lubricationekvation
Lubricationekvation, commonly referred to in English as the Reynolds equation, is a fundamental partial differential equation used to predict the pressure distribution within a thin viscous lubricant film between closely spaced, moving surfaces. It is central to hydrodynamic lubrication theory and is applied in the design and analysis of bearings, gears, seals, and other tribological contacts.
The equation is derived from the Navier–Stokes equations under lubrication approximations: the lubricant film thickness h(x,y)
∂/∂x[(h^3/12μ) ∂p/∂x] + ∂/∂y[(h^3/12μ) ∂p/∂y] = ∂/∂x(hU/2),
where p(x,y) is the pressure, μ is the dynamic viscosity, h(x,y) is the film thickness, and U is
Key variables and boundary conditions are chosen to reflect device geometry and operating conditions, with ambient
Applications include predicting load-bearing capacity, friction, and film stability in bearings and seals. Extensions of the
Limitations include neglect of inertial effects at higher speeds, into highly compressible or non-Newtonian fluids, and