Variable coefficients reciprocal squared model based on multi-constraints of aircraft assembly tolerance allocation

Wang, Gong-dong; Yang, Yongrong; Wang, Wei; Lu, Sichao

doi:10.1007/s00170-015-7299-4

Cited by 15 publications

(4 citation statements)

References 11 publications

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“…In [142], the parameters of cost-tolerance functions for single processes are estimated from the manufacturing difficulty of the feature with respect to the process, calculated using a method based on fuzzy logic. In [71], an equation based on process constraints (machine tools, workers, machining and assembly accuracy) is iteratively solved with the Newton's method to calculate the coefficients of a reciprocal squared function, thus obtaining a more complex model depending on a multiplicity of variables (variable coefficients reciprocal squared). The cost data available in literature cover a small part of the possible combinations of influencing factors (product type, feature type, manufacturing process etc.).…”

Section: Methods For Parameter Selectionmentioning

confidence: 99%

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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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Section: Methods For Parameter Selectionmentioning

confidence: 99%

“…In [69], the function is extended to the case of multiple features machined on the same component: the fixed cost is counted only once for the part, while the variable costs are added together for the different features. [53] 0.3-0.5 0.45 [49] 0.01-0.07 0.7-0.9 [71] 7-15 1-4 [67,72] -0.45 [47,48,60,73] -…”

Section: Reciprocal Powermentioning

confidence: 99%

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

Armillotta

2020

Int J Adv Manuf Technol

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“…This adds robustness to the results of this work, because any uncertainty on the parameters (especially the exponent k and the coefficients related to material and feature type) is unlikely to have a strong impact on the optimal proportions between the tolerances. If k = 0.55, the tolerances can be set proportionally to the following factor: (32) which can be simplified into:…”

Section: Properties and Scaling Proceduresmentioning

confidence: 99%

“…As an alternative to regression, neural networks have been trained with cost-tolerance data for both single [29] and combined processes [30]; the resulting cost-tolerance models are said to allow a more accurate approximation of actual costs. This drives allocation away from the use of an explicit cost-tolerance function, as it has also been attempted using fuzzy methods [31] and the iterative solution of an equation based on process constraints [32]. As opposed to using published cost data, some studies propose procedures to allow the collection and maintenance of cost data at manufacturing companies.…”

Section: Introductionmentioning

confidence: 99%

An extended form of the reciprocal-power function for tolerance allocation

Armillotta

2022

Int J Adv Manuf Technol

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The optimization of dimensional tolerances requires that a cost-tolerance function is evaluated consistently for all the part features involved in a given functional requirement. This is difficult because the parameters of commonly used functions are set using cost data from various sources and on possibly different scales. As an alternative, the paper proposes a revised form of one of the available cost-tolerance functions (reciprocal power), which expresses its parameters in empirical relationship with a set of design specifications on the toleranced features. These include the nominal dimension, the shape, the surface area, and the material. Following a previous study based on cost data available in literature, the values and expressions of the parameters are validated and refined using a feature-based method for the estimation of machining cost. The properties of the extended function allow to develop a simplified method for tolerance allocation that avoids the task of solving the optimization problem; it is a modified version of proportional scaling where the initial solution satisfies optimal ratios between tolerances. The discussion of the results and an application example help to justify the proposed function on grounds of correctness, convenience, and reference value.

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