Illustrated Physics
physics, drawn
Concept

Contact mechanics — where it appears

The description of what happens where two solids touch, in which elasticity fixes a small contact area and therefore a large pressure. Hertz's solution gives both from the load and the curvatures, and the pressures reached in a bearing are gigapascals from ordinary loads.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Force against slip, and the knee between them. The force a tyre delivers against how much faster its tread is going than the road, for a patch 120 mm long under 4000 N with a friction coefficient of 1. The curve is the integral over the bristles, and the dashed line is the cubic the brush model gives in closed form; they agree to 0.00 per cent of the sliding force. The first slope is 80 kN per unit slip, and it belongs entirely to the elasticity of the rubber — at vanishing slip nothing is sliding, so no friction coefficient can appear in it. Full sliding is reached at 15.0 per cent slip and not before. Everything a driver calls grip lives on the rising part of this curve, at a few per cent of slip, where the patch is partly stuck and partly sliding — and the quantity that decides handling in that region is the slope rather than the friction coefficient at the top.

The grip that needs a little slipping

A wheel that transmits any force at all is not rolling. Part of its contact patch is stuck to the road and part is already sliding, and the force it delivers is a measure of how much has given up. The useful part of the curve is a few per cent of slip, the peak is not the end of it, and everything past the peak is unstable.

mechanics · Friction The pressure at which an oil becomes a glass. Viscosity against pressure for 4 liquids on a logarithmic axis, from Barus's rule with the pressure coefficient each one actually has. The rule is an exponential, so a gigapascal multiplies an ordinary oil's viscosity by a hundred million or more, and the curves cross the line conventionally taken to mark a glass — a million million pascal-seconds — at 1.37 GPa for a mineral oil, 0.98 GPa for a traction fluid. The vertical line is the peak pressure inside the loaded contact this figure is about, 1.32 gigapascals, computed from the Hertz solution for that geometry and load. Water is drawn for contrast: its pressure coefficient is thirty times smaller, it never approaches a glass over this range, and that is why it is useless as a lubricant in a rolling contact however clean it is. Each curve is drawn solid up to the glass line and dashed above it, because past that point the material is not a liquid and its viscosity is not what decides how it shears — the exponential continues, and the substance it was written for does not.

The oil that is a glass for a quarter of a millisecond

Every other account of viscosity here varies the temperature. Pressure does something larger and in the same direction for every liquid: viscosity rises exponentially, by a factor of ten to the eight or more at the gigapascal inside a loaded gear tooth. That is not a curiosity — it is the only reason there is a film there at all. Remove the pressure dependence from the calculation and the predicted film is five nanometres, under the roughness, and the surfaces touch.

fluids · Viscosity

Named alongside it

The objects these essays reach for when they reach for this one.

ElasticityFrictionContact areaDissipationExponentialExtrapolationFree volumeGlass transitionHysteresisInstabilityLubricationNormal force

All concepts