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Calculation of Correction Factors for Vickers’ Hardness Measurements on a Non-Planar Surface

https://doi.org/10.21122/2220-9506-2022-13-3-189-198

Abstract

The exact determination of Vickers HV hardness is important for determining of the product material mechanical properties. An important aspect of measuring HV is to obtain its values on a non-planar surface. Regulatory documents contain table values of correction factors which depend on the surface shape (convex or concave, spherical or cylindrical), its curvature (diameter D) and hardness (arithmetic mean of indentation diagonal lengths) but this does not solved the problem. The values for d/ratios not given in the tables are determined by interpolation from the closest to the measured tabulated d/values. The error in the representation of these tabulated d/values is fully included in the error of determining the coefficient for the measured d/ratio. The aim of the work was to simplify the calculation of correction factors for Vickers hardness measurements on non-planar surfaces and to reduce the calculation error compared to the methodology governed by the regulations.

The method presented is based on a statistical analysis of coefficients, presented in regulatory documents for cases considered in the form of tables. The sufficiency of using of a quadratic power function for approximating K(d/D) dependences and the necessity of fulfilling the physically justified condition ≡ 1 at zero curvature of tested surface have been substantiated. Simplification of calculation of coefficient and decrease of calculation error in comparison with the recommended in the regulatory documents obtaining of value by linear interpolation relative to two adjacent table values are shown.

The reduction of the calculation error in comparison with the calculation recommended in the regulatory documents occurred because of the reason that when calculating by the developed formulas, the error in the value of the calculated for a specific value of d/coefficient is averaged over all n values of d/given in the table of GOST for a given surface. That is, the error is reduced by a factor of about √n 2 in comparison with the calculation according to the regulated procedure. This is illustrated by the above numerical data and an example of the use of the method.

The obtained formulas for calculation of correction coefficients when measuring hardness HV on spherical and cylindrical (concave and convex) surfaces are reasonable to use for automatic calculation of HV on items with a non-planar surface.

About the Authors

S. G. Sandomirski
Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus
Belarus

Address for correspondence:
Sandomirski S.G. –
Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus,
Akademicheskaya str., 12, Minsk 220072, Belarus
 e-mail: sand_work@mail.ru




A. L. Val’ko
Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus
Belarus

Akademicheskaya str., 12, Minsk 220072



S. P. Rudenko
Joint Institute of Mechanical Engineering of the National Academy of Sciences of Belarus
Belarus


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For citations:


Sandomirski S.G., Val’ko A.L., Rudenko S.P. Calculation of Correction Factors for Vickers’ Hardness Measurements on a Non-Planar Surface. Devices and Methods of Measurements. 2022;13(3):189-198. https://doi.org/10.21122/2220-9506-2022-13-3-189-198

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ISSN 2220-9506 (Print)
ISSN 2414-0473 (Online)