Hertzian stress (subsurface) calculator – Line Contact

TriboNet

December, 2 2018

Hertzian stress for line contact

This is a Hertzian stress calculator for subsurface stress components in case of a contact between cylinders (line contact). Equations and the references are given below the calculator.

Hertzian stress for line contact — Copyright: Wikipedia, Valentin Popov

As shown in the figure, a contact of two cylinders is considered here. Hertzian subsurface stresses can be obtained using following equations:

(1) $\begin{eqnarray*} \sigma_x = -2\nu P_{max}(\sqrt{1+\frac{z^2}{b^2}} - |{\frac{z}{b}}|) \\ \end{eqnarray*}$

where $\sigma_x$ is the stress component in x direction, $P_{max}$ is the maximum Hertzian pressure and $b$ is Hertzian contact radius.Please find all the related equations here. Corresponding Matlab code for Hertzian solution can be found here. The online Hertzian contact stress calculator can be found here.

Equations were taken from [1].

[1]. Contact Mechanics and Friction: Physical Principles and Applications, V. Popov, 2010

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