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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Número de Sommerfeld
O número de Sommerfeld (S) é o parâmetro adimensional que governa todo o comportamento de um mancal de deslizamento hidrodinâmico — aquele em que um eixo gira sobre um filme de óleo que ele próprio bombeia ao girar, sem nunca tocar o metal do mancal. Ele reúne, num único número, as quatro variáveis que importam: S = (r ÷ c)²·(μ·N ÷ P), onde r/c é a razão entre o raio do eixo e a folga radial (tipicamente ~1000), μ é a viscosidade dinâmica do lubrificante, N a velocidade de rotação (rev/s) e P a pressão específica (a carga dividida pela área projetada do mancal). Conhecido S, as clássicas cartas de Raimondi-Boyd fornecem todas as características de operação do mancal: a espessura mínima do filme de óleo (a folga real entre eixo e mancal no ponto mais carregado, que não pode ser menor que a soma das rugosidades), a posição angular do eixo, o coeficiente de atrito, a vazão de óleo bombeada e a temperatura. A leitura física é direta: S baixo significa mancal muito carregado, lento ou com óleo fino — o filme afina e há risco de contato; S alto significa filme espesso e folgado. O projeto busca um S que garanta filme suficiente sem desperdiçar potência em atrito. Informe a razão r/c, a viscosidade, a rotação e a pressão.
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.
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