Optimization of clearance variation in selective assembly for components with multiple characteristics

Quality is an important aspect of any manufacturing process. Only high quality products can survive in the market. The consumer not only wants quality, precision and trouble-free products, but also wants them at attractive prices. When a product consists of two or more components, the quality of that product depends upon the quality of the mating parts. The mating parts may be manufactured using different machines and processes with different standard deviations. Therefore, the dimensional distributions of the mating parts are not similar. This results in clearance or interference between the mating parts. In some high precision assemblies, it may not be possible to have closer assembly clearance variation with interchangeable system. Selective assembly meets the above requisite and gives an enhanced solution. Selective assembly is a method of obtaining high precision assemblies from relatively low precision components. In this paper, a new selective assembly method is proposed to minimize the clearance variation and surplus parts for a complex assembly which consists of the components viz. piston, piston ring. In this assembly, each component will have more than one quality characteristic contributing for the assembly, for e.g., piston diameter will assemble with cylinder inner diameter; piston groove diameter will assemble with piston ring inner diameter, etc. In selective assembly each quality characteristic will fall in different groups. Non-dominated sorting genetic algorithm (NSGA) is used to find the best combination to obtain the minimum clearance variation in this assembly.     

Particle swarm optimization for minimizing assembly variation in selective assembly

Quality of a product is based on the quality of the mating parts. When the parts are assembled interchangeably, the assembly variation will be the sum of the component tolerances. If the assembly variation is to be less than the sum of the component tolerances, selective assembly is the only solution. In conventional selective assembly, the corresponding selective groups are assembled. In this paper, selective group combinations for assembling the mating parts is obtained using particle swarm optimization (PSO). The combination obtained has resulted in an appreciable reduction in assembly variation. The proposed algorithm has been demonstrated for a linear assembly, which consists of three components having equal dimensional distributions. The assembly variation obtained by interchangeable assembly is 36 μm. By implementing the proposed method, the assembly variations are reduced from 36 to 7.2 μm. However, this algorithm can be extended for assemblies with more number of components and with different dimensional distributions.     

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.     

基于蚁群算法的选择装配

选择装配是一种由低加工精度零件获得高精度装配件的方法,可归纳为一个组合优化问题,蚁群算法是解决这类问题的有效方法.综合考虑选择装配中的匹配率和匹配精度,提出以综合装配质量指标为选择装配的目标函数.为了求解选择装配的组合优化问题,在蚁群算法的框架内提出一个考虑信息素分布为节点模式的蚁群算法解构造图模型,并详细讨论蚁群算法的实现过程.通过对实例的仿真计算,考证该方法的实效性.     

A review of information flow diagrammatic models for product–service systems

Quality of an assembly of any manufactured product is mainly based on the quality of mating components. Due to random variations in sources such as materials, machines, operators, and measurements, mating components manufactured by even the same process may vary in their dimensions. When mating components are assembled linearly, the resulting assembly tolerance will be the sum of the mating components tolerances. All precision assemblies demand for a closer assembly tolerance. A significant amount of research has already been done to minimize assembly variation using selective assembly, when the dimensions of components follow normal distribution. However, in reality, the dimensions of components produced especially in smaller to medium size batches, invariably have some skewness (non-normality), which makes the methods developed and reported in the literature, often not suitable for practice. In this work, batch selective assembly methodology is proposed for components having non-normal distributions to minimize the assembly tolerance variations. The proposed method which employs a genetic algorithm for obtaining the best combination of mating components is able to achieve minimum variations in assembly tolerances and also maximum number of acceptable assemblies. The proposed algorithm is tested with a set of experimental problem datasets and is found outperforming the other existing methods found in the literature, in producing solutions with minimum assembly variation.     

