Machine Vibration Isolation Screening Worksheet
For one harmonic force acting on a rigid mass supported by ideal linear springs and viscous dampers, solve the frequency ratio required to meet a user-specified force-transmissibility target. The worksheet does not certify an isolator, machine, foundation or installation.
Define the idealized operating case
Select units first. US customary inputs use avoirdupois pounds mass and pounds-force. Changing the unit selector reinterprets—not converts—numbers already entered. Enter peak, RMS or peak-to-peak force consistently;the transmitted force has the same amplitude convention.
Required frequency ratio
Required undamped natural frequency
Target transmitted-force amplitude
Total vertical stiffness
Per-mount stiffness
Static deflection
Static load per mount
Total viscous damping coefficient
Steady relative displacement amplitude
Equations and dimensional basis
| Ilość | Equation | Meaning and limitation |
|---|---|---|
| Transmisyjność siły | T=√[(1+(2ζr)²)/((1−r²)²+(2ζr)²)] | Linear viscously damped SDOF under a harmonic applied force;T=Ftrans/F0. |
| Required isolation-branch ratio | x=r²;T²x²+[T²(−2+4ζ²)−4ζ²]x+(T²−1)=0 | The larger positive root is used. At ζ=0,this reduces to r=√(1+1/T). |
| Frequencies | f=n/60; fn=f/r; ωn=2πfn | fn is the undamped natural frequency of the ideal model. |
| Sztywność | kcałkowity=mωn²; kmount=kcałkowity/N | Per-mount division assumes identical mounts and equal load/stiffness. |
| Tłumienie | ccałkowity=2ζmωn | Equivalent linear viscous coefficient;not a universal material property. |
| Static quantities | δst=mg₀/kcałkowity; Wmount=mg₀/N | Uses g₀=9.80665 m/s² and the same linear vertical stiffness. |
| Harmonic response | D=√[(1−r²)²+(2ζr)²]; X=F₀/(kcałkowityD); Ftrans=TF₀ | Steady-state amplitude only;no startup,shutdown,shock or multi-harmonic response. |
Internal calculations use kg,N,m,N/m and N·s/m. Exact definitions:1 lbm=0.45359237 kg and1 lbf=4.4482216152605 N. Therefore1 N/m=0.00571014715476285 lbf/in.
Co skorygowano
The former page inverted the undamped formula T=1/(r²−1) but described the result as a complete isolation design. It did not ask for damping even though its own text acknowledged that damping controls resonance and worsens high-frequency isolation. Fixed 0.20,0.10,0.05,0.03 and0.01 targets were presented as generic machinery recommendations without a controlled project or normative source. They have been removed.
The exciting-force input was labelled “unbalance force”,although it could be any harmonic force amplitude and the page did not derive it from residual unbalance. The new wording separates the force-isolation screen from ISO 21940 balance-quality calculations. Approximate pound conversions,9.81 m/s²,prefix-tolerant parsing,pre-filled results and quick presets were also removed.
Source and applicability boundary
MIT 16.07 Dynamics, Lecture D33: Forced Vibration gives the damped force-transmissibility relation used here and shows the damping tradeoff above r=√2. The algebraic inversion for r is derived on this page from that general engineering equation;it is not an ISO formula.
ISO 2017-1:2005,edition1,is published and was last confirmed in2019;the ISO lifecycle currently shows stage90.60 (close of review). Its public scope concerns the technical information exchanged among users,manufacturers and suppliers when applying resilient mounting systems. It does not establish the former universal target percentages. Exact clauses and required data fields need the licensed standard and are marked NEEDS_LICENSED_SOURCE.
NIST SP811 Appendix B supplies the exact pound and inch/foot conversion basis used for SI/US equivalence tests.
Information still needed before selection
- Supported mass,centre of gravity,rotary inertia and load carried by each mount.
- All excitation harmonics and force/moment amplitudes across startup,normal operation,variable speed and shutdown.
- Dynamic—not merely static—stiffness and damping versus preload,frequency,amplitude,temperature,ageing and tolerances.
- Six-degree-of-freedom natural frequencies,coupled modes,support/foundation flexibility and piping/duct/cable forces.
- Allowable motion,clearances,snubbing,shock/seismic/wind restraint,stability,creep,fatigue and environment.
- Acceptance criteria and commissioning measurements agreed by the responsible parties.
