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.
Resultado
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Razão de excentricidade
Quando um mancal hidrodinâmico está sem carga, o eixo gira centrado no furo. Mas ao receber carga, o eixo se desloca para baixo (e lateralmente, por efeito da rotação do óleo), aproximando-se da parede do mancal — é exatamente essa aproximação que aperta o óleo de um lado e gera a pressão hidrodinâmica que sustenta a carga. A razão de excentricidade mede o quanto o eixo se deslocou: ε = e ÷ c, a excentricidade e (distância entre o centro do eixo e o centro do mancal) dividida pela folga radial c. O resultado vai de 0 a 1 e é uma das saídas mais importantes da análise do mancal: ε = 0 significa eixo perfeitamente centrado (carga nula); ε próximo de 1 significa que o eixo quase encosta no mancal (carga máxima, filme no limite). A relação com a espessura mínima do filme é direta e crucial: h_min = c·(1 − ε) — quanto maior a excentricidade, mais fino o filme no ponto crítico. Um mancal bem projetado opera com ε intermediário (digamos 0,6 a 0,8): excêntrico o suficiente para gerar boa pressão de sustentação, mas com folga mínima ainda segura (h_min > soma das rugosidades, para não haver contato). A excentricidade cresce com a carga e diminui com mais viscosidade ou rotação (que engrossam o filme). Informe a excentricidade e a folga radial.
Related Tools
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.
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 Radial Clearance
Calculate the radial clearance of a journal bearing, c = (D_bore − D_shaft) ÷ 2, subtracting the shaft diameter from the bearing bore diameter and dividing by two. The result is the radial space between shaft and bearing, where the lubricant oil film forms. Clearance is a critical design parameter: too small hampers film formation and heat dissipation (seizure risk); too large reduces load capacity and increases vibration and noise. A rule of thumb uses a radial clearance of about one thousandth of the diameter. Enter the bore and shaft diameters.
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