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](MaterialsScience) — Fatigue limits of hardened steels.

- [Structural Engineering](StructuralEngineering) — Load bearing analysis.

- [Tensor Theory](TensorTheory) — For the calculus of stress fields.

- [Mathematics Hub](MathematicsHub) — Central index.