ENGINEERING – MECHANICAL ENGINEERING CALCULATOR
Hertz Contact Stress
A precise tool.
What is the Hertz Contact Stress & How does it work?
The Hertzian contact stress model predicts the peak stress that develops when two curved elastic bodies press together, such as a steel ball rolling on a bearing race. It assumes that the contacting surfaces are smooth, the materials behave linearly elastically, and the contact area is small compared with the radii of curvature, allowing the deformation to be treated as a local ellipsoidal flattening. Under these assumptions the maximum contact pressure (also called Hertzian stress) can be expressed analytically. For a sphere (or a cylinder of long length) contacting a flat surface the stress is
The effective modulus combines the elastic properties of both bodies:
\sigma_{h} = \left( \frac{6F E^{*2}}{\pi R} \right)^{1/3}
sigma_{h} = Hertzian contact stress (Pa)
F = normal load (N)
E^{*} = effective Young’s modulus (Pa)
R = effective radius of curvature (m)
F = normal load (N)
E^{*} = effective Young’s modulus (Pa)
R = effective radius of curvature (m)
1/E^{*} = (1-nu_{1}^{2})/E_{1} + (1-nu_{2}^{2})/E_{2}. The effective radius for a sphere‑on‑flat contact is simply the sphere radius, while for two spheres it follows 1/R = 1/R_{1} + 1/R_{2}. By inserting the user‑provided material and geometry data into these relations, the calculator returns the peak Hertzian stress.
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Frequently Asked Questions
What is Hertzian contact stress?
Hertzian contact stress is the peak stress that occurs when two curved, elastic objects come into contact.
When would I use this calculator?
Use this calculator to predict the maximum contact pressure between two curved surfaces in mechanical systems.
What assumptions does the Hertzian contact stress model make?
The model assumes smooth surfaces, linear elastic behavior of materials, and a small contact area compared to curvature radii.
Can this calculator be used for any type of material?
This calculator is suitable for materials that behave linearly elastically under the given assumptions.
What are some examples of applications for Hertzian contact stress calculations?
Applications include analyzing ball bearings, gears, and other mechanical components where surface contact occurs.
How do I interpret the results from this calculator?
The result represents the maximum pressure at the point of contact between the two surfaces.
What is the difference between Hertzian stress and other types of stress?
Hertzian stress specifically deals with localized contact pressures in curved surfaces, while other stresses may refer to tension, compression, or shear throughout a material.
Results are for informational purposes only and do not constitute professional advice.