一种保证分组装配零件数量均衡的新方案

分组装配是一种用较低精度的零件实现高装配精度的方法。传统的分组装配方法常用某些组内相配零件数量不均衡而导致剩余零件增加。为使分组装配中剩余零件为最少，提出一种新的分组算法。在此基础上发展了一种保证分组装配零件数量均衡的新方法。     

基于混合算法的内燃机曲柄连杆机构复合目标选配

在曲柄连杆机构的选配中,为实现在多种装配要求的条件下,对多对零部件同时进行选配,并使剩余的零部件数量最少的复合目标,以提高曲柄连杆机构各零部件的选配成功率和装配质量,建立了复合目标选配的目标函数,确定了约束条件。针对该组合优化问题的特殊性,对传统的基于遗传算法和模拟退火算法的混合算法进行了改进,提高了在初始种群产生阶段进行定向变异的方法,以提高初始种群的平均适应度;并设计了特定的编码方式、交叉运算和变异运算,建立了曲柄连杆机构的复合目标选配方法。最后对该方法进行了有效性验证。     

面向自动化装配的轴孔装配参数选择研究

在面向装配的设计中,很少考虑装配工艺参数,在一定程度上削弱了面向装配的设计思想对装配过程的指导作用.对此,提出了一种面向自动化装配设计的圆柱轴孔装配工艺参数优化算法.该算法以装配成本为边界条件,建立了解析几何求解模型,能帮助设计者选择合理的工艺参数,如配合零件的尺寸公差、自动化装配设备的定位精度和转角精度等.最后,编制了相应的程序优化装配工艺参数.     

基于Witness仿真软件的分组装配适配率预测

分组装配技术是一种对按经济加工精度设定配合尺寸公差,对完工后的配合尺寸检测、分组、同组号零件装配的方法。基于不同理论的分组方法都是在保证装配精度的前提下,以较低制造成本获得预期的适配率。在讨论等批量配合零件统计分组装配技术的基础上,提出了一种根据配合零件批的统计参数采用Witness仿真软件对分组装配适配率进行预测的方法,并据此来确定投入加工的配合零件批的数量,从而为编制生产计划提供了指导。     

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.     

Active variation compensation in vehicle body conceptual assembly

In this paper, an intelligent heuristic optimization algorithm in active variation compensation is proposed to improve the dimension accuracy in the assembly of a vehicle body by finding the optimal configuration of joint types and the corresponding assembly sequence to compensate variation accumulation in the conceptual assembly process. The authors develop and apply the algorithm to predict variation accumulation and then develop compensating assembly schemes to accomplish optimal joint configuration and assembly sequence compensating for the unnecessary or surplus variation. The essence of the active variation compensation algorithm means measuring and correcting assembling variations during the assembly conceptual process. The paper employs the design of experiment (DOE) approach to verify the heuristic optimization method in the simple application case.     

Optimal design of weld pattern in sheet metal assembly based on a genetic algorithm

In the sheet metal assembly process, welding operations join two or more sheet metal parts together. Since sheet metals are subject to dimensional variation resulting from manufacturing randomness, a gap may be generated at each weld pair prior to welding. These gaps are forced to close during the welding operation and accordingly undesirable structural deformation results. Optimizing the welding pattern (the number and locations of weld pairs) in the assembly process was proven to improve significantly the quality of the final assembly. This paper presents a genetic-algorithm-based optimization method to search automatically for the optimal weld pattern so that assembly deformation is minimized. The application result for a real industrial part demonstrated that the proposed algorithm effectively achieved the objective.     

New approach for robust multi-objective optimization of turning parameters using probabilistic genetic algorithm

Limited by techniques, the process of remanufacturing exists masses of uncertainties which have a great impact on the remanufactured parts quality, how to achieve a higher quality of mechanical products by using limited remanufactured parts precision, has become one of the key issues of remanufacturing industry. Firstly, with a target to reduce uncertainties and improve the quality of automatic products, a method of tolerance grading allocation for remanufactured parts is proposed based on the uncertainty analysis of the remanufacturing assembly. The dimensional tolerances of the mechanical parts are divided into positive and negative two groups. We use selective assembly method to reduce assembling deviation. Then, the method is proven by mathematical formulas that the remanufactured parts variance can be expanded to two times, and the tolerances can be liberalized 40 % through tolerance grading allocation method. It is also the theoretical basis for improving the reuse radio and quantitatively describing the tolerance liberalization in this paper. Finally, feasibility research on this method is studied from the angle of cost–benefit. Furthermore, a tolerance grading allocation example of remanufactured engine piston assembly in a power corporation shows the validity and practicality of the proposed method.     

