Isolation Principles & Techniques — Abridged Guide
Quick-reference guide to vibration isolation — natural frequency, transmissibility, passive and active methods, VC criteria, and system selection. For full derivations and worked examples, see the Comprehensive Guide.
Comprehensive Isolation Principles Guide →
1.Introduction to Vibration Isolation
Vibration isolation prevents mechanical energy from reaching sensitive payloads by introducing a compliant element (isolator) between the vibration source and the equipment. Isolation is distinct from damping — isolation blocks energy transmission; damping dissipates energy already present.
The three isolation strategies in order of increasing performance (and cost): passive (pneumatic springs), active (sensors + actuators), hybrid active-passive. Most optical labs need only passive pneumatic isolation.
Precision optical systems — interferometers, lithographic tools, scanning probe microscopes — require nanometer-level position stability. Building vibrations at 5–50 Hz are the primary threat, transmitted through the floor into equipment supports. Isolation systems create a mechanical low-pass filter that attenuates these disturbances above a characteristic natural frequency.
2.Isolation Theory — SDOF Model
Natural Frequency
Natural Frequency from Static Deflection
The SDOF mass-spring-damper model captures the essential physics of all isolation systems. The natural frequency f_n sets the boundary between amplification (below √2·f_n) and isolation (above √2·f_n). Lower f_n = wider isolation bandwidth.
A 1 Hz natural frequency requires ~250 mm of effective static deflection — this is why pneumatic (air spring) isolators dominate precision applications. No practical mechanical spring can achieve this compliance in a compact package.
3.Transmissibility and Isolation Efficiency
Transmissibility
Isolation Efficiency
Transmissibility T = payload motion / floor motion. At the resonance peak, T ≈ 1/(2ζ). Above √2·f_n, T drops below 1 and the system isolates. Rolloff is −40 dB/decade undamped, but degrades to −20 dB/decade with significant damping.
The √2·f_n crossover is the hard floor — no SDOF system isolates below this frequency. For f_n = 1.5 Hz, isolation begins above ~2.1 Hz. Use the existing Transmissibility Calculator to visualize curves interactively.
| Regime | Frequency Range | T Value | Effect |
|---|---|---|---|
| Amplification | f < √2·f_n | > 1 | Payload vibrates MORE than floor |
| Crossover | f = √2·f_n | = 1 | No isolation, no amplification |
| Isolation | f > √2·f_n | < 1 | Payload vibrates LESS than floor |
4.Multi-DOF and Coupled Systems
Rocking Mode Frequency
Real payloads have 6 DOF (3 translational + 3 rotational). Rocking modes (pitch/roll) are often the lowest-frequency modes and can be more damaging to beam alignment than translational vibration. Symmetric isolator placement and CG alignment decouple the modes.
If heavy instruments are loaded asymmetrically on a table, reposition equipment or add ballast to center the CG over the isolator support pattern. Pneumatic self-leveling valves compensate for static load differences but cannot fix CG-induced mode coupling.
5.Damping Strategies
TMD Optimal Tuning (Den Hartog)
Broadband damping (viscous, constrained-layer) attenuates uniformly but limits rolloff to −20 dB/decade. Tuned mass dampers target specific resonances with deep notches while preserving −40 dB/decade rolloff elsewhere. Choose broadband for general-purpose work; choose tuned for fixed installations with known problem frequencies.
Broadband-damped tables settle faster after impulse disturbances (door slams, bumps). Tuned-damped tables provide better steady-state isolation at target frequencies. If your lab has both transient and persistent vibration problems, consider a table with both treatments.
| Feature | Broadband | Tuned (TMD) |
|---|---|---|
| Bandwidth | Wide (all frequencies) | Narrow (target resonance) |
| Resonance suppression | Moderate (3–10×) | Deep (notch at target) |
| HF rolloff | −20 dB/decade | −40 dB/decade |
| Settling time | Fast | Slower |
| Tuning needed | No | Yes |
| Payload sensitivity | Low | High (detunes with mass change) |
6.Passive Isolation Methods
Pneumatic Isolator Stiffness
Pneumatic (air spring) isolators are the standard for precision photonics — they achieve f_n = 1–3 Hz, support 50–2000 kg per unit, and provide automatic self-leveling. Elastomeric mounts (f_n = 8–25 Hz) are for machinery isolation, not precision optics. Mechanical springs (f_n = 3–10 Hz) are intermediate.
