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The purpose of this paper is to establish a tolerance optimization method based on manufacturing difficulty computation using the genetic algorithm (GA) method. This proposal is among the authors’ perspectives of accomplished previous research work to cooperative optimal tolerance allocation approach for concurrent engineering area.

This study introduces the proposed GA modeling. The objective function of the proposed GA is to minimize total cost constrained by the equation of functional requirements tolerances considering difficulty coefficients. The manufacturing difficulty computation is based on tools for the study and analysis of reliability of the design or the process, as the failure mode, effects and criticality analysis (FMECA) and Ishikawa diagram.

The proposed approach, based on difficulty coefficient computation and GA optimization method [genetic algorithm optimization using difficulty coefficient computation (GADCC)], has been applied to mechanical assembly taken from the literature and compared to previous methods regarding tolerance values and computed total cost. The total cost is the summation of manufacturing cost and quality loss. The proposed approach is economic and efficient that leads to facilitate the manufacturing of difficult dimensions by increasing their tolerances and reducing the rate of defect parts of the assembly.

The originality of this new optimal tolerance allocation method is to make a marriage between GA and manufacturing difficulty. The computation of part dimensions difficulty is based on incorporating FMECA tool and Ishikawa diagram This comparative study highlights the benefits of the proposed GADCC optimization method. The results lead to obtain optimal tolerances that minimize the total cost and respect the functional, quality and manufacturing requirements.

This paper aims to illustrate the tolerance optimization method based on the assembly accuracy constrain, precession constrain and the cost of production of the assembly product.

A tolerance optimization method is an excellent way to perform product assembly performance. The tolerance optimization method is adapted to the process analysis of the hatch and skin of an aircraft. In this paper, the tolerance optimization techniques are applied to the tolerance allocation for step difference analysis (example: step difference between aircraft cabin door and fuselage outer skin). First, a mathematical model is described to understand the relationship between manufacturing cost and tolerance cost. Second, the penalty function method is applied to form a new equation for tolerance optimization. Finally, MATLAB software is used to calculate 170 loops iteration to understand the efficiency of the new equation for tolerance optimization.

The tolerance optimization method is based on the assembly accuracy constrain, machinery constrain and the cost of production of the assembly product. The main finding of this paper is the lowest assembly and lowest production costs that met the product tolerance specification.

This paper illustrated an efficient method of tolerance allocation for products assembly. After 170 loops iterations, it founds that the results very close to the original required tolerance. But it can easily say that the different number of loops iterations may have a different result. But optimization result must be approximate to the original tolerance requirements.

It is evident from Table 4 that the tolerance of the closed loop is 1.3999 after the tolerance distribution is completed, which is less than and very close to the original tolerance of 1.40; the machining precision constraint of the outer skin of the cabin door and the fuselage is satisfied, and the assembly precision constraint of the closed loop is satisfied.

The research may support further research studies to minimize cost tolerance allocation using tolerance cost optimization techniques, which must meet the given constrain accuracy for assembly products.

The purpose of this paper is to present a state‐of‐the‐art review of dimensional tolerance synthesis and to demonstrate the evolution of tolerance synthesis from product to process‐oriented strategy, as well as to compare the same for single stage and multistage manufacturing systems (MMS). The main focus is in delineating the different approaches, methods and techniques used with critical appraisal of their uses, applicability and limitations, based on which future research directions and a generic methodology are proposed.

Starting with issues in tolerancing research, the review demonstrates the critical aspects of product and process‐oriented tolerance synthesis. The aspects considered are: construction of tolerance design functions; construction of optimization functions; and use of optimization methods. In describing the issues of process‐oriented tolerance synthesis, a comparative study of single and multistage manufacturing has been provided.

This study critically reviews: the relationship between the tolerance variables and the variations created through manufacturing operations; objective functions for tolerance synthesis; and suitable optimization methods based upon the nature of the tolerance variables and the design functions created.

