Hertzian contact stress

In mechanical engineering and tribology, Hertzian contact stress, is a description of the stress within mating parts. The term is named after Heinrich Rudolf Hertz whose name is also found in the SI unit Hertz. In general, this is usually described with respect to contacting spheres of different radii.

Overview

Hertzian contact stress refers to the localized stresses that develop as two curved surfaces come in contact and deform slightly under the imposed loads. This amount of deformation is dependent on the elasticity of the the material in contact, i.e., its modulus of elasticity. It gives the contact stress as a function of the normal contact force,the radii of curvature of both bodies and the modulus of elasticity of both bodies.

In gears and bearings in operation, these contact stresses are cyclic in nature and over time lead to sub-surface fatigue cracks.

Hertzian contact stress forms the foundation for the equations for load bearing capabilities in bearings, gears, and any other bodies where two surfaces are in contact.

Heinrich Rudolf Hertz first studied these stresses, and published his work on the topic in “Ueber die Beruehrung elastischer Koerper (On Contact Between Elastic Bodies),” in "Gesammelte Werke" (Collected Works), Vol. 1, Leipzig, Germany, 1895.

References

* More about contact stresses and the evolution of bearing stress equations can be found in this publication by NASA Glenn Research Center head the NASA Bearing, Gearing and Transmission Section, Erwin Zaretsky, [http://gltrs.grc.nasa.gov/reports/1997/TM-107440.pdf]

There is a section on this topic with a full description of the equations in the popular textbook for mechanical engineering design, with the same name by J.E. Shigley and C.R. Mischke, Chapter 2.
* Shigley, J.E., Mischke, C.R., "Mechanical Engineering Design", Fifth Edition, McGraw-Hill, Inc, 1989, ISBN 0-07-056899-5

ee also

* Contact mechanics
* Bearing (mechanical)