Tolerance allocation for compliant beam structure assemblies

This paper presents a tolerance allocation methodology for compliant beam structures in automotive and aerospace assembly processes. The compliant beam structure model of the product does not require detailed knowledge of product geometry and thus can be applied during the early design phase to develop cost-effective product specifications. The proposed method minimizes manufacturing costs associated with tolerances of product functional requirements (key product characteristics, KPCs) under the constraint(s) of satisfying process requirements (key control characteristics, KCCs). Misalignment and fabrication error of compliant parts, two critical causes of product dimensional variation, are discussed and considered in the model. The proposed methodology is developed for stochastic and deterministic interpretations of optimally allocated manufacturing tolerances. An optimization procedure for the proposed tolerance allocation method is developed using projection theory to considerably simplify the solution. The non-linear constraints, that ellipsoid defined by τ(stochastic case) or rectangle defined by T x (deterministic case) lie within the KCC region, are transformed into a set of constraints that are linear in σ(or T x )-coordinates. Experimental results verify the proposed tolerance allocation method.     

Evolutionary multi-objective concurrent maximisation of process tolerances

Concurrent tolerancing which simultaneously optimises process tolerance based on constraints of both dimensional and geometrical tolerances (DGTs), and process accuracy with multi-objective functions is tedious to solve by a conventional optimisation technique like a linear programming approach. Concurrent tolerancing becomes an optimisation problem to determine optimum allotment of the process tolerances under the design function constraints. Optimum solution for this advanced tolerance design problem is difficult to obtain using traditional optimisation techniques. The proposed algorithms (elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE)) significantly outperform the previous algorithms for obtaining the optimum solution. The average fitness factor method and the normalised weighting objective function method are used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of the NSGA-II and MODE algorithms. Comparison of the results establishes that the proposed algorithms are superior to the algorithms in the literature.     

Optimisation of assembly sequences for compliant body assemblies

Multi-sequence modelling is proposed to optimise assembly sequences for compliant body assemblies such as automotive and aircraft bodies. Multi-sequence modelling is composed of assembly modelling, assembly sequences, tolerance analysis, and assembly operations. Assembly modelling describes the geometric modelling through the liaison graph, which is based on assembly sequence optimisation. Assembly sequences provide information for assembly sequence optimisation. Three-dimensional tolerance analysis is employed to evaluate assembly operations, which is different from previous conceptual tolerance analysis. A genetic algorithm is presented to optimise assembly operations among components. Results show that different sequences lead to a different tolerance of key product characteristics because assembly operations among components are not identical. This paper provides the flowchart of optimising assembly sequences according to the tolerance of key product characteristics.     

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.     

Concurrent optimal allocation of design and process tolerances for mechanical assemblies with interrelated dimension chains

Concurrent tolerance allocation has been the focus of extensive research, yet very few researchers have considered how to concurrently allocate design and process tolerances for mechanical assemblies with interrelated dimension chains. To address this question, this paper presents a new tolerance allocation method that applies the concept of concurrent engineering. The proposed method allocates the required functional assembly tolerances to the design and process tolerances by formulating the tolerance allocation problem into a comprehensive model and solving the model using a non-linear programming software package. A multivariate quality loss function of interrelated critical dimensions is first derived, each component design tolerance is formulated as the function of its related process tolerances according to the given process planning, both manufacturing cost and quality loss are further expressed as functions of process tolerances. And then, the objective function of the model, which is to minimize the sum of manufacturing cost and expected quality loss, is established and the constraints are formulated based on the assembly requirements and process constraints. The purpose of the model is to balance manufacturing cost and quality loss so that concurrent optimal allocation of design and process tolerances is realized and quality improvement and product cost reduction is achieved. The proposed method is tested on a practical example.     

