NBS Internal Report 73-243; 67p. July 19, 1973.
Contact stresses; cylinder measurement; deformation; Hertzian contact problem; line contact; mechanical measurement; metrology.
The measurement of a diameter of a cylinder has widespread application in the metrology field and industrial sector. Since the cylinder is usually placed between two flat parallel anvils, one needs to be able to apply corrections, to account for the finite measuring force used, for the most accurate determination of a diameter of the cylinder.
An extensive literature search was conducted to assemble the equations which have been developed for deformation of a cylinder to plane contact case. There are a number of formulae depending upon the assumptions made in the development. It was immediately evident hat this subject has been unexplored in depth by the metrology community, and thus no coherent treatise for practical usage has been developed.
This report is an attempt to analyze the majority of these equations and to compare their results within the force range normally encountered in the metrology field. Graphs have been developed to facilitate easy computation of the maximum compressive stress encountered in the steel cylinder-steel plane contact case and the actual deformation involved.
Since the ultimate usefulness of any formula depends upon experimental verification, we have compiled results of pertinent experiments and various empirical formulae. A complete bibliography has been included for the cylinder-plane contact case for the interested reader.