What is Hertzian Contact Stress?

Hertzian contact stress describes the localized stresses that develop between two curved surfaces when they are pressed against each other under a load. Named after Heinrich Hertz, who published the fundamental theory in 1882, this is a cornerstone of mechanical engineering and tribology. Unlike simple stress calculations, contact stress accounts for the elastic deformation of the materials at the point of contact, turning what theoretically would be a single point or line into a small contact area (ellipse or rectangle).

How to Use the Contact Stress Calculator

To use this tool accurately, follow these steps:

1. Select Geometry: Choose between "Sphere on Sphere" (point contact) or "Cylinder on Cylinder" (line contact). For a sphere or cylinder on a flat plate, enter "0" for Radius 2.
2. Input Materials: Enter the Young's Modulus in Gigapascals (GPa) and the Poisson's Ratio (usually between 0.25 and 0.33 for metals).
3. Define Geometry: Enter the radii in millimeters and the total normal load in Newtons.
4. Calculate: The tool will provide the maximum contact pressure (Pmax), which is typically the critical value for preventing surface fatigue or pitting.

Frequently Asked Questions

Why is contact stress important?

Contact stress is vital for designing bearings, gears, cam-followers, and railway wheels. High contact pressure leads to material failure through surface pitting, spalling, or plastic deformation even if the bulk stress is low.

What happens if I use a flat surface?

By entering 0 for Radius 2, the calculator treats the second body as a flat plane (infinite radius). This is common in testing scenarios like a ball-on-disk setup.

Is this valid for plastic deformation?

No, Hertzian theory assumes purely elastic behavior. If the calculated stress exceeds the material's yield strength (modified by a factor for triaxiality), permanent deformation will occur, and these formulas will no longer be accurate.