Mathematic Model of the General Approach to Tolerance Control in Quality Assessment

Abstract

A mathematical model for the numerical determination of the quality indicator value allowing one to obtain non-dimensional values in the range from minus infinity to 1 (the maximum usable value) is proposed. Unlike the traditional system of tolerances, in which the suitability can take two values -0 or 1, the proposed model allows you to obtain intermediate values of the suitability, depending on the proximity of the actual parameter to the desired value. The model uses the suitability function suggested in the paper, and the shape indicator drives it. The characteristic ranges of the shape indicator of the suitability function have been considered. Those of practical importance has been highlighted. In addition to the general dependence, exceptional cases (linear and parabolic suitability functions, which are mathematically simpler) are also given. It is shown how the use of the proposed model allows sorting parts into quality grades and introducing a technological margin of accuracy. The mathematical model is illustrated by the example of the dimensional suitability of an engineering part. The traditional system of dimensional tolerances is a particular case of the proposed generalized system, which is recommended for high-precision manufacturing.

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