This study is limited to dimensional tolerance synthesis problems and evolution of process‐oriented tolerance synthesis to counteract dimensional variation problems in assembly manufacturing.

The paper provides a comprehensive and step‐by‐step approach of review of dimensional tolerance synthesis.

This paper aims to comprehensively achieve the requirements of high assembly precision and low cost, a precision-cost model of assembly based on three-dimensional (3D) tolerance is established in this paper.

The assembly precision is related to the tolerance of parts and the deformation of matching surfaces under load. In this paper, the small displacement torsor (SDT) theory is first utilized to analyze the manufacturing tolerances of parts and the assembly deformation deviation of matching surface. In the meanwhile, the extracting method of SDT parameters is proposed and the assembly precision calculation model based on the 3D tolerance is established. Second, an integrated optimization model based on the machining cost, assembly cost (mapping the deviation domain to the SDT domain) and quality loss cost is built. Finally, the practicability of the precision-cost model is verified by optimizing the horizontal machining center.

The assembly deviation has a great influence on cost fluctuation. By setting the optimization objective to maximize the assembly precision, the optimal total cost is CNY 72.77, decreasing by 16.83 per cent from the initial value, which meets economical requirements. Meanwhile, the upper bound of each processing tolerance is close to the maximum value of 0.01 mm, indicating that the load deformation can be offset by appropriately increasing the upper bound of the tolerance, but it is necessary to strictly restrict the manufacturing tolerances of lower parts in a reasonable range.

In this paper, a 3D deviation precision-cost model of assembly is established, which can describe the assembly precision more accurately and achieve a lower cost compared with the assembly precision model based on rigid parts.

This study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.

A robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.

Compared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.

This study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.

The purpose of this paper is to propose an approach to determine the optimal parameters and tolerances in concurrent product and process design in the early design stages utilizing fuzzy goal programming. A wheelchair design is provided for illustration.

The product design is developed on the basis of both customer and functionality requirements. The critical product components are then determined. The design and analysis of experiments are performed by using simulation, and then the probability distributions are adopted to determine the values of desired responses under each combination of critical product parameters and tolerances. Regression nonlinear models are then developed and inserted as constraints in the complete optimization model. Preferences on product specifications and process settings, as well as process capability index ranges, are also set as model constraints. The combined objective functions are finally formulated to minimize the sum of positive and negative deviations from desired targets and maximize process capability. The optimization model is applied to determine the optimal wheelchair design.

The results showed that the proposed approach is effective in determining the optimal values of the design parameters and tolerances of the critical components of the wheelchair with their related process means and standard deviations that enhance desired multiple quality responses under uncertainty.

This work provides a general methodology that can be applied for concurrent optimization of product design and process design in a wide range of business applications. Moreover, the methodology is beneficial when uncertainty exists in quality responses and the parameters and tolerances of product design and its critical processes.

The fuzziness is rarely considered in research and development stage. This research considers membership functions for parameters and tolerances of a product and its related processes rather than crisp values. Moreover, presented optimization model considers multiple objective functions, sum of deviations and process capability. Finally, the indirect quality responses are calculated from the best-fit probability distributions rather than assuming a normal distribution.

The purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties.

In the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions.

The proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results.

The proposed method is limited to the dimensional tolerances of components with the normal distribution.

The proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications.

In conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.

The purpose of this paper is to provide an optimal tolerance allocation model for assemblies with consideration of the manufacturing cost, the quality loss, the design reliability index with various distributions to enhance existing models. Results of two case studies are presented.

The paper develops a model with consideration of the manufacturing cost, the Taguchi's asymmetric quadratic quality loss and the design reliability index for the optimal tolerance allocation of assemblies. The dimensional variables in normal distributions are initially used as testing and compared with the data from the prior researches. Then, the dimensional variables in lognormal distributions with the mean shift and the correlation are applied and investigated.

