Vibration Transmissibility
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.
Resultado
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Transmissibilidade de vibração
O objetivo de um isolador de vibração (um coxim sob um motor, uma base de molas sob uma máquina) é impedir que a vibração da fonte chegue à estrutura de apoio — ou, ao contrário, proteger um equipamento sensível da vibração do piso. A transmissibilidade (TR) mede o quanto da vibração passa pelo isolador: para o caso não amortecido, TR = 1 ÷ |r² − 1|, onde r = f ÷ f_n é a razão de frequências (frequência de excitação dividida pela frequência natural do sistema isolado). A curva de transmissibilidade conta uma história crucial em três regiões. Para r < 1 (excitação abaixo da natural), TR > 1 — o isolador não isola nada, apenas transmite quase integralmente. Em r = 1 (ressonância), TR dispara ao infinito (sem amortecimento) — a pior situação possível, deve ser evitada a todo custo. Há um ponto-chave em r = √2 ≈ 1,41, onde TR = 1 (transmite o mesmo que sem isolador). E só acima de r = √2 começa o isolamento de verdade (TR < 1): quanto maior r, menor a transmissibilidade. A consequência prática é contraintuitiva: para isolar bem, o isolador deve ser macio (baixa frequência natural), de modo que a frequência de operação da máquina caia bem na região r ≫ √2. Isoladores rígidos demais (f_n alta) podem até amplificar a vibração. Por isso bases antivibratórias usam molas flexíveis e o sistema é projetado para que a rotação da máquina seja pelo menos 3 a 4 vezes a frequência natural. (Atenção: ao ligar e desligar, a máquina cruza a ressonância — daí a importância de algum amortecimento para limitar o pico nessa passagem.) Informe a razão de frequências.
Related Tools
Vibration Isolation Efficiency
Calculate the vibration isolation efficiency, I = (1 − TR) × 100%, from the transmissibility TR. The result, in %, shows how much of the source vibration is blocked by the isolator before reaching the supporting structure (or vice versa): TR = 0.1 corresponds to 90% isolation. High efficiencies require soft isolators (low natural frequency), so that the frequency ratio r is well above √2. It is the practical indicator to specify mounts and antivibration bases for machines, engines and sensitive equipment. Enter the transmissibility.
Rubber Apparent Compression Modulus
Computes the apparent compression modulus of a rubber block squeezed between two bonded plates, Ec = E₀ × (1 + 2 × k × S²), where E₀ is the Young's modulus of the compound, k is a numerical constant tabulated by hardness (running from about 0.93 for soft 30 IRHD rubber to 0.53 for hard 75 IRHD) and S is the shape factor, which for a circular block equals the diameter divided by four times the thickness. Rubber is essentially incompressible in volume, so what resists the load is not compression of the material but friction on the bonded faces, which stops the sides from bulging; that is why the apparent modulus can sit many times above the compound's own Young's modulus. The result, in megapascals, is what you use to get the vertical stiffness of the mount (stiffness = Ec × area ÷ thickness) and from there the natural frequency of the isolated system. Because the shape factor is S = D ÷ 4t and the dominant term goes with S squared, diameter and thickness are levers of equal weight and opposite sign: halving the thickness and doubling the diameter do exactly the same thing, and in the example both take the apparent modulus from 11.3 to 35.3 MPa — a thin mount is a stiff mount, and that ruins vibration isolation. Enter the compound's Young's modulus, the constant k, the block diameter and the thickness.
Shaft Critical Speed
Calculate the critical speed of a rotating shaft, ω_c = √(k ÷ m), from the shaft stiffness k and the rotor mass m. The result, in rad/s, is the rotational speed that coincides with the shaft's bending natural frequency — at it, any small unbalance causes large-amplitude resonant vibration that can damage the equipment. Shafts should run with a safe margin below the first critical speed (rigid rotors) or pass through it quickly to a range above (flexible rotors). It is an essential calculation in designing high-speed turbines, pumps and motors. Enter the stiffness and the mass.
Equivalent Stiffness (Springs in Parallel)
Calculate the equivalent stiffness of two springs in parallel, k_eq = k₁ + k₂, by adding the individual stiffnesses. The result, in the same unit (N/m), is always larger than the largest stiffness — springs in parallel are stiffer, since they share the load under the same displacement and the forces add. This is the case of mounts, isolators and supports placed side by side carrying the same component. Reducing spring assemblies to an equivalent stiffness is the first step to compute a vibrating system's natural frequency. Enter the two stiffnesses.
Amplification Factor (Q)
Calculate the resonance amplification factor (quality factor Q), Q = 1 ÷ (2·ζ), from the damping ratio ζ. The dimensionless result shows how many times the vibration amplitude at resonance exceeds the equivalent static deflection: lightly damped systems (small ζ) have high Q and sharp, dangerous resonance peaks; well-damped systems have low Q and smooth response. It is central to designing structures, machines and instruments to avoid destructive amplification and to characterizing the selectivity of filters and resonators. Enter the damping ratio.
Hand-Arm Vibration A(8)
Calculate the normalized hand-arm vibration exposure A(8), A(8) = a_w·√(t ÷ 8), from the resultant acceleration a_w (m/s²) and the exposure time t (hours). The result, in m/s², normalizes the exposure to an 8-hour shift, allowing comparison with the action and tolerance levels. Prolonged exposure to tool vibration (grinders, breakers, chainsaws) causes hand-arm vibration syndrome, with vascular and neurological damage. Enter the resultant acceleration and the exposure time.
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