Genetic algorithm for minimizing assembly variation in selective assembly

Selective assembly is a method of obtaining high-precision assemblies from relatively low-precision components. In selective assembly, the mating parts are manufactured with wide tolerances. The mating part population is partitioned to form selective groups, and corresponding selective groups are then assembled interchangeably. If the mating parts are manufactured in different processes and in different machines, their standard deviations will be different. It is impossible that the number of parts in the selective group will be the same. A large number of surplus parts are expected according to the difference in the standard deviations of the mating parts. A method is proposed to find the selective groups to minimize the assembly variation and surplus parts when the parts are assembled linearly. A genetic algorithm is used to find the best combination of the selective groups to minimize the assembly variation. Selective assembly is successfully applied using a genetic algorithm to achieve high-precision assemblies without sacrificing the benefit of wider tolerance in manufacturing.     

Developing a selective assembly technique for sheet metal assemblies

Applying the concept of Digital Twin in production processes supports the manufacturing of products of optimal geometry quality. This concept can be further supported by a strategy of finding the optimal combination of individual parts to maximise the geometrical quality of the final product, known as selective assembly technique. However, application of this technique has been limited to assemblies where the final dimensions are just function of the mating parts' dimensions and this is not applicable in sheet metal assemblies. This paper develops a selective assembly technique for sheet metal assemblies and investigates the effect of batch size on the improvements. The presented method utilises a variation simulation tool (Computer-Aided Tolerancing tool) and an optimisation algorithm to find the optimal combination of the mating parts. The approach presented is applied to three industrial cases of sheet metal assemblies. The results show that using this technique leads to a considerable reduction of the final geometrical variation and mean deviation for these kinds of assemblies. Moreover, increasing the batch size reduces the amount of achievable improvement in variation but increases the amount of achievable improvement in the mean deviation.     

A New Method in Selective Assembly to Minimize Clearance Variation for a Radial Assembly Using Genetic Algorithm

Selective assembly is the method of obtaining high-precision assemblies from relatively low-precision components. A relatively smaller clearance variation is achieved than in interchangeable assembly, with the components manufactured with wider tolerance. In selective assembly, the mating parts are partitioned to form selective groups with smaller tolerance, and the corresponding groups are assembled interchangeably. The mating parts are manufactured in different machines, using different processes, and with different standard deviations. Therefore, the dimensional distributions of the mating parts are not similar. In selective assembly, the number of parts in the corresponding selective groups is not similar and will result in surplus parts. The clearance variation is also very high. In this article, a new method is proposed in selective assembly. Instead of assembling components from corresponding selective groups, the components from different combination of selective groups can be assembled to achieve minimum clearance variation. Genetic algorithm is used to find the best combination of the selective groups for minimizing the clearance variation. A case of hole and shaft (radial) assembly is analyzed in this article, and the best combination is obtained to minimize assembly clearance variation. The assembly is done in three stages to completely use all the components. The best combination for the selective groups and the resulting clearance variations are tabulated. The surplus parts are minimized to a large extent.     

Modelling and analysis of selective assembly using Taguchi's loss function

An assembly is the integrative process of joining components to make a completed product. It brings together the upstream process of design, engineering and manufacturing processes. The functional performance of an assembled product and its manufacturing cost are directly affected by the individual component tolerances. But, the selective assembly method can achieve tight assembly tolerance through the components manufactured with wider tolerances. The components are segregated by the selective groups (bins) and mated according to a purposeful strategy rather than being at random, so that small clearances are obtained at the assembly level at lower manufacturing cost. In this paper, the effect of mean shift in the manufacturing of the mating components and the selection of number of groups for selective assembly are analysed. A new model is proposed based on their effect to obtain the minimum assembly clearance within the specification range. However, according to Taguchi's concept, manufacturing a product within the specification may not be sufficient. Rather, it must be manufactured to the target dimension. The concept of Taguchi's loss function is applied into the selective assembly method to evaluate the deviation from the mean. Subsequently, a genetic algorithm is used to obtain the best combination of selective groups with minimum clearance and least loss value within the clearance specification. The effect of the ratio between the mating part quality characteristic's dimensional distributions is also analysed in this paper.     

