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.
Resultado
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Razão de espessura de filme específica (λ)
Saber a espessura do filme de óleo não basta — o que importa é se esse filme é espesso o suficiente em relação à aspereza das superfícies. A razão de espessura de filme específica (lambda) faz essa comparação: λ = h_min ÷ √(Ra₁² + Ra₂²), dividindo a espessura mínima do filme lubrificante pela rugosidade combinada (a raiz da soma dos quadrados das rugosidades médias Ra das duas superfícies). O resultado, adimensional, diz quantas 'alturas de aspereza' cabem dentro do filme, e define diretamente o regime de lubrificação elastohidrodinâmica (EHL, típica de engrenagens e rolamentos, onde as pressões de contato são tão altas que deformam elasticamente as superfícies). A interpretação é clara: λ < 1 significa que os picos das asperezas se tocam através do filme — lubrificação limítrofe, com atrito e desgaste elevados e vida curta; 1 < λ < 3 é lubrificação mista, com contato parcial; e λ > 3 garante separação completa das superfícies, sem contato metal-metal, conduzindo a vida muito longa (fadiga de contato torna-se o único limitante). Projetar engrenagens e rolamentos para operar com λ acima de 2 ou 3 — escolhendo óleo de viscosidade adequada e superfícies bem acabadas (Ra baixo) — é uma das decisões mais importantes para a durabilidade. Informe a espessura mínima do filme e as rugosidades das superfícies.
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.
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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