Always size pneumatic isolators to 60–80% of rated load capacity. This leaves margin for future payload additions without exceeding the rated range.
| Type | Typical f_n (Hz) | Best For |
|---|---|---|
| Pneumatic (air spring) | 1–3 | Optical tables, precision instruments |
| Mechanical spring | 3–10 | Moderate isolation, no compressed air |
| Elastomeric mount | 8–25 | Machinery, pumps, HVAC |
| Pendulum | 0.5–2 (horiz.) | Specialized low-frequency horizontal |
7.Active Isolation Systems
Active isolation uses sensors (geophones, accelerometers), a controller, and actuators (voice coils) to cancel vibration below the passive system’s natural frequency. Hybrid active-passive systems extend effective isolation to 0.5–0.7 Hz — below the ~1.5 Hz limit of passive pneumatic systems alone.
Active isolation is justified when the site has significant vibration below 2–3 Hz, or when the application demands VC-E or better. For most optical labs at VC-C or VC-D, passive pneumatic isolation is sufficient and far less expensive.
8.Isolation System Design Parameters
The four critical design parameters are: (1) load capacity (size for 60–80% of rated), (2) natural frequency (lower is better, limited by stability and settling time), (3) settling time (0.5–2 s for general optics, <0.3 s for production), (4) CG alignment (symmetric loading decouples modes).
When specifying isolators, budget the total payload mass including the table, all instruments, all mounts and posts, and any anticipated future additions. Underestimating payload mass raises the natural frequency above the design target.
9.Environmental Considerations
Floor vibration measurement is step one of every isolation design. The IEST Vibration Criterion (VC) curves classify environments from VC-A (50 µm/s, optical microscopy) to VC-G (0.78 µm/s, next-gen nanotech). Site selection (ground floor, slab-on-grade, away from HVAC) is often more impactful than upgrading isolation hardware.
Ground floor slab-on-grade is always the best choice for vibration-sensitive equipment. If you must use an upper floor, measure the floor vibration spectrum before committing — upper floors can amplify building vibrations 10–100× at the floor’s structural resonance.
| Criterion | Max Velocity (µm/s) | Typical Use |
|---|---|---|
| VC-A | 50 | Optical microscopes (400×) |
| VC-B | 25 | Optical microscopes (1000×) |
| VC-C | 12.5 | Lithography ≥1 µm, confocal |
| VC-D | 6.25 | Sub-µm lithography, interferometry |
| VC-E | 3.1 | E-beam litho, SPM |
| VC-F | 1.56 | Demanding TEM/SPM |
| VC-G | 0.78 | Next-gen nanotechnology |
10.Performance Metrics
RMS Displacement from PSD
Isolation performance is verified by measuring compliance spectra (displacement/force vs. frequency) and payload vibration PSD. RMS displacement is calculated by integrating the PSD over the frequency band of interest. Results are compared to VC curves using 1/3-octave band analysis.
When comparing manufacturer compliance specs, ensure both use the same measurement conditions (excitation point, measurement point, frequency range). Compliance measured at a table corner is always higher than at the center.
11.Selection Workflow
1
Characterize environment
Measure floor vibration; classify against VC curves.
2
Define requirements
Determine equipment vibration sensitivity (VC level or RMS limit).
3
Choose strategy
Passive (f_n > 1.5 Hz adequate), active (need < 1 Hz), or hybrid.
4
Size components
Select isolators for load, f_n, and CG alignment.
5
Verify performance
Measure transmissibility and payload vibration after installation.
The five-step selection workflow: (1) Measure floor vibration → (2) Define equipment vibration requirements → (3) Choose strategy (passive / active / hybrid) → (4) Size and select components → (5) Verify installed performance.
Start with the environment, not the equipment catalog. The most common mistake is selecting isolators before measuring the floor — resulting in either over-specification (wasted budget) or under-specification (failed performance).
Continue Learning
Comprehensive Guide →Isolation System Designer →Transmissibility Calculator →Vibration Unit Converter →
The Comprehensive Guide includes 7 worked examples, 7 SVG diagrams, 4 data tables, and 10 references.