NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.
Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.
An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
The resonant frequency of a sphere in contact with a flat surface was measured as a function of loading force for contacting materials with different elastic moduli. Comparisons were made with predictions based on the Hertzian theory of elastic deformation. With a 4 mm radius, stainless steel ball on a ground stainless steel flat supporting an inertial mass of 180 g, the measured resonant frequencies ranged from 970 Hz to 1.73 kHz as the loading force was increased from 0.85 N to 23 N. This compares favorably with the theoretical predictions which range from 930 Hz to 1.62 kHz. For a 4 mm radius ruby ball on a sapphire flat, where the inertial mass was 200 g, the resonant frequencies ranged from 1.34 kHz to 1.81 kHz compared to a theoretical range of 1.09 kHz to 1.98 kHz as the loading force was increased from 0.97 N to 31 N.
Conference Dates
January 1, 1994
Conference Location
Cincinnati, OH
Conference Title
Proceedings of American Society of Precision Engineering
Kramar, J.
, Mcwaid, T.
, Schneir, J.
and Teague, E.
(1994),
Hertzian Contact Resonances, Proceedings of American Society of Precision Engineering, Cincinnati, OH
(Accessed October 10, 2025)