Bearing Design: The Physics of Rolling Contact

Rolling element bearings are the critical interfaces of rotary motion, converting sliding friction into rolling motion to minimize energy dissipation.

1. Contact Mechanics: Beyond Hertz

Hertzian theory provides the first-order approximation for contact pressure ( $\sigma$ ). However, modern research requires analyzing the Subsurface Stress Tensor to identify failure initiation points.

\sigma_{max} = f(F, R, E, \nu)

2. Elastohydrodynamic Lubrication (EHL)

EHL describes the separation of surfaces by a viscous lubricant film. The critical parameter is the Minimum Film Thickness ( $h_{min}$ ), which must exceed surface roughness to prevent metal-on-metal contact.

3. Failure Mechanisms

Bearing life is defined as the $L_{10}$ point—where 10% of a population is expected to fail due to Rolling Contact Fatigue (RCF).

See Also:

Materials Science — Fatigue limits of hardened steels.
Structural Engineering — Load bearing analysis.
Tensor Theory — For the calculus of stress fields.
Mathematics Hub — Central index.