Isolator Static Deflection for a Target Isolation
Enter the running speed and the isolation efficiency you want, get the static deflection to specify for the mount.
Example
You enter
- Running speed (rpm) 900
- Target isolation efficiency (%) 90
You get
- Required static deflection 0.48 in
- Fn (Hz) 4.5227
- Ratio 3.3166
Details, formula, and sources
From T = 1 - efficiency, ratio = sqrt(1 + 1/T), fn = (rpm/60)/ratio, and deflection = (3.13/fn)^2 in. 90% isolation of a 900 rpm fan needs 0.48 in of deflection (a 4.5 Hz mount); tighten to 95% and it nearly doubles to 0.91 in - the softer the mount, the better the isolation, and this says how soft. Feeds straight back into the forward calculation. Undamped single-DOF; the isolator selection and the mechanical engineer govern.
T = 1 - efficiency/100; ratio = sqrt(1 + 1/T) (> sqrt(2)); fn = (rpm/60)/ratio Hz; deflection = (3.13/fn)^2 in.
ASHRAE Handbook -- Fundamentals, Sound and Vibration chapter, the single-degree-of-freedom vibration isolator (the classical Den Hartog transmissibility relation) solved for the required static deflection, by name.
The single-DOF isolator relations are standard vibration theory published in the ASHRAE Handbook -- Fundamentals and every mechanical-vibration text; inverting them for the deflection is public arithmetic.
Estimate. AHJ and licensed professional govern.
Field names used by the API: equipment_rpm, target_efficiency, deflection_in, fn_hz, ratio
- Inverse of the forward tile deflection = (3.13/fn)^2 with fn set so the frequency ratio meets the target transmissibility; feeding the result into vibration-isolation returns the target efficiencyASHRAE Fundamentals, Sound and Vibration
- sqrt(2) floor any real target efficiency gives a frequency ratio above sqrt(2), inside the isolating region; the softer the mount, the higher the efficiencysingle-DOF vibration theory