Rough Contact — Simplified Greenwood-Williamson Calculator

Surface and contact inputs

Results update as values change. Calculations convert the public units to SI internally.

Effective elastic modulus E*GPa Mean summit radius Rµm Summit-height standard deviation σ_sµm Summit density ηmm⁻² Nominal area A₀mm² Normalized separation h = d/σ_s0–6Mean plane separation divided by summit-height standard deviation.

Contact result

Classical independent elastic summit response.

Nominal contact pressure, p₀—

Normal load, W—

Real contact area, A_r—

Area ratio, A_r/A₀—

Expected contacts, N—

Mean real-contact pressure—

Method, interpretation and limits

The classical Greenwood-Williamson model represents a rough surface as statistically independent spherical summits with Gaussian heights. For F_n(h) = ∫₀^∞ tⁿφ(t+h) dt:

N = ηA₀F₀

A_r = πηA₀Rσ_sF₁

W = (4/3)E*ηA₀√R σ_s^3/2F_3/2

p₀ = W/A₀

The expected contact count is a statistical average. A high mean real-contact pressure can indicate that elastic-plastic contact modeling is more appropriate.

Assumptions

Gaussian independent summit heights and one spherical summit radius.
Nonadhesive, frictionless Hertz elasticity without plasticity, summit interaction, coalescence or bulk coupling.
No tangential loading, wear, lubrication or thermal effects.

Summit density, radius and height variation depend on surface measurement filtering and bandwidth; use statistics derived at an appropriate scale.

Reference: Greenwood, J. A. and Williamson, J. B. P., “Contact of Nominally Flat Surfaces,” Proceedings of the Royal Society A 295 (1966). doi:10.1098/rspa.1966.0242.