Maximising manufacturing system efficiency for multi-characteristic linear assembly by using particle swarm optimisation in batch selective assembly

Quality of an assembly is mainly based on the quality of mating parts. Due to random variation in sources such as materials, machines, operators and measurements, even those mating parts manufactured by the same process vary in their dimensions. When mating parts are assembled linearly, the resulting variation will be the sum of the mating part tolerances. Many assemblies are not able to meet the assembly specification in the available assembly methods. This will decrease the manufacturing system efficiency. Batch selective assembly is helpful to keep the assembly requirement and also to increase the manufacturing system efficiency. In traditional selective assembly, the mating part population is partitioned to form selective groups, and the parts of corresponding selective groups are assembled interchangeably. After the invention of advanced dimension measuring devices and the computer, today batch selective assembly plays a vital role in the manufacturing system. In batch selective assembly, all dimensions of a batch of mating parts are measured and stored in a computer. Instead of forming selective groups, each and every part is assigned to its best matching part. In this work, a particle swarm optimisation based algorithm is proposed by applying the batch selective assembly methodology to a multi-characteristic assembly environment, to maximise the assembly efficiency and thereby maximising the manufacturing system efficiency. The proposed algorithm is tested with a set of experimental problem data sets and is found to outperform the traditional selective assembly and sequential assembly methods, in producing solutions with higher manufacturing system efficiency.     

Robust fixture layout design for multi-station sheet metal assembly processes using a genetic algorithm

The optimal fixture layout is crucial to product quality assurance in the multi-station sheet metal assembly processes. Poor fixture layout may lead to product variation during the assembly processes. In this paper, a genetic algorithm (GA)-based optimisation approach has been presented for the robust fixture layout design in the multi-station assembly processes. The robust fixture layout is developed to minimise the sensitivity of product variation to fixture errors by selecting the appropriate coordinate locations of pins and slot orientations. In this paper, a modified state space model for variation propagation in the multi-station sheet metal assembly is developed for the first time, which is the mathematical foundation of optimal algorithm. An e-optimal is applied as the robust design criteria. Based on the state space model and design criteria, a genetic algorithm is used to find the optimal fixture layout design. The proposed method can greatly reduce the sensitivity level of product variation. A four-station assembly process of an inner-panel complete for a station wagon (estate car) is used to illustrate this method.     

Robust design of assembly and machining tolerance allocations

Tolerancing is one of the most important tasks in product and manufacturing process design. The allocation of design tolerances between the components of a mechanical assembly and manufacturing tolerances in the intermediate machining steps of component fabrication can significantly affect a product's quality and its robustness. This paper presents a methodology to maximize a product's robustness by appropriately allocating assembly and machining tolerances. The robust tolerance design problem is formulated as a mixed nonlinear optimization model. A simulated annealing algorithm is employed to solve the model and an example is presented to illustrate the methodology.     

Robust design of assembly and machining tolerance allocations

Tolerancing is one of the most important tasks in product and manufacturing process design. The allocation of design tolerances between the components of a mechanical assembly and manufacturing tolerances in the intermediate machining steps of component fabrication can significantly affect a product's quality and its robustness. This paper presents a methodology to maximize a product's robustness by appropriately allocating assembly and machining tolerances. The robust tolerance design problem is formulated as a mixed nonlinear optimization model. A simulated annealing algorithm is employed to solve the model and an example is presented to illustrate the methodology     

Concurrent optimization of assembly tolerances for quality with position control using scatter search approach

Tolerance allocation to individual parts in any assembly should be a vital design function with which both the design and manufacturing engineers are concerned. Generally design engineers prefer to have tighter tolerances to ensure the quality of their design, whereas manufacturing engineers prefer loose tolerances for ease of production and the need to be economical. This paper introduces a concurrent tolerance approach, which determines optimal product tolerances and minimizes combined manufacturing and quality related costs in the early stages of design. A non-linear multivariable optimization model is formulated here for assembly. A combinatorial optimization problem by treating cost minimization as the objective function and stack-up conditions as the constraints are solved using scatter search algorithm. In order to further explore the influence of geometric tolerances in quality as well as in the manufacturing cost, position control is included in the model. The results show how position control enhances quality and reduces cost.     