A new grouping method to minimize surplus parts in selective assembly for complex assemblies

Selective assembly is the method of obtaining high precision assemblies from relatively low precision components. The mating parts are manufactured with wide tolerances. The mating part population is then partitioned to form selective groups. The corresponding selective groups are then assembled interchangeably. The mating parts are manufactured in different processes and in different machines. The standard deviation of the mating parts will be different. The probability of the number of parts in the selective group cannot be the same. A large number of surplus parts is expected according to the difference in standard deviations of the mating parts. In this paper, a complex assembly with three mating parts (as in a ball bearing: an inner race, ball and outer race) is considered for analysis. A new method is proposed for partitioning the lots to form selective groups. By this method, the number of surplus parts is reduced to a large extent. The variation in clearance is minimized and the total number of groups is also less when compared with traditional methods.     

Optimal process design in selective assembly when components with smaller variance are manufactured at three shifted means

Selective assembly is an effective approach for improving the quality of a product that is composed of two mating components, when the quality characteristic of the product is the clearance between the mating components. In this approach, the components are sorted into several groups according to their dimensions, and the product is assembled by randomly selecting mating components from corresponding groups. A number of previous studies focused on equal width partitioning schemes, in which the dimensional distributions of the two components are partitioned so that all groups have equal widths. When there is a large difference between the variances of the two component dimensions, equal width partitioning will result in a large number of surplus components due to differences between the numbers of components in corresponding groups. Some authors have proposed a method of manufacturing the component with smaller variance at three shifted means to cope with this difficulty. In the present paper, an optimal manufacturing mean design that minimises the number of surplus components is derived. It is shown that the use of the optimal design considerably reduces the number of surplus components compared with using another previously proposed manufacturing mean design and the no-shift design.     

A new algorithm for minimizing surplus parts in selective assembly by using genetic algorithm

Precision assemblies are produced from low precision subcomponents by partitioning and assembling them randomly from their corresponding groups. Surplus part is one of the important issues, which reduces the implementation of selective assembly in real situations. A new algorithm is introduced in this present paper to reduce surplus parts almost to zero and it is achieved in two stages by using a genetic algorithm. For demonstrating the proposed algorithm, a gearbox shaft assembly is considered as an example problem in which the shaft and pulley are manufactured in wider tolerance and partitioned in three to nine bins. The surplus parts are divided into three bins equally and a best combination of groups is obtained for both cases. It is observed that nearly 995 assemblies are produced out of one thousand subcomponents with the manufacturing cost savings of 19.5% for T _max and 992 assemblies are produced with 13.5% saving in manufacturing cost for 0.9T _max.     

基于网络的实时虚拟装配系统的研究

基于网络的虚拟装配为虚拟制造领域提出了一个崭新的思路和方法.提出了虚拟装配过程中约束的实时控制与虚拟装配仿真磁心定位的概念,从产品的装配分析角度出发,实现了网络环境下虚拟装配系统的智能化动态仿真、装配信息实时反馈以及虚拟环境下数据库的快速查询,并研究了仿真动画和交互的关键技术.     

Hybrid systems for planning and optimization of virtual assembly

Virtual assembly is the simulation of parts assembly processes by computer, analysing, evaluating and optimizing the feasibilities and procedures of assembly. It can thus avoid the potential problems and risks from designing to assembling. In this way, we can achieve the global optimization of the products and timely respond to the needs of the market. This paper presents a modelling framework for virtual assembly paths design and optimization of two objects on the basis of a class of hybrid system, which is applicable in many manufacturing environments. We propose an elementary hybrid machine containing time-driven and event-driven dynamics. We describe in detail a method of assembly paths design. The objective of optimization is evaluated in terms of time in the transition dynamics so as to make the problem more tractable. An explicit algorithm for deriving optimal assembly policies is developed. The optimal results indicate the feasibility and efficacy of the model and control algorithms.     

Integration of geometric variation and part deformation into variation propagation of 3-D assemblies

This paper introduces a novel modelling method for variation propagation calculation of 3-D assemblies taking into account geometric variation and part deformation, which are neglected in most models in tolerance analysis. Initially, numerical studies are carried out in order to illustrate the characteristics of strain distribution in components and contact forces on the mating surfaces of a 3-D assembly. According to these characteristics, a linear equivalent model using springs to represent the elastic mating surfaces with geometric variation was presented. Then, the equilibrium criterions corresponding to actual contact situations and iterative searching algorithm of the equilibrium status of contacting were developed. The proposed modelling and calculation method were finally applied to the assembly of two machined parts, on which finite-element analyses and experimental tests were conducted to validate the effectiveness and accuracy. This linear contact model also shows an important advantage on modelling and calculating efficiency, which enable the practical application to variation propagation calculation in both tolerance design and assembly process.     

