Journal Bearing Sommerfeld Number

Journal Bearing Sommerfeld Number

A journal bearing supports a rotating shaft on a thin, continuously renewed film of lubricating oil rather than direct metal-to-metal contact, and the Sommerfeld number is the single dimensionless parameter that characterizes how that bearing is operating — combining the bearing's geometry, the oil's viscosity, the shaft speed, and the applied load into one number used to look up performance characteristics like minimum film thickness and friction from standard design charts.Because the Sommerfeld number packages so many variables together, it lets engineers compare bearings of very different size and speed on a common basis, and design charts built from decades of journal bearing research (most notably the Raimondi-Boyd charts) are indexed directly by this number — getting it right is the entry point to essentially all classical hydrodynamic bearing design.

The Sommerfeld number is Somm = (r_j/c_j)^2·(mu_oil·N_j)/P_b, combining the radius-to-clearance ratio squared with the ratio of viscous shear effects to unit bearing pressure. where r_j is the journal radius, c_j is the radial clearance between journal and bearing, mu_oil is the lubricant's absolute viscosity, N_j is the shaft rotational speed, P_b is the unit bearing pressure (load per projected area), and Somm is the resulting dimensionless Sommerfeld number.

Squaring the radius-to-clearance ratio captures how sensitive bearing performance is to this very small clearance dimension, and multiplying by the viscosity-speed-to-pressure ratio combines the remaining operating parameters into the single dimensionless characteristic number used for bearing design charts.

Results

A Sommerfeld number around 0.06 here is a plausible value for a lightly-to-moderately loaded journal bearing, and this number would be looked up directly on a standard Raimondi-Boyd chart (indexed by Sommerfeld number and bearing length-to-diameter ratio) to read off the minimum oil film thickness and friction coefficient. Because the radius-to-clearance ratio is squared, bearing clearance has an outsized effect on the Sommerfeld number — a clearance that is too tight raises Somm and can starve the bearing of adequate film thickness, while excessive clearance lowers it and can allow metal-to-metal contact under shock loading. This single number cannot by itself confirm the bearing is safe; it is the entry point into design charts that then give the actual film thickness, which is what is compared against the surface roughness to judge whether full hydrodynamic lubrication is actually achieved.

Assumptions & limitations

• Full hydrodynamic lubrication assumed (a continuous oil film, not boundary or mixed lubrication).
• Newtonian lubricant behavior with constant viscosity assumed at the operating oil temperature.
• Result is a single dimensionless number; interpreting it requires a standard bearing design chart (not included here) indexed by bearing length-to-diameter ratio.
• Steady-state, constant-speed operation is assumed — start-up and shutdown are boundary-lubrication regimes not captured by this number.

Related calculations

• Bolted Joint Shear Stress
• Torsion of a Circular Shaft
• Helical Compression Spring Rate
• Shaft Power from Torque and Speed