hertz pressure calculator

What is Hertz pressure?

Hertz pressure (or Hertzian contact stress) describes the localized pressure that forms where two curved elastic bodies touch under load. This is common in bearings, gears, cams, rail-wheel systems, and rolling/sliding contacts. Instead of spreading the load over a large area, contact happens over a small patch, causing high stress.

Why use a Hertzian contact calculator?

A Hertz pressure calculator helps you quickly estimate whether a design is likely to exceed material limits. Engineers use these calculations in early design checks for pitting, surface fatigue, and permanent deformation risk.

• Estimate maximum contact pressure at the center of contact.
• Estimate contact radius and effective contact area.
• Compare contact stress against allowable limits for steel, ceramics, and polymers.
• Screen design options before detailed finite element analysis.

Equations used in this hertz pressure calculator

1) Reduced elastic modulus

The combined compliance of both materials is represented by the reduced modulus E*:

1 / E* = (1 - ν1²)/E1 + (1 - ν2²)/E2

2) Effective radius

For two spheres in point contact:

1 / R* = 1 / R1 + 1 / R2

If body 2 is flat, R2 = ∞ and therefore 1/R2 = 0, so R* ≈ R1.

3) Contact radius and pressure

With normal load F:

a = [(3 F R*) / (4 E*)]^(1/3)

p0 = 3F / (2πa²) (maximum pressure at center)

pmean = F / (πa²) (average pressure over contact patch)

How to use this tool

1. Enter load in newtons.
2. Enter geometry in millimeters.
3. Enter material stiffness in GPa and Poisson ratio (typically 0.2 to 0.35 for many metals).
4. Click Calculate.
5. Review max pressure and compare to material/contact fatigue guidance.

Example interpretation

If your result shows max contact pressure around 1500 MPa for hardened steel, that may be acceptable in rolling contact applications depending on lubrication, hardness, residual stress, and fatigue life target. If pressure is too high, common fixes include increasing radius, reducing load, changing material pair, or modifying contact geometry.

Assumptions and limitations

• Linear elastic behavior.
• Small deformations.
• Smooth, non-conforming contact.
• No frictional tangential stress in this simplified model.
• No edge effects, thermal effects, or roughness-based local peaks.

For plasticity, coatings, rough surfaces, or mixed lubrication analysis, use more advanced models or finite element simulation.