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An Efficient Method for Statistical and Deterministic Tolerances Synthesis Using the Jacobian Torsor Model


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DOI: https://doi.org/10.15866/ireme.v16i10.22505

Abstract


This research aims to create an efficient way to guide designers in selecting tolerances more cost-effectively through the Jacobian-Torsor unified model by performing an iterative statistical and deterministic analysis of geometric tolerances. This model is created based on the assembly's Functional Requirements (FR) and the starting tolerance values of the Functional Elements (FE) that comprise the tolerance chain. The model initially produces deterministic results. However, the Monte Carlo simulation allows converting it into a statistical model. The model is assessed iteratively, with each simulation iteration employing random values of the torsor components that correspond to the functional elements as inputs. The simulation ends when the number of iterations approaches the maximum value set at the star, and a collection of values representing the components of the Functional Requirement (FR) torsor is created based on repeated multiplications of the model. Finally, the percentage calculation defines the contribution of each Functional Element (FE) to the total Functional Requirement (FR). A numerical example is provided to demonstrate the use of the suggested method. A comparison of the two approaches, deterministic and statistical, reveals that the latter has a more significant economic impact.
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Keywords


Statistical Tolerance Synthesis; Jacobian Torsor Model; Monte Carlo Simulation; Functional Requirement

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References


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