An effective strategy for improving the precision and computational efficiency of statistical tolerance optimization

Zeng, Wenhui; Rao, Yunqing; Wang, Peng

doi:10.1007/s00170-017-0256-7

Cited by 14 publications

(6 citation statements)

References 30 publications

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“…This is consistent with the simple tolerance analysis procedures described in handbooks [26,27] and commonly used in practice. The same approach is used in allocation methods taking into account the uncertainty on cost-tolerance functions [28,29] as well as in methods based on the optimization of objective functions including cost [30] and quality loss [31] by genetic algorithms.…”

Section: Literature Reviewmentioning

confidence: 99%

Allocation of geometric tolerances in one-dimensional stackup problems

Armillotta

2022

Int J Adv Manuf Technol

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Many tolerancing problems on mechanical assemblies involve a functional requirement depending on a chain of parallel dimensions on individual parts. In these one-dimensional cases, simple methods are available for the analysis and the allocation of dimensional tolerances. However, they are difficult to extend to geometric tolerances, which must be translated into equivalent dimensional tolerances; this allows the analysis but makes the allocation generally impossible without Monte Carlo simulation and complex search strategies. To overcome this difficulty, the paper proposes a way of dealing directly with geometric tolerances in the allocation problem. This consists in expressing the functional requirement as a linear model of geometric tolerances rather than equivalent dimensional tolerances; the coefficients of the model (sensitivities) are calculated considering both the dimension chain and the standard definition of the geometric tolerances. The approach can be combined with any constrained optimization method based on sensitivities. The optimal scaling method, previously proposed for dimensional tolerances, is extended to geometric tolerances and used in two examples to demonstrate the simplicity of the overall workflow and the quality of the optimal solution.

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Section: Literature Reviewmentioning

confidence: 99%

Allocation of geometric tolerances in one-dimensional stackup problems

Armillotta

2022

Int J Adv Manuf Technol

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“…However, an optimal statistical allocation by Lagrange multipliers can be found only with an iterative numerical procedure [75,76]. Consequently, most applications of the functions use advanced allocation methods, such as genetic algorithms [62,[77][78][79][80][81][82][83][84][85], the bat algorithm [86], cuckoo search and particle swarm optimization [85], constraint networks [34,35], scatter search [87,88], pattern search [89], simulated annealing [90], a method based on Lambert W function [91,92], and fuzzy methods [93]. The function has also been used to solve problems with special formulations, such as interrelated tolerance chains [94,95], pre-selection of manufacturing processes [96], minimization of nonconforming fraction [97,98], allocation of geometric tolerances [99][100][101], minimization of cost and quality loss [102][103][104], robust design [105], simultaneous allocation of process averages and tolerances [106][107][108], multistation systems [109], and allocation combined with scheduling [110].…”

Section: Exponentialmentioning

confidence: 99%

“…1.5-2.5 (10-12 geometric tol.) [88] 25-400 small, 4-9 large 3-17 small, 300-800 large [4] 4.5-12 0.008-0.012 [78] 8-75 1.5-85 [31] 30-100 2.5-20 [89] 25-400 3-17 [85] -3-40 [94] 5-70 15-45 [104] 80-300 15-85 [92] 30-300 15-200 [106] 2-2500 30-300 [96] 200-300 40-100 [115] 0.2-15 50-4000 [86] 30-70 80-220 [84] 30-150 700-1400 [34] 2.5-4.2 1100-1400…”

Section: Tab 2: Values Of the Parameters Of The Exponential Function ...mentioning

confidence: 99%

Selection of parameters in cost-tolerance functions: review and approach

Armillotta

2020

Int J Adv Manuf Technol

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The paper deals with the cost-tolerance functions used in minimum-cost tolerance allocation on mechanical assemblies. The consistency of the cost-tolerance functions associated with different dimensions of a tolerance chain is a necessary condition for a correct optimization of tolerance values. This requires a careful selection of function parameters, in order to take into account all the variables influencing the cost, and thus to compare the costs of the different dimensions in a common scale. The cost-tolerance functions proposed in the literature are reviewed, revealing that the parameters are often selected without explicit reference to empirical data or objective rules. The development of procedures for parameter selection has been addressed in several studies, which are also reviewed along with the needed cost data published in textbooks and reports. Finally, an original approach is proposed to build cost-tolerance functions for combined processes, for which fewer results or methods are available. The parameters of a reciprocal power function, chosen for the favorable balance between accuracy and ease of use, are expressed through an empirical relationship with some design variables; these include the nominal dimensions, and the type and size of the part features involved in the allocation problem. An application example shows that the proposed procedure results in optimal tolerance values consistent with common design criteria.

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“…Later, due to the advantages that the stochastic algorithms are not restricted by the gradient information of the objective function, compared with the deterministic algorithms, they can handle more complex tolerance allocation models, so they have been more widely used. Among the stochastic algorithms, there are some more common algorithms, such as simulated annealing (SA) [9], genetic algorithm (GA) [10], particle swarm optimization (PSO) [11], and ant colony algorithm; besides, some less common algorithms are also used for tolerance-cost optimization, such as the imperial competition algorithm [12], self-organizing migration algorithm [13], bat algorithm [14], artificial bee colony algorithm [15], and cuckoo search [16]. In addition, the application of hybrid algorithm in the field of tolerance allocation is also studied.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Optimization Method and Application of Tolerance Allocation for the Steam Turbine Based on Cooperative Game Theory

Chen

Gao

et al. 2021

Shock and Vibration

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Aiming at the optimization problem of multiple objectives with contradictions and conflicts in the process of allocating the tolerance for complex products, taking advantage of the features of coordinating, and balancing contradictions and conflicts of cooperative game theory, this paper uses cooperative game theory to solve the multiobjective optimization problem of tolerance allocation. The quality requirements and cost requirements of assembly products are used as the game decision parties, and the fuzzy clustering method is used to group the design variables of tolerance allocation problem of the steam turbine to form the strategic space of game parties. Take the quality level and cost level of the assembly product as the optimization goals, complete the calculation of the utilities of the two game parties, and establish the multiobjective optimization model of tolerance allocation based on cooperative game theory. Finally, the Shapley value method based on cooperative game theory, the Nash equilibrium method based on noncooperative game theory, and the traditional single-objective optimization method with the quality as the constraint and the cost as the optimization objective are used to solve the tolerance allocation problem of steam turbine. The solution results show that the method of cooperative game realized the balance, coordination, and comprehensive optimization of the quality and cost from the perspective of collective interests, overcame the shortcomings of the traditional single-objective optimization method, and obtained better result than the Nash equilibrium method.

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An effective strategy for improving the precision and computational efficiency of statistical tolerance optimization

Cited by 14 publications

References 30 publications

Allocation of geometric tolerances in one-dimensional stackup problems

Allocation of geometric tolerances in one-dimensional stackup problems

Selection of parameters in cost-tolerance functions: review and approach

Multiobjective Optimization Method and Application of Tolerance Allocation for the Steam Turbine Based on Cooperative Game Theory

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