Optimal design of weld pattern in sheet metal assembly based on a genetic algorithm

In the sheet metal assembly process, welding operations join two or more sheet metal parts together. Since sheet metals are subject to dimensional variation resulting from manufacturing randomness, a gap may be generated at each weld pair prior to welding. These gaps are forced to close during the welding operation and accordingly undesirable structural deformation results. Optimizing the welding pattern (the number and locations of weld pairs) in the assembly process was proven to improve significantly the quality of the final assembly. This paper presents a genetic-algorithm-based optimization method to search automatically for the optimal weld pattern so that assembly deformation is minimized. The application result for a real industrial part demonstrated that the proposed algorithm effectively achieved the objective.     

粒子群算法在装配顺序规划中的应用

装配顺序规划是计算机辅助工艺设计的一个重要环节,影响着轿车车身的装配质量和效率.针对当前装配顺序规划易产生组合爆炸等问题,提出了基于粒子群算法的装配顺序规划算法.装配偏差是影响装配质量的重要因素,因此应用装配体的装配偏差评价装配顺序.在装配顺序规划过程中,首先将装配顺序编码为粒子,根据所建立的判断规则进行识别粒子的可行性,并通过装配偏差评估可行粒子的适应度值,然后根据粒子群算法过程规划装配顺序,最后采用前翼子板案例阐述装配顺序的生成和优化过程.     

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.     

Three-dimensional precision analysis with rigid and compliant motions for sheet metal assembly

This paper quantifies the detailed assembly motions by taking into account the mating gaps and gravities of fixtures and sheet metals. Finite element (FE) models are firstly generated for fixtures and parts. Their nodes are ordered according to an appointed assembly sequence where the last assembled part is behind the first one by the assembly platform or mating surface. Three noncollinear feature points are selected from each last assembled part near the mating surface. Their translational displacements (gaps) represent the part rigid motion near that surface omitting the local joint deformation. Based on the given feature point gaps, kinematic formulations are proposed to compute the rigid motions for any FE nodes behind the mating surface in assembly sequence. Compliant motions are then reached by the modified FE analysis where variable mesh method is applied to change the FE nodal coordinates using the gap-induced rigid motions and deformations. Code integrations of sequence and parallel assemblies are finally proposed and validated via simulations and experiments. Results suggest the following: (1) the proposed method is effective and accurate for engineer application; (2) the integration approach requires to be further studied for the precision analysis of more complex assemblies and implies a feasible way for adding local deformations of joints to the deterministic dimensional precision analysis.     

基于多装配尺寸链的计算机辅助选择装配

现有计算机辅助选择装配理论中只有针对单一装配尺寸链的选配模型,提出基于多装配尺寸链的选配模型,将计算机辅助选择装配转化为多目标优化问题,新模型为各装配尺寸链提供了权值和修正值.采用遗传模拟退火优化算法求解,最后通过事例分析该模型的效率与可行性.     

基于质量特征产品装配顺序规划的逆向推理算法探究

在Petri网柔性装配系统装配顺序规划中引入装配质量要素,并以装配零件的装配自由度,装配作业后稳定性,装配零件配合精度对装配质量的影响作为基本因子,提出装配质量置信度概念,解决柔性装配系统装配规划中装配质量及其定量化问题。根据装配形成的产品在Petri网装配状态图中表示为一个最终库所的特点,应用改进B树模型,提出仅以变迁信息的产品装配顺序规划Petri网逆向推理算法,简化装配顺序规划推理过程,对于多个变迁均可生成最终成品的情况,亦给出装配顺序规划的解决方案,并以摩托车发动机的装配为例,证明该算法是可行的。     

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.