Hybrid algorithm based on improved extended shifting bottleneck procedure and GA for assembly job shop scheduling problem

With the makespan as the optimisation goal, we propose a hybrid solving method that combines improved extended shifting bottleneck procedure (i-ESB) and genetic algorithm (GA) for the assembly job shop scheduling problem (AJSSP). Hybrid genetic algorithm (HGA) uses a GA based on operation constraint chain coding to achieve global search and a local search based on an i-ESB. In the design of i-ESB, an extended disjunctive graph model (EDG) corresponding to AJSSP is presented. The calculation method of the operation head and tail length based on EDG is studied, as well as the searching method of key operations. The Schrage algorithm with disturbance is used to solve the single-machine scheduling subproblem. The selection criterion for bottleneck machines is increased. A greedy bottleneck machine re-optimisation process is designed. The effectiveness and superiority of the proposed algorithm are verified by testing and analysing the relevant examples in the literature.     

Simultaneous balancing and sequencing of mixed-model parallel two-sided assembly lines

Growing interests from customers in customised products and increasing competitions among peers necessitate companies to configure their manufacturing systems more effectively than ever before. We propose a new assembly line system configuration for companies that need intelligent solutions to satisfy customised demands on time with existing resources. A mixed-model parallel two-sided assembly line system is introduced based on the parallel two-sided assembly line system previously proposed in the literature. The mixed-model parallel two-sided assembly line balancing problem is illustrated with examples from the perspective of simultaneous balancing and sequencing. An agent-based ant colony optimisation algorithm is proposed to solve the problem. This algorithm is the first attempt in the literature to solve an assembly line balancing problem with an agent-based ant colony optimisation approach. The algorithm is illustrated with an example and its operational procedures and principles are explained and discussed.     

Tolerance analysis and synthesis for cam mechanisms

Tolerance is one of the most important parameters in product and process design, so tolerancing plays a key role in design and manufacturing. Tolerance synthesis is in a period of extensive study due both to increased demands for quality products and to increasing automation of machining and assembly. Optimum tolerance design and synthesis ensures good quality product at low cost. This paper presents an analytical methodology for tolerance analysis and synthesis for a disk cam-translating follower system. Both dimensional ( size) and geometric tolerances ( position and profile ) on the components are considered. Tolerance analysis is performed on individual tolerances as well as on total tolerance accumulation. With the lowest manufacturing cost as its objective function a nonlinear optimization model is formulated for tolerance synthesis and solved by a sequential quadratic programming ( SQP) algorithm. An example is provided to illustrate the optimization model and solution procedure.     

Concurrent optimal allocation of geometric and process tolerances based on the present worth of quality loss using evolutionary optimisation techniques

Concurrent tolerancing becomes an optimisation problem to find out the optimum allocation of the process tolerances in the given design function constraints. In traditional optimisation methods, finding out the optimum solution for this advanced tolerance design problem is complex. The proposed algorithms (elitist non-dominated sorting genetic algorithm) and differential evolution extensively do better than the previous algorithms for attaining the optimum result. The aim of this paper is to suggest a model for optimal tolerance allocation by considering both tolerance cost and the present worth of quality loss such that the total manufacturing cost/loss is minimised. The suggested model takes into account the time value of money for quality loss and product degradation over time and consists of two new parameters: the planning horizon and the product user’s discount rate. From the outcome 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 gives up a decrease in both tolerance cost and quality loss. Finally, a practical example is brought into reveal the effectiveness of the suggested method.     

Applying an electromagnetism-like mechanism algorithm on parameter optimisation of a multi-pass milling process

Multi-pass milling is a common manufacturing process in practical production. Parameter optimisation is of great significance since the parameters largely affect the production time, quality, cost and some other process performance measures. However, the parameter optimisation of the multi-pass milling process is a nonlinear constrained optimisation problem. It is very difficult to obtain satisfactory results by the traditional optimisation methods. Therefore, in this paper, a new optimisation technique based on the electromagnetism-like mechanism (EM) algorithm is proposed to solve the parameter optimisation problem in a multi-pass milling process. The EM algorithm is a population based meta-heuristic algorithm for unconstrained optimisation problems. As the parameter optimisation problem is a constrained problem, the proposed approach handles the constraints of the problem by improving the charge calculation formula combined with the feasibility and dominance rules at the same time. This paper also puts forward flexible cutting strategies to simultaneously optimise the depth of cut for each pass, cutting speed and feed to improve solutions. A case study is presented to verify the effectiveness of the proposed approach. The results show that the proposed method is better than other algorithms and achieves significant improvement.     