Kanban number optimisation in a supermarket warehouse feeding a mixed-model assembly system

Following just-in-time principles, a growing number of manufacturers are adopting the so-called supermarket concept. Supermarkets are decentralised storage areas scattered throughout the shopfloor that serve as an intermediate store for parts required by nearby assembly lines. From these stores, a certain number of handling operators deliver parts from the supermarket to, and collect empty bins from, assembly stations. Finally, they return to the supermarket and are refilled for their next tours. The assembly stations are typically refilled from the supermarket through the constant replacement of the consumed parts pulled by the kanban system. Considering a mixed model assembly system composed of different assembly lines, feeding problems can occur as an effect of the replenishment lead time, of the production mix variation, of the commonality between the different models assembled. The aims of this paper are (i) to highlight how the supermarket/multi-mixed assembly-line system presents specific attributes that prohibit the simple application of well-known kanban dimensioning formulations and (ii) to provide an innovative procedure to optimally set all decision variables related to such a feeding system.     

A multi-decision genetic approach for workload balancing of mixed-model U-shaped assembly line systems

A mixed-model assembly line is a type of production line where a variety of product models similar in product characteristics are produced. As a consequence of introducing the just-in-time (JIT) production principle, it has been recognised that a U-shaped assembly line system offers several benefits over the traditional straight line system. This paper proposes a new evolutionary approach to deal with workload balancing problems in mixed-model U-shaped lines. The proposed method is based on the multi-decision of an amelioration structure to improve a variation of the workload. This paper considers both the traditional straight line system and the U-shaped assembly line, and is thus an unbiased examination of line efficiency. The performance criteria considered are the number of workstations (the line efficiency) and the variation of workload, simultaneously. The results of experiments enhanced the decision process during multi-model assembly line system production; thus, it is therefore suitable for the augmentation of line efficiency in workstation integration and simultaneously enhancement of the variation of the workload. A case study is examined as a validity check in collaboration with a manufacturing company.     

Fuzzy-based analysis of process capability for assembly quality assessment in mechanical assemblies

Process capability indices are useful tools for evaluating the ability of a process to produce products that meet certain specifications. The assembly quality is dependent on the distribution of variations of assembly dimensions, which is in turn dependent on mating conditions in the mechanical assembly. Since it is often difficult to measure the assembly dimensions in the production stages, they are not considered as a direct inspection objective. Rather, the inspection and evaluation of quality is carried out by specifying whether the assembly requirements satisfy the specified limits. Therefore, we can basethe process capability indices on the assembly dimensions. In most real life cases, the observations are fuzzy. In this paper, a novel method based on fuzzy concepts for process capability analysis of assembly dimensions in mechanical assemblies is presented. According to this scheme, sample observations of manufactured variables are described as fuzzy numbers. The proposed method is able to estimate the ability of the manufacturing process in satisfying the assembly quality in the mechanical assemblies with asymmetric tolerances which have non-normal distributions. In this paper, a proper criterion based on the probability of fuzzy set to interpret the computed fuzzy results is proposed, so these results are converted to the interpretable results for making a decision to evaluate the assembly quality. Furthermore, a new fuzzy-based quantity factor for expressing the percent contributions of effective manufacturing variables on the assembly quality is presented. The application of the presented method is demonstrated through an example and its results are discussed.     

基于装配特征的装配顺序生成算法

研究了基于装配特征的装配顺序生成算法,装配特征是在零件设计模型的基础上识别产生的,它给出了零件间参与装配的面集,通过对面集的判断,可以地确定两零件能否直接装配,实现了简化零件搓接图,以达到减少割集的求解空间,并用装配特征进行零件可装配性判别,使判别方便简单。     

Change management in modular assembly systems to correspond to product geometry change

Modular assembly systems are a category of changeable manufacturing systems, which can handle the rapid change in customer demands, product design change and market fluctuations. On the operational level, jigs and fixtures are fundamental elements of assembly systems. They are used to hold parts and subassemblies in place, and directly affect assembly cost, quality and time. Therefore, modular fixtures that can adapt to different geometries are becoming a very important enabler for changeable manufacturing. In this paper, two mathematical models are presented to optimise the use of a passive modular assembly fixture plan in an automated assembly system by considering different production scenarios and constraints. These models optimise the changeability plan of the modular fixture by minimising the number of dowel replacements between different part geometries assuming that the candidate dowels locations for each part have been determined using existing methods in the literature by considering different assembly requirements. The first model, LRTE, considers all possible part rotations and translations on the fixture to minimise setup time. In addition, the second model, SLRTE, enables the system to simultaneously optimise job sequence. This paper presents various examples in different sizes, and the results show that the model can effectively reduce the fixture setup time up to %50.     

