Vibration isolation

Check the mounts under a machine, or find the ones it needs: natural frequency on the mounts, transmissibility, isolation efficiency, the force passed into the structure and the amplitude through resonance on start-up — with the damping trade-off shown.

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INPUTSI · kg · kN/m · Hz

1 · Task I want to What is isolated

2 · Mass and frequency

Total mass M [kg] with base frame or inertia block Number of mounts

Disturbing frequency Unit

3 · Isolators From the catalogue Stiffness per mount k₁ [kN/m] Damping ratio ζ [%] steel springs: about 1 or less · elastomers: a few

4 · Excitation optional Disturbing force

Rotor mass [kg] Balance grade ISO 21940-11

Results update as you type. Isolation starts at r = √2; most installations aim well above it.

TRANSMISSIBILITY

f_n · ON THE MOUNTS5.03 Hz

r · FREQUENCY RATIO4.90

T · TRANSMISSIBILITY0.048

δ_st · STATIC DEFLECTION10 mm

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HOW IT'S CALCULATED · WITH YOUR NUMBERS

Step by step, with your numbers

01
Equilibrium████ ██ ███████ · ██████ = ██.██
02
Reactions████ ██ ███████ · ██████ = ██.██
03
Shear force████ ██ ███████ · ██████ = ██.██
04
Bending moment████ ██ ███████ · ██████ = ██.██
05
Deflection████ ██ ███████ · ██████ = ██.██
06
Stress████ ██ ███████ · ██████ = ██.██

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References: single-degree-of-freedom transmissibility (Rao, Mechanical Vibrations; Harris & Piersol, Shock and Vibration Handbook); ISO 21940-11 balance quality grades for the unbalance force.

ASSUMPTIONS & LIMITS

The machine (or the equipment with its base) is a rigid body; one vertical mode is considered. Rocking and horizontal modes are not — they matter when the centre of gravity is high or off the centroid of the mounts.
Mounts are linear springs in parallel with equal load per mount. For unequal loads, find the load per support with C-02 and size each mount for its own load.
The supporting structure is rigid compared with the mounts. A floor whose own natural frequency is near the disturbing frequency can undo the isolation — check it with C-14.
Viscous damping. Elastomers behave closer to hysteretic damping, which isolates better than this model predicts at high frequency ratios, so the result there is on the safe side.
Rubber mounts are stiffer under vibration than under static load. A natural frequency worked out from the static deflection is then too low — use the catalogue dynamic stiffness where it is given.
One disturbing frequency. Harmonics (2× running speed, blade-pass, gear mesh) are separate checks at their own frequencies.

DISCLAIMER · For education and preliminary sizing only. Results must be reviewed by a qualified engineer before use in design.

BEYOND ONE DEGREE OF FREEDOM

Rocking modes, flexible floors, inertia blocks and measured spectra — we model the whole installation.

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