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.     

Balancing Multi-Manned Assembly Lines With Walking Workers: Problem Definition,Mathematical Formulation,and an Electromagnetic Field Optimisation Algorithm

Assembly lines are widely used in industrial environments that produce standardised products in high volumes. Multi-manned assembly line is a special version of them that allows simultaneous operation of more than one worker at the same workstation. These lines are widely used in large-sized product manufacturing since they have many advantages over the simple one. This article has dealt with multi-manned assembly line balancing problem with walking workers for minimising the number of workers and workstations as the first and second objectives, respectively. A linear mixed-integer programming formulation of the problem has been firstly addressed after the problem definition is given. Besides that, a metaheuristic based on electromagnetic field optimisation algorithm has been improved. In addition to the classical electromagnetic field optimisation algorithm, a regeneration strategy has been applied to enhance diversification. A particle swarm optimisation algorithm from assembly line balancing literature has been modified to compare with the proposed algorithm. A group of test instances from many precedence diagrams were generated for evaluating the performances of all solution methods. Deviations from lower bound values of the number of workers/workstations and the number of optimal solutions obtained by these methods are concerned as performance criteria. The results obtained by the proposed programming formulations have been also compared with the solutions obtained by the traditional mathematical model of the multi-manned assembly line. Through the experimental results, the performance of the metaheuristic has been found very satisfactory according to the number of obtained optimal solutions and deviations from lower bound values.     

Optimization of machining datum selection and machining tolerance allocation with genetic algorithms

In machining process planning, selection of machining datum and allocation of machining tolerances are crucial as they directly affect the part quality and machining efficiency. This study explores the feasibility to build a mathematical model for computer aided process planning (CAPP) to find the optimal machining datum set and machining tolerances simultaneously for rotational parts. Tolerance chart and an efficient dimension chain tracing method are utilized to establish the relationship between machining datums and tolerances. A mixed-discrete nonlinear optimization model is formulated with the manufacturing cost as the objective function and blueprint tolerances and machine tool capabilities as constraints. A directed random search method, genetic algorithm (GA), is used to find optimum solutions. The computational results indicate that the proposed methodology is capable and robust in finding the optimal machining datum set and tolerances. The proposed model and solution procedure can be used as a building block for computer automated process planning.     

Quality design of tolerance allocation for sheet metal assembly with resistance spot weld

Tolerance directly influences the functionality of the products and the related manufacturing costs, and tolerance allocation is of great importance for improving the assembly quality. However, the information required to allocate tolerances for complex 3D assemblies is generally not available at the initial design stage. In this paper, a new quality design methodology is developed, which makes use of both original design data obtained by the response surface methodology and the extra interpolation data obtained by the Kriging method. The finite element modelling is presented for the sheet metal assembly process as no explicit relationship of the variations for key characteristic points are available. The robust tolerances can be allocated based on the quality design model. A case study with the typical assembly process of the rear compartment pan and the wheelhouse is carried out in the paper, the tolerance allocation results show that the developed quality design methodology is capable of determining the robust manufacturing tolerance before assembly, which satisfies the product requirements. This method enables a robust tolerancing scheme to be used in the sheet metal assembly process.     

Ant colony optimisation with parameterised search space for the job shop scheduling problem

The job-shop scheduling problem (JSSP) is known to be NP-hard. Due to its complexity, many metaheuristic algorithm approaches have arisen. Ant colony metaheuristic algorithm, lately proposed, has successful application to various combinatorial optimisation problems. In this study, an ant colony optimisation algorithm with parameterised search space is developed for JSSP with an objective of minimising makespan. The problem is modelled as a disjunctive graph where arcs connect only pairs of operations related rather than all operations are connected in pairs to mitigate the increase of the spatial complexity. The proposed algorithm is compared with a multiple colony ant algorithm using 20 benchmark problems. The results show that the proposed algorithm is very accurate by generating 12 optimal solutions out of 20 benchmark problems, and mean relative errors of the proposed and the multiple colony ant algorithms to the optimal solutions are 0.93% and 1.24%, respectively.