The objective of this paper is to demonstrate how the curvatures can be calculated from measured profile using Heron’s formula. A progression of three measurements of an edge, rounded by mass finishing, is used for the demonstration. This is a multi-scale characterization method, because curvature, like slope, changes with scale of observation, or calculation, on profiles measured on rough surfaces. Curvatures on a surface influence behavior and are, in turn, influenced by the processing and use of the surface; it is an important aspect of surface topographies that has not been well characterized. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. The curvature calculations rely on three measured heights, and the separation of the heights represents the scale. The calculation method is based on Heron’s formula for circumscribed triangles. Two faces and a corner on machined and mass finished parts are measured using a scanning laser confocal microscope. Plots of curvature as a function of position and scale are presented, and mean, minimum, and maximum curvatures are plotted as a function of scale. Heron’s formula is reasonable for determining the curvature, unless the height difference between the middle and the two exterior heights is greater than the radius. In that circumstance, the curvature calculated by Heron’s formula would be smaller than that which would be reasonably expected based on an intuitive examination of the three heights.

Creator

• Gleason, M. A.
• Lemoine, A.
• Brown, C. A.
• Kordell, S. P.

Publisher

• International Conference on Metrology and Properties of Engineering Surfaces

Mot-clé

• Curvatures
• Heron's Formula

Year

• 2013

Date created

• June 2013

Resource type

• Conference Proceeding

Event

• 14th International Conference on Metrology and Properties of Engineering Surfaces (14th ICMPES); Taipei, Taiwan

Rights statement

• In Copyright

Citation

• Gleason, M. A., Kordell, S., Lemoine, A., & Brown, C. A. (2013, June). Profile curvatures by Heron’s formula as a function of scale and position on an edge rounded by mass finishing. In 14th International Conference on Metrology and Properties of Engineering Surfaces, Taipei, Taiwan, paper TS4-01 (Vol. 22).

Dernière modification

• 2024-08-16