Vibration Isolation Calculator: Transmissibility, Isolation Efficiency, Natural Frequency and Static Deflection of Machine Mounts

How well do the mounts isolate a machine from the floor?

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the machine mass, the number of mounts and the stiffness of each, and the running speed.

Enter the damping ratio of the mounts and the isolation you want.

The calculator gives the natural frequency, the transmissibility, the isolation efficiency and the static deflection needed to reach the target.

Formulas used

  • f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}}
  • TR = \sqrt{\frac{1 + (2\zeta r)^2}{(1 - r^2)^2 + (2\zeta r)^2}}
  • \delta_{st} = \frac{g}{(2\pi f_n)^2}

Worked example

With the default numbers in the calculator above:

  1. Total stiffness and natural frequency on the mounts: 4.5016 Hz (270.09 rev/min)
  2. Static deflection of the mounts under the weight: 12.26 mm
  3. Frequency ratio: the disturbing frequency over the natural frequency: 5.554 (disturbing frequency 25 Hz)
  4. Transmissibility: the share of the force that reaches the floor: 0.03832
  5. Isolation efficiency: 96.17 %
  6. Natural frequency needed for the target isolation (no damping, so slightly generous): 7.538 Hz, a frequency ratio of 3.317
  7. Static deflection needed for that: 4.372 mm of deflection under the weight

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What frequency ratio do I need to isolate vibration?

More than 1.414 (the square root of 2). Above that the mounts reduce the force. A ratio of 3 or more gives good isolation.

Why does stiffer not mean better?

Soft mounts have a low natural frequency, so a given running speed is further above it and more of the vibration is isolated.

What does damping do?

It limits the vibration at resonance, but it slightly reduces the isolation at higher speeds.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any vibration or machine dynamics text (vibration isolation and transmissibility).

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