A quality control method for complex product selective assembly processes

Selective assembly is an important step during the manufacturing process for a complex product to meet precision requirements. The high precision requirement of complex product often results in producing a large number of surplus components in selective assembly process current practices. In this paper, we develop a comprehensive model which permits the integration of machining process parameters design, variation analysis and fault diagnosis, process adjustment and control strategy, process capability index calculation and matchable degree calculation. The model can be applied to evaluate and improve product, process and system design at early development stages, or support the improvement of matchable degree for a complex production selective assembly process. In this model, we have introduced a navel concept of general matchable degree for a multiple components selective assembly process. The implementation procedure and functional modules of the proposed model are given in details with an industrial case presented to illustrate the implementation of the proposed method.     

Integrated modelling and algorithm of material delivery and line-side storage for aircraft moving assembly lines

This paper considers the material supply problem for aircraft moving assembly lines. Distinguished from general automobile assembly lines, multiple parallel jobs are assembled concurrently and durations of assembly jobs are quite long, thus amounts of materials are orderly stored at the line-side space at the same time. In addition, the line-side space should be reused in the time dimension. With these characteristics, decisions on line-side storage of materials were introduced on the basis of material batching and tow-trains scheduling problems. An integrated decision–making mathematical model with the objective of minimising the number of deliveries was established. A hybrid endocrine-immune algorithm (HEIA) was proposed to jointly make decisions on the delivery batch, delivery time and storage positions of each job’s materials. Numerical experiments with the real-world data and randomly generated instances validate the effectiveness and efficiency of HEIA.     

U-shaped assembly line balancing problem with genetic algorithm

This paper presents a multi-objective genetic algorithm (moGA) to solve the U-shaped assembly line balancing problem (UALBP). As a consequence of introducing the just-in-time (JIT) production principle, it has been recognized that U-shaped assembly line systems offer several benefits over the traditional straight line systems. We consider both the traditional straight line system and the U-shaped assembly line system, thus as an unbiased examination of line efficiency. The performance criteria considered are the number of workstations (the line efficiency) and the variation of workload. The results of experiments show that the proposed model produced as good or even better line efficiency of workstation integration and improved the variation of workload.     

Partitioning the production processes when assembling a bore and shaft

The problem of assembling of two mating parts is considered. Making use of the probability distributions of the bore and shaft, and the specifications on the fit between them, it is desired to define the dimensions of separate groups for the bore and for the shaft that these parts can be placed in, such that the specifications on the fit when parts in these groups are assembled will be met with certainty. This is accomplished by formulating an optimisation problem such that the number of such groups is made a minimum subject to a specified lower bound on the sum of the probabilities of a sample lying in each group, and introducing a method of generating approximate solutions. The method makes use of the ‘solver’ and ‘chart wizard’ functions that are contained in Microsoft Excel^©. Using the dimensions of the groups, an expression for the expected number of assemblies generated by each group is presented.     

Evaluation of performance measures for multi-part,single-product kanban controlled assembly systems with stochastic acquisition and production lead times

We consider the following kanban-controlled, multi-stage production assembly system. A number of raw parts are acquired from various suppliers and assembled into a single product. The raw-part acquisition lead times, the production lead time and demand arrival are all random variables. The raw-part acquisition order is made when the inventory level of the common part buffer, consisting of a number of sets of raw parts where a set of raw parts forms a single product, depletes to a reorder point. A production stage consists of the input queue, the output buffer, and the kanban board. The finished product can be backordered with a given allowable quantity. The problem is to evaluate the various system performance measures for a given set of design parameters: the raw-part batch order size, the common buffer size, the reorder point, the number of kanbans circulating in each production stage. A system is decomposed into a number of semi-autonomous Markov processes. A mathematical model is formulated and an iterative algorithm is proposed to evaluate system performance measures. Extensive numerical experiments with simulation analyses show that the computational time is very short and the model proposed is reasonably accurate. Thus, resorting to a genetic algorithm we can find an optimal set of system design parameters.