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.
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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.
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Calculate the transmissibility of an undamped vibration isolator, TR = 1 ÷ |r² − 1|, from the frequency ratio r = f ÷ f_n (excitation frequency over natural frequency). The dimensionless result is the fraction of force (or motion) transmitted through the isolator: TR < 1 means isolation (the transmitted vibration is less than the applied one), which only occurs for r > √2. Near r = 1 (resonance), TR spikes; the higher r, the lower the transmissibility and the better the isolation. It is the key criterion in designing antivibration mounts. Enter the frequency ratio.
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