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.
Resultado
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Eficiência de isolamento de vibração
A eficiência de isolamento traduz a transmissibilidade — um número técnico — para uma linguagem mais intuitiva: a porcentagem de vibração que o isolador consegue bloquear. Ela é I = (1 − TR) × 100%, onde TR é a transmissibilidade. A leitura é direta: uma transmissibilidade de 0,1 significa que 10% da vibração passa e 90% é isolada; TR = 0,05 dá 95% de isolamento, e assim por diante. Especificações de isolamento de máquinas costumam ser dadas justamente nesses termos ('isolamento mínimo de 90%'), e a partir da eficiência desejada o projetista trabalha de trás para frente: determina a transmissibilidade necessária, depois a razão de frequências r correspondente (lembrando que só há isolamento para r > √2), e finalmente a frequência natural — e, portanto, a rigidez dos isoladores — que coloca a frequência de operação da máquina na razão certa. Eficiências muito altas (acima de 95–98%) exigem isoladores extremamente macios (frequências naturais de poucos hertz), o que pode comprometer a estabilidade da máquina e exigir cuidado com a passagem pela ressonância na partida. Há sempre um compromisso entre isolamento, estabilidade e deslocamento estático aceitável. Esse cálculo é rotina no projeto de fundações de máquinas, no isolamento de equipamentos de precisão (microscópios, máquinas de medição) e no conforto de veículos. Informe a transmissibilidade.
Related Tools
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.
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.
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.
Ball Pass Frequency, Outer Race (BPFO)
Computes the ball pass frequency of the outer race (BPFO), the signature a localized defect on a bearing outer ring leaves in the vibration spectrum: BPFO = (number of elements ÷ 2) × shaft rotation frequency × (1 − element diameter ÷ pitch diameter × cosine of the contact angle). The result, in hertz, is the frequency at which a peak appears every time a ball or roller rides over the flaw; because it is not an integer multiple of shaft speed, it is distinguishable from unbalance and misalignment, which show up at 1× and 2× rotation. Since the races slip slightly, the measured frequency usually falls 1% to 2% below the theoretical one, so look for the band rather than the exact line. A 6205 deep-groove ball bearing has a BPFO near 3.6 times shaft speed, and it is always worth checking that BPFO plus the inner race frequency equals exactly the number of elements times the rotation frequency. Enter the number of rolling elements, the shaft rotation frequency, the rolling element diameter, the pitch diameter and the contact angle.
Stack Heat Loss (Siegert)
Calculate the heat loss through the exhaust gases by the Siegert formula, loss = K × (T_gas − T_air) ÷ CO₂, from the fuel factor K (~0.5 for natural gas, ~0.6 for oil), the gas and combustion air temperatures (°C) and the CO₂ percentage in the gases. The result, in %, is the largest energy loss of a boiler or furnace — the heat escaping hot through the stack. Lowering the gas temperature (with economizers and preheaters) and adjusting the excess air (which dilutes CO₂) minimizes this loss. The combustion efficiency is approximately 100% minus this loss. Enter the K factor, the temperatures and the CO₂.
Guitar String Vibration Frequency Calculator
Computes the fundamental frequency of a guitar string from vibrating length, tension and linear mass density via f = (1/2L) sqrt(T/mu).
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.