proposed methodology is illustrated through presenting an example problem.     

Optimum manufacturing tolerance to selective assembly technique for different assembly specifications by using genetic algorithm

Tolerance on parts dimension plays a vital role as the quality of the product depends on sub components tolerance. Thus, precision products that are manufactured reflect at high manufacturing cost. To overcome this situation, sub components of an assembly may be manufactured with wider tolerance, measured (using latest technologies like image processing) and grouped in partition and corresponding group components may be mated randomly. This present work is to obtain an optimum manufacturing tolerance to selective assembly technique using GA and to obtain maximum number of closer assembly specification products from wider tolerance sub components. A two components product (fan shaft assembly) is considered as an example problem, in which the subcomponents are manufactured with wide tolerance and partitioned into three to ten groups. A combination of best groups is obtained for the various assembly specifications with different manufacturing tolerances. The proposed method resulted nearly 965 assemblies produced out of one thousand parts with 15.86% of savings in manufacturing cost.     

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.     

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。     

基于吸振原理的轮边驱动电动车垂向振动负效应的抑制

针对轮边驱动电动车非簧载质量引起车辆垂向振动负效应,提出了一种在车轮转向节上加装动力吸振器的方案,并建立了数学模型;根据某轮边驱动电动车参数,对吸振器参数进行了优化设计.结果表明,优化后的悬架性能较优化前有明显提高.     

对韶山4改型机车整体车轮压装质量问题的轮对组装工艺研究

文章针对韶山4改型电力机车整体车轮压装中轮、轴易拉伤及组装尺寸难以保证这一质量问题,分析研究了该车型传统的轮对组装、车轴、车轮加工工艺,结合技术引进方面的知识,找出轮、轴拉伤及组装尺寸难以保证的主要原因。通过改进传统的工艺方法,解决了该质量问题,同时为其它车型机车类似质量问题的解决提供了新的方法。     

Effect of ultrasonic impact treatment on the ultra high cycle fatigue properties of SMA490BW steel welded joints

This paper presents bi-criteria formulation of a tolerance allocation model for an interchangeable assembly to simultaneously evolve suitable combination of manufacturing facility in multiple facility shaft-hole production environments of medium- and large-scale industries and tolerances to complement the need of customers. An Exhaustive Search Procedure is used to obtain the optimal solution for small and medium size problems and simulated annealing algorithm is used for large size problems. The usefulness of the Pareto front in manufacturing tolerance allocation decisions is demonstrated with three case study problems. The effect of process capability of shaft-hole assembly manufactured from alternative manufacturing machines and the optimality is analyzed in three cases to understand their criticality in decision-making. The models discussed in this paper could be useful for medium- and large-scale manufacturing industries, where there will be a variety of manufacturing facilities (specifications, capabilities, models, and types) for making both shaft-hole assembly and play a key role to meet the tolerance and cost requirements of different customers. This paper further discusses how this formulation and methodologies can be used for two hole and two shaft assemblies and multiple shaft-hole assemblies. Finally, the paper ends with highlighting directions of future research avenues in the shaft-hole assembly.     

基于宽容分层序列法的飞机装配公差稳健设计技术

飞机制造中由于工序能力指数和公差等设计变量存在变差,可能导致无法满足飞机装配质量要求以及制造成本波动较大的问题。运用稳健设计方法建立了飞机装配公差的可行稳健性和敏感稳健性两类设计模型。可行稳健设计考虑了公差等设计变量对装配可行性的影响,使其变差不影响装配功能的实现;敏感稳健性设计则考虑了公差等设计变量对制造成本和装配质量的影响,在目标成本较小的前提下使得目标成本和装配质量受设计变量变差的影响最小。提出了针对飞机装配公差可行敏感稳健设计的多目标优化问题的宽容分层序列求解算法。将公差设计中制造成本、装配质量波动、制造成本波动多个设计目标按照重要性依次排序。首先求解成本最小情况下的公差一般优化解,然后在成本最小值的宽容约束下,求得具有装配质量波动最小值的公差,最后在上述两个优化目标的宽容约束下,求得成本波动最小的最优公差。应用实例和分析结果表明了方法的有效性。       

一种基于制造环境的统计公差分析方法

在并行公差设计理论的基础上,提出基于制造环境的面向装配的统计公差分析方法,使得在公差设计中,考虑实际加工环境的加工状况,即各种加工方法的工序能力。在此基础上,建立基于工序能力的统计公差分析模型。在假定过程平均漂移为均匀分布和正态分布两种情况下,计算出制造偏差的概率密度函数,进而推导出线性装配相应函数的概率统计特性值,为统计公差优化设计奠定了基础．     

基于工序加工能力的并行公差优化设计

提出一种基于工序加工能力的并行工序公差优化设计方法。在产品的初步结构设计阶段，通过相配零件的加工工艺规划把装配功能公差表示为零件的工序公差，建立以加权制造总成本最小为目标，以并行公差链、标准化的工序公差系数、机床最大经济极限公差为约束的非线性并行公差优化设计模型，求解该模型得到最佳的工序公差。最后给出了并行公差优化设计的一个工程实例，结果表明，所提的方法具有比传统串行等精度方法更合理、工序公差数值更大的优点。     

Closed-form solutions for multi-objective tolerance optimization

Component tolerances have important influence on the cost and performance of products. In order to obtain suitable component tolerances, multi-objective tolerance optimization model is studied, in which the combined polynomial and exponential functions are used to model manufacturing cost. In this paper, analytical methods are proposed to solve the multi-objective optimization model. In this model, the objective function is not a monotone function, and it is possible that the assembly tolerance constraint, including worst-case method and root sum square method, is inactive. Therefore, two closed-form solutions are proposed for each component tolerance in terms of the Lambert W function. When the assembly tolerance constraint is not considered, the component tolerances are obtained and named as the initial closed-form solutions. If the initial solutions satisfy assembly tolerance constraint, it is the final value of optimal tolerances. Otherwise, constrained optimization model is established and Lagrange multiplier method is applied to obtain the new closed-form solution of component tolerances as the final value of optimal tolerances. Several simulation examples are used to demonstrate the proposed method.     

