| name | vibration-isolation |
| description | Vibration isolation design — transmissibility, mount stiffness selection, damping optimization, active vs passive isolation, multi-axis isolation, machinery mounting, seismic isolation. |
| metadata | {"priority":7,"promptSignals":{"phrases":["vibration isolation","isolation mount","anti-vibration","transmissibility","vibration mount","machinery isolation","seismic isolation"],"minScore":4}} |
Vibration Isolation — Complete Skill
Isolation Principle
Isolation works by making system natural frequency f_n << excitation frequency f_exc
As r = f_exc/f_n → large: transmissibility T_R → 0 (less vibration transmitted)
CRITICAL: At r = 1 (resonance), T_R → ∞ (if ζ=0) — ALWAYS pass through quickly during startup
Transmissibility
T_R = √((1+(2ζr)²)/((1-r²)²+(2ζr)²))
Key values:
r = √2: T_R = 1 (isolation begins)
r = 2, ζ=0.05: T_R = 0.37 (63% isolation)
r = 3, ζ=0.05: T_R = 0.13 (87% isolation)
r = 5, ζ=0.05: T_R = 0.04 (96% isolation)
Isolation efficiency: IE = (1-T_R) × 100%
Mount Stiffness Selection
Required: r = f_exc/f_n ≥ r_target (e.g., 3 for 87% isolation)
Required f_n = f_exc/r_target
Required k = (2πf_n)² × m [N/m]
Or from static deflection:
f_n = 0.498/√(δ_st) [Hz, δ_st in meters]
δ_st_required = (0.498/f_n)² [m]
k = mg/δ_st [N/m]
Damping Selection
Isolation region (r > √2): Less damping → better isolation
Resonance region (r ≈ 1): More damping → safer startup/shutdown
Compromise: ζ = 0.05-0.10 (5-10%) for most industrial isolators
Rubber mounts: ζ ≈ 0.05-0.10
Pneumatic mounts: ζ ≈ 0.02-0.05 (very low, excellent isolation)
Wire rope: ζ ≈ 0.05-0.08 (bi-directional, aerospace)
Viscoelastic: ζ ≈ 0.1-0.3 (high damping, moderate isolation)
Common Excitation Sources and Frequencies
| Source | Frequency |
|---|
| 2-pole motor (60Hz supply) | 3600 rpm = 60 Hz |
| 4-pole motor (60Hz supply) | 1800 rpm = 30 Hz |
| 4-pole motor (50Hz supply) | 1500 rpm = 25 Hz |
| Reciprocating engine (4-cyl, idle) | ~20-30 Hz (2nd order) |
| HVAC fan | 600-1500 rpm = 10-25 Hz |
| Rotating imbalance: n rpm | n/60 Hz (1× per rev) |
| Gear mesh: N_teeth × n rpm | Gear mesh frequency |
Rubber Mount Types
| Type | Deflection | Load range | Applications |
|---|
| Pad isolator | 1-5mm | 50-5000N per mount | Pumps, generators |
| Sandwich mount | 3-12mm | 100-10000N | General machinery |
| Compression mount | 5-25mm | 100-100,000N | Heavy equipment |
| Shear mount | 5-20mm | Low-medium | Lateral isolation |
| Bobbin/bushing | Varies | Precision | Automotive, electronics |
| Air spring | 20-100mm | 1000-100,000N | Best isolation, adjustable |
Multi-Axis Isolation
Real machinery has 6 DOF: 3 translational + 3 rotational
Mounts placed symmetrically around CG:
- CG below elastic center: stable (self-leveling)
- CG above elastic center: unstable in pitch/roll — avoid
Mount layout for 4-mount system:
Place mounts at corners of rectangle, equidistant from CG (both x and y)
Coupled modes: if CG ≠ geometric center of mount pattern → coupling between translation and rotation
Decouple by: moving CG to geometric center (add mass), or using 3 mounts arranged around CG
Seismic / Earthquake Isolation
Building base isolation: large rubber bearings (lead rubber bearings, LRB)
f_n = 0.3-0.5 Hz (period T = 2-3 seconds, well below seismic content 1-10 Hz)
Response reduction: 3-10× vs. fixed base
Displacement: 200-500mm at bearings must be accommodated
Active Vibration Control
Sensor (accelerometer) → controller → actuator (piezo, voice coil)
Cancels vibration at source with inverse signal
Effective for narrow-band, low-frequency excitation (< 500 Hz)
Examples: active engine mounts, precision stage isolation, MEMS
Design Procedure
- Identify excitation frequency f_exc (rpm/60 or Hz directly)
- Specify required T_R (and therefore IE = 1-T_R)
- Calculate required r: from T_R formula, solve for r (with assumed ζ=0.07)
- Calculate required f_n = f_exc/r
- Calculate required static deflection: δ_st = (0.498/f_n)²
- Calculate required k = mg/δ_st (for total mass m supported)
- Calculate k per mount = k_total/N_mounts
- Select mount from catalog (k, load capacity, ζ)
- Verify resonance is passable: ζ > 0.05 ensures T_R < 10 at resonance
Output
Provide: f_n required [Hz], δ_st [mm], k per mount [N/mm], T_R achieved, IE%, recommended mount type.