The results obtained based on a lognormal distribution and a normal distribution of the dimension are similar, but the tolerance with a lognormal distribution is little smaller than that with a normal distribution. The result of the reliability with the lognormal distribution obtained by the Monte‐Carlo is higher than that with a normal distribution. This paper shows that effects of the mean shift, the correlation coefficient and the replacement cost on the cost are significant and designers should pay attention to them during the tolerance optimization. The optimum tolerances of components of a compressor are recommended.

The model is limited to the dimensions of components with the normal distribution and lognormal distributions. The implication should be enhanced with more data of dimension distributions and cost of assembly components.

Two case studies are presented. One is an assembly of two pieces and another is a compressor with many components.

This model provides an optimal tolerance allocation method for assemblies with the lowest manufacturing cost, the minimum quality loss, and the required reliability index for the normal distribution and lognormal distribution.

This study aims to develop an optimal tolerance allocation strategy involves integrating the unique transfer (UT) approach and the difficulty coefficient evaluation (DCE) routine in an interactive hybrid method. This method combines the strengths of both UT and DCE, ensuring simultaneous utilization for enhanced performance. The proposed tolerancing model manifests an integrated computer-aided design (CAD) tool.

By combining UT and DCE based on failure mode, effects and criticality analysis (FMECA) tool and the Ishikawa diagram, the proposed collaborative hybrid tool ensures an efficient and optimal tolerance allocation approach. The integration of these methodologies not only addresses specific transfer challenges through UT but also conducts a thorough evaluation of difficulty coefficients via DCE routine using reliability analysis tools as FMECA tool and the Ishikawa diagram. This comprehensive framework contributes to a robust and informed decision-making process in tolerance allocation, ultimately optimizing the design and manufacturing processes.

The presented methodology is implemented with the aim of generating allocated tolerances that align with specific difficulty requirements, facilitating the creation of a mechanical assembly characterized by high quality and low cost. To substantiate and validate the conceptual framework and methods, an integrated tool has been developed, featuring a graphical user interface (GUI) designed in MATLAB. This interface serves as a platform to showcase various interactive and integrated tolerance allocation approaches that adhere to both functional and manufacturing prerequisites. The proposed integrated tool, designed with a GUI in MATLAB, offers the capability to execute various examples that effectively demonstrate the benefits of the developed tolerance transfer and allocation methodology.

The originality of the proposed approach is the twining between the UT and DCE simultaneous in an integrated and concurrent tolerance transfer and allocation model. Therefore, the proposed approach is named an integrated CAD/tolerance model based on the manufacturing difficulty tool. The obtained results underscore the tangible advantages stemming from the integration of this innovative tolerance transfer and allocation approach. These benefits include a notable reduction in total cost and a concurrent enhancement in product quality.

Dimensional quality of sheet metal assemblies is an important factor for the final product. However, the part tolerance is not easily controlled because of the spring back deformation during the stamping process. Selective assembly is a means to decrease assembly tolerance of the assembly from low-precision components. Therefore, the purpose of this paper is to propose a fully efficient method of selective assembly optimization based on an improved genetic algorithm for optimization toolbox (IGAOT) in MATLAB.

The method of influence coefficient is first applied to calculate the assembly variation of sheet metal components since the traditional rigid assembly variation model cannot be used due to welding deformation. Afterwards, the IGAOT is proposed to generate optimal selective groups, which consists of advantages of genetic algorithm for optimization toolbox (GAOT) and simulated annealing.

The cases of two simple planes and the tail lamp bracket assembly are used to illustrate the flowchart of optimizing combinations of selective groups. These cases prove that the proposed IGAOT has better precision than that of GAOT with the same parameters for selective assembly.

The research objective of this paper is to evaluate the changes from rigid bodies to sheet metal parts which are very complex for selective assembly. The method of IGAOT was proposed to the selected groups which has better precision than that of current optimization algorithms.