Open AccessAnalysis of Requirements and the Feasible Limit for Error Reduction in Two-Parameter Magnetic Determination of Steels’ Hardness
Author(s) -
С. Г. Сандомирский
Publication year - 2020
Publication title -
pribory i metody izmerenij
Language(s) - English
Resource type - Journals
eISSN - 2414-0473
pISSN - 2220-9506
DOI - 10.21122/2220-9506-2020-11-3-236-244
Subject(s) - standard deviation , limit (mathematics) , reduction (mathematics) , materials science , coercivity , correlation coefficient , hardness , mathematics , thermodynamics , statistics , condensed matter physics , physics , mathematical analysis , metallurgy , geometry
All measurements of mechanical properties of materials in the magnetic structural analysis are indirect and relationships between the measured parameters are correlated. An important physical parameter of steel is hardness. An increase in the correlation coefficient R and a reduction in the standard deviation (SD) are achieved when controlling the hardness of steels with two-parameter magnetic methods compared to methods that use a single measured parameter. However, the specific conditions and requirements for application of the two-parameter methods remain unclear. The purpose of this article was to analyze conditions and the achievable error reduction limit for two-parameter indirect determination of steels hardness and to compare those with one-parameter methods. In particular, we considered the mean Square Deviation (SD), σ F , of indirect calculation of the physical quantity F using two measured parameters x 1 and x 2 that are correlated with F . It was found that reduction of σ F is most pronounced when x 1 and x 2 are inversely correlated with the maximum modulus | R | of the correlation coefficient R between them. The most significant reduction in σ F occurs at similar values of the SDs σ1 and σ2 between the true value of F and the values calculated based on the results of indirect measurements of F using each of the parameters x 1 and x 2 . The Results of the analysis are confirmed by an example of reduction in SD when determining the hardness of carbon steels by measuring their remanent magnetization and coercive force compared to use any one of these parameters. This result can be applied to measurements in non-destructive testing and in related fields of physics and technology. The Results of the analysis allow us to compare different parameters for indirect two-parameter determination of a physical quantity, to select the optimal parameters, and to evaluate the minimum achievable measurement error of a physical quantity by a two-parameter method before performing the measurements.