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.
Equivalent Static Load (Bearing)
Calculate a bearing's equivalent static load, P_0 = X_0·F_r + Y_0·F_a, from the radial load F_r (N), the axial load F_a (N) and the static factors X_0 and Y_0 (tabulated by the maker). Unlike the equivalent dynamic load (related to FATIGUE under rotation), the equivalent static load is used to check the bearing under loads with the bearing STOPPED or turning very slowly, or under PEAK loads (shocks, momentary overloads). The risk here is not fatigue but PERMANENT DEFORMATION (indentation) of the races by the rolling elements: an excessive static load 'dents' permanent marks (brinelling) into the races, which then cause noise, vibration and early failure when the bearing turns again. The equivalent static load is the pure radial load that would cause the same maximum permanent deformation (at the most-loaded contact) as the real radial-axial combination. It is compared with the bearing's static load rating C0 (also tabulated) via the static safety factor s0 = C0/P0. This check is especially important in bearings carrying loads with the machine stopped (shafts of equipment parked under load) or subject to shocks. Enter the radial load, axial load and the static factors X0 and Y0.
Load-Life Ratio (Bearing)
Calculate how a bearing's life changes when the load changes, L₂ = L₁·(P₁/P₂)^p, from the initial life L₁ (under load P₁), the loads P₁ and P₂ (N) and the exponent p (3 for balls, 10/3 for rollers). This relation expresses the essence of bearing life law: life is INVERSELY proportional to load raised to the exponent p. It lets you quickly answer, without recomputing everything, 'if I change the load, what happens to the life?'. And the answer is dramatic due to the high exponent: REDUCING the load by 20% (P₂ = 0.8·P₁) INCREASES life by (1/0.8)³ = nearly DOUBLE; INCREASING the load by 26% (P₂ = 1.26·P₁) halves the life; DOUBLING the load cuts life to 1/8. This extreme load sensitivity has important practical consequences: small overloads (from misalignment, imbalance, wrong mounting or inadequate clearance, which concentrate load) drastically cut the real life versus the calculated one — explaining why many bearings fail 'too early'. Conversely, reducing parasitic loads (better alignment, balancing) greatly extends life. This formula is a valuable tool for sensitivity analysis and failure diagnosis. Enter the initial life, the two loads and the exponent.
Cubic Mean Load (Bearing)
Calculate the equivalent mean load of a bearing under a cycle with two different loads, P_m = ∛(P₁³·U₁ + P₂³·U₂), from the loads P₁ and P₂ (N) and the time (or revolution) fractions during which they act U₁ and U₂ (with U₁ + U₂ = 1). Many bearings do not work under CONSTANT load: the load varies over the operating cycle (a press loading and unloading, a motor accelerating and decelerating, a machine with different work phases). To compute life in this case, the variable cycle is replaced by an equivalent CONSTANT load causing the same fatigue damage — the mean load. But the mean is NOT arithmetic: since fatigue damage is proportional to load CUBED (the life exponent p=3), the mean load is a time-fraction-weighted mean, but with the loads cubed (then cube-rooted) — the so-called cubic mean or 'fatigue-weighted mean'. This makes HIGH loads weigh disproportionately more (a double load causes 8× more damage), so even a small fraction of time at high load dominates the result. This formula (here for two load levels; it generalizes to several) is essential to size bearings in variable-load machines, avoiding underestimating the damage. Enter the two loads and their time fractions.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.