基于广义装配原理的产品生长型设计

通过研究生物生长与产品设计之间的相似性,提出了基于广义装配原理的生长型设计过程,研究了广义装配原理的三个理论构成。首先,在产品生长阶段,为实现生长过程中的自然选择,提出了以复杂度理论为控制因素的设计推理策略;其次,提出了功能公差设计理论,通过加工成本以及基于多因素的模糊质量损失成本体现广义装配成本,在确保产品功能的同时,以较低的装配与制造成本为公差的分配策略;在产品进化阶段,为保证产品良好的装配性能,采用了虚实结合设计技术。将以装配质量因素为核心的产品复杂度、精度以及制造、装配成本等众多设计因素并行集成于生长型设计过程中,实现了以全生命周期装配质量保障为核心的产品生长型设计。     

基于有限元模型的汽车薄板焊装公差分配研究

当前的汽车车身薄板覆盖件焊装公差分配方法,通过收紧装配公差以期达到车身焊装高的质量要求,而公差过小不仅提高了制造成本,还往往超出了装配件制造能力。本文提出一种基于有限元模型的公差分配方法用于薄板装配,利用该方法可在装配前确定满足产品整体质量要求的最大允许加工公差,这样既可以降低装配件制造成本,又可以保证车身焊装的质量。此方法为汽车薄板件冲压工艺设计提供了依据。     

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.     

A systematic method of adaptive joint design considering different assembly sequence in sheet metal product

In sheet metal assembly, not only the component variations and tool errors, but also the component structure (joint type) and assembly process (assembly sequence) affect the final dimensional quality. In this paper, a systematic method for adaptive joint design considering different assembly sequence is proposed to meet the in-process dimensional adjustability of KCs (key characteristics). First, the adaptive characteristic of the sheet metal joint is depicted. Then, the mathematical model in order for concurrently optimizing both joint type and different assembly sequence is presented. How to evaluate the combination of joint type and assembly sequence is carried out according to two conditions: (1) for single KC, and (2) for multiple KCs. The KC confliction is considered to ensure the important KCs. Genetic algorithm is used to resolve the optimization of joint design. An example is chosen to demonstrate our method finally, and various joint designs are acquired according to different assembly sequences by this means. The proposed methods make it possible for us to improve the dimensional quality of product in the design stage.     

Computational path planner for product assembly in complex environments

Assembly path planning is a crucial problem in assembly related design and manufacturing processes. Sampling based motion planning algorithms are used for computational assembly path planning. However, the performance of such algorithms may degrade much in environments with complex product structure, narrow passages or other challenging scenarios. A computational path planner for automatic assembly path planning in complex 3D environments is presented. The global planning process is divided into three phases based on the environment and specific algorithms are proposed and utilized in each phase to solve the challenging issues. A novel ray test based stochastic collision detection method is proposed to evaluate the intersection between two polyhedral objects. This method avoids fake collisions in conventional methods and degrades the geometric constraint when a part has to be removed with surface contact with other parts. A refined history based rapidly-exploring random tree (RRT) algorithm which bias the growth of the tree based on its planning history is proposed and employed in the planning phase where the path is simple but the space is highly constrained. A novel adaptive RRT algorithm is developed for the path planning problem with challenging scenarios and uncertain environment. With extending values assigned on each tree node and extending schemes applied, the tree can adapts its growth to explore complex environments more efficiently. Experiments on the key algorithms are carried out and comparisons are made between the conventional path planning algorithms and the presented ones. The comparing results show that based on the proposed algorithms, the path planner can compute assembly path in challenging complex environments more efficiently and with higher success. This research provides the references to the study of computational assembly path planning under complex environments.     

Concurrent tolerance design for manufacture and assembly with a game theoretic approach

This paper proposes a game theoretic approach for concurrent tolerance design considering the practical manufacturing process and assembly process, to achieve lower manufacturing cost and good product assemblability. The optimization objectives and constraints for concurrent tolerance design for manufacture and assembly are discussed, and the key technologies for concurrent tolerance design with game theory are investigated, including the strategy set division, payoff calculation, and Nash equilibrium evolution. An optimization algorithm is proposed to achieve concurrent tolerance design with a game theoretic approach, and the genetic algorithm is used to conclude the Nash equilibrium of the game for manufacture and assembly. Finally, a case study is given to verify the proposed approach.     

Generation of assembly models from kinematic constraints

In this paper, we propose a new joint-based assembly modeling method. In joint-based assembly modeling, the assembly constraints are specified on the components, but not on the geometric elements of the components. The proposed method generates assembly models from kinematic joint constraints by applying three procedures (1) to extract all feasible JMFs (Joint Mating Feature) for each mating component using information on joint constraints, (2) to derive mating alternatives for each pair of mating components after reducing the number of JMFs using the pruning criteria, and (3) to generate an assembly model by choosing the intended one from the mating alternatives for each pair of mating components and solving the JMF constraints. Since the joint constraints are expressed in terms of the relations between components rather than relations between geometric elements, the proposed method is more intuitive and natural for assembly modeling and supports modeling activities effectively by minimizing user interactions. By using joint mating constraints for assembly modeling, moreover, the kinematic behaviors of assemblies determined in the conceptual design stage can be directly applied and consistently maintained up to the detailed design stage. In the proposed method, it is also not necessary to re-input the mating constraints even when the component topology is changed.