Hertzian Contact Pressure Calculator
Free online Hertz contact calculator for elliptic (point) and line contacts: contact semi-axes, contact area, maximum and mean contact pressure, with pressure profiles.
What the app does
The Hertzian Pressure app computes the elastic contact between two loaded bodies according to Hertz theory. The contact can be elliptic (point contact, e.g. ball or ellipsoid on a cylinder) or a line contact (e.g. cylinder on cylinder). It is the starting point for almost every rolling and sliding contact analysis: bearings, gears, cams, wheel–rail, and the ball-on-disc or ball-on-flat set-ups used on tribometers.
Inputs
- Normal load (with unit selection).
- For each body: shape (for example ellipsoid or cylinder), Young’s modulus, Poisson ratio and the principal radii of curvature Rx and Ry.
Outputs
- Semi-axes of the contact ellipse in the x and y directions (or the half-width for line contact).
- Contact area.
- Maximum and mean contact pressure.
- Pressure profiles along both axes of the contact, and a 3D view of the two bodies.
Worked example
Steel on steel (E = 200 GPa, ν = 0.3): an ellipsoid with Rx = 68 mm and Ry = 150 mm pressed against a cylinder of radius 68 mm with 1000 N.
The app returns:
| Quantity | Value |
|---|---|
| Semi-axis of contact ellipse (x) | 0.4691 mm |
| Semi-axis of contact ellipse (y) | 1.243 mm |
| Contact area | 1.832 mm² |
| Maximum contact pressure | 0.8188 GPa |
| Mean contact pressure | 0.5459 GPa |
As Hertz theory predicts, the maximum pressure is 1.5 times the mean pressure for an elliptic contact. Comparing the maximum pressure with the material’s allowable contact stress is a quick first check of a design.
Assumptions
Classical Hertz theory: linear-elastic, homogeneous and isotropic materials; smooth, non-conforming surfaces; a contact much smaller than the radii of curvature; no friction or lubricant in the contact. For lubricated contacts, continue with the EHL Film Thickness Simulator.
How to access the app
The Hertzian Contact Pressure Calculator runs in your web browser on Tribology Universe, the app platform of i-TRIBOMAT: The European Tribology Centre. Use is free; you only need a Tribology Universe account, which takes a minute to create.
Need more than the free app?
Our Modelling & Simulation team builds custom models for your geometry, materials and lubricants, and can validate them against tests on more than 130 tribometers across our partner laboratories. Contact us or write to office@i-tribomat.eu.
References
- H. Hertz, Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik 92 (1882) 156–171
- B. J. Hamrock, D. E. Brewe, Simplified solution for stresses and deformations, Journal of Lubrication Technology 105 (1983) 171–177
- K. L. Johnson, Contact Mechanics, Cambridge University Press, 1985
- Hertz Contact Theory: Key Concepts Explained, TriboNet Wiki
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