Sommerfeld Number
Calculate the Sommerfeld number of a journal bearing, S = (r ÷ c)²·(μ·N ÷ P), from the radius-to-clearance ratio (r/c), the lubricant dynamic viscosity μ, the rotational speed N (rev/s) and the specific pressure P (load over projected area). The dimensionless result is the characteristic parameter defining a hydrodynamic bearing's behaviour: it sets the minimum oil film thickness, shaft position, friction and lubricant flow. Low values mean a heavily loaded bearing (contact risk); high values, excessive clearance. It is the basis of bearing design via Raimondi-Boyd charts. Enter the r/c ratio, the viscosity, the speed and the pressure.
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Sommerfeld number
The Sommerfeld number (S) is the dimensionless parameter that governs the whole behaviour of a hydrodynamic journal bearing — the kind where a shaft spins on an oil film that it pumps itself as it turns, never touching the bearing metal. It gathers, in a single figure, the four variables that matter: S = (r ÷ c)²·(μ·N ÷ P), where r/c is the ratio of shaft radius to radial clearance (typically ~1000), μ is the dynamic viscosity of the lubricant, N the rotational speed (rev/s) and P the specific pressure (load divided by the projected bearing area). Once S is known, the classic Raimondi-Boyd charts yield every operating characteristic of the bearing: the minimum film thickness (the real clearance between shaft and bearing at the most heavily loaded point, which must stay above the sum of the surface roughnesses), the attitude angle of the shaft, the friction coefficient, the oil flow pumped and the temperature. The physical reading is direct: a low S means a heavily loaded bearing, slow running or thin oil — the film thins out and contact becomes a risk; a high S means a thick, generous film. Design aims at an S that secures enough film without wasting power in friction. Enter the r/c ratio, the viscosity, the speed and the pressure.
Related Tools
Eccentricity Ratio
Calculate the eccentricity ratio of a hydrodynamic bearing, ε = e ÷ c, dividing the eccentricity e (shaft centre offset from bearing centre) by the radial clearance c. The result (between 0 and 1) describes the shaft position within the bearing under load: ε = 0 means a centred shaft (no load); ε near 1 means the shaft nearly touches the bearing (heavily loaded, minimum film at the limit). Eccentricity grows with load and decreases with viscosity and speed. The minimum film thickness is h_min = c·(1 − ε). Enter the eccentricity and the radial clearance.
Hersey Number
Calculate the Hersey number of a bearing, H = μ·N ÷ P, from the dynamic viscosity μ, the rotational speed N and the specific pressure P. The dimensionless result is the horizontal-axis variable of the Stribeck curve, which maps the lubrication regimes: very low values indicate boundary lubrication (metal-to-metal contact, high friction and wear); intermediate values, mixed lubrication; and high values, full hydrodynamic lubrication (complete film, minimum friction). Tracking the Hersey number helps keep the bearing in the hydrodynamic regime, away from contact. Enter the viscosity, the speed and the pressure.
Friction Torque
Calculate the friction torque in a shaft or bearing, T = μ·F·r, multiplying the friction coefficient μ by the normal force (load) F and the radius r where friction acts. The result, in N·m, is the moment friction opposes to rotation — the torque the motor must overcome just to turn the assembly, without doing useful work. Reducing friction torque (with lubrication, rolling bearings and good finishes) saves energy and lowers heating. Multiplied by the angular velocity, it gives the power dissipated by friction. Enter the friction coefficient, the force and the radius.
Bearing Power Loss
Calculate the power dissipated by friction in a bearing, P = T × ω, multiplying the friction torque T by the angular velocity ω (rad/s). The result, in watts, is the mechanical energy converted to heat per unit time by friction — a loss that reduces efficiency and heats the lubricant and components. This heat must be dissipated (by convection or oil circulation) to keep a safe operating temperature, since overheating degrades the lubricant and can cause seizure. Estimating the dissipated power is essential to size the cooling and the oil flow. Enter the friction torque and the angular velocity.
Film Thickness Ratio (λ)
Calculate the specific film thickness ratio (lambda), λ = h_min ÷ √(Ra₁² + Ra₂²), from the minimum lubricant film thickness h_min and the surface roughnesses Ra of the two contacting surfaces. The dimensionless result indicates the elastohydrodynamic lubrication regime: λ < 1 means direct asperity contact (boundary lubrication, high wear); 1 < λ < 3, mixed lubrication; and λ > 3, full separation of the surfaces by the oil film (full regime, long life). It is a key criterion in gear and rolling-bearing design. Enter the minimum film thickness and the surface roughnesses.
Bearing PV Factor
Calculate the PV factor of a bearing or self-lubricating bushing, PV = P × V, multiplying the specific pressure P (load over projected area) by the sliding velocity V at the surface. The result, in MPa·m/s, is the limiting criterion for selecting materials for non-force-lubricated bearings (sintered bronze bushings, polymers like PTFE and nylon): each material has a maximum allowable PV value, above which the friction heat cannot be dissipated and the bearing fails by melting or accelerated wear. PV is kept below the material limit with a safety margin. Enter the specific pressure and the velocity.
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