Determination of test cycle sensitivity coefficients for the Rockwell HR45N hardness scale

Abstract

This report describes investigations carried out to determine test cycle sensitivity coefficients for the Rockwell HRA hardness scale. Sensitivity coefficients were determined for the preliminary-force, total-force and recovery-force dwell times. The work was carried out in 2017 at the National Institute of Standards and Technology (NIST) in Gaithersburg, USA.

Determination of sensitivity coefficients and their uncertainties in Rockwell hardness measurement: a Monte Carlo method for multiple linear regression

“…• Even when the uncertainties of the sensitivity coefficients are given, the authors of this paper have not found a unifying methodology that explains how such uncertainty contributions were calculated (i.e. are those uncertainties based only on the standard uncertainty given from the OLS for the linear regression as in [3], or are they given the same uncertainty of the hardness measurements as in [2]?). Additionally, even when given, the uncertainty contributions of the sensitivity coefficients are generally not propagated through the law of propagation of uncertainty to calculate the combined standard uncertainty of the measurement model.…”

“…One of the major problems regarding the calculation of sensitivity coefficients is due to a handful of factors: the first one is due to a poor experimental design, which leads to the difficulty in decoupling the parameters and therefore the inability to clearly attribute the cause of a certain change in the measurement to a specific variable; the second one is that, even in the case of a successful experimental design, many doubts arise on how to calculate the uncertainty of the sensitivity coefficients. For instance, in the field of hardness measurement, it often happens that the uncertainty of the hardness measurement is associated directly to the sensitivity coefficients [2,3], while in other cases, the uncertainty contribution of the sensitivity coefficients is simply given by the standard error from the MLR. However, the authors point out that due to the variability of the hardness measurements and the variability of the input influence variables (V fa and t aa ), the usual MLR cannot be used to evaluate the sensitivity coefficients.…”

“…In the field of hardness measurements, in order to evaluate the measurement uncertainty, researchers have tried to understand and quantify the effect of possible influence parameters on the measurement itself [1][2][3][4][5][6][7][8][9][10][11]. Such scientific interest is greatly motivated by the new international definitions recently adopted for the realization of these hardness scales at the level of National Metrology Institutes (NMIs), which prescribe the operative measurement procedures and fix reference values for influence parameters (i.e.…”

“…the depth of the indenter h for the Rockwell scale), but are examined in the related Standards [12][13][14]. In this paper, two influence parameters are investigated for superficial Rockwell hardness scales: (1) the velocity of the total force application; (2) the time interval of the force variation from the preliminary force to the total force value. One major difficulty is related to the physical decoupling of the two variables (velocity and time) [6], so a careful experimental design has been carried out beforehand.…”

Determination and Uncertainty Propagation of Sensitivity Coefficients in Rockwell Hardness Measurements

“…The considerations above are of practical interest in the field of hardness measurement, where researchers have been trying to quantify-via experimentally determined sensitivity coefficients-how factors such as operating temperature, speed of indenter, force, etc. influence the hardness measurement itself [2,3,4,5,6,7,8,9]. In this paper a Monte Carlo method applied to linear regression [10,11] is used to deal with the determination of 1 This preprint research paper has not been peer reviewed.…”