Vibration Isolator Resonance Transmissibility Case Study

This case study follows a supply fan skid that made the supporting floor vibrate after a mount replacement. The fan rotor was balanced, the bearings were healthy, and the motor current was normal. The hidden problem was that the replacement isolators were selected mainly by static load capacity, not by dynamic stiffness. Their natural frequency landed close to the fan running speed, so the mounts amplified transmitted vibration instead of isolating it.

The case teaches a practical mechanical engineering lesson: vibration isolation is not the same as putting a machine on soft-looking pads. The supported mass, mount stiffness, damping, forcing frequency, static deflection, pipe connections, frame flexibility, and validation measurements must work together.

Case Summary

Item	Engineering relevance
Machine	Belt-driven supply fan on a skid, installed above occupied technical space.
Operating speed	900\ \text{rpm} during normal duty.
Symptom	Floor vibration exceeded the site limit while fan casing vibration was moderate.
Initial suspicion	Rotor imbalance after maintenance.
Actual root cause	Isolator natural frequency was close to 1x running speed.
Hidden contributor	Rigid duct and pipe connections partly short-circuited the isolator system.
Corrective action	Lower mount stiffness, add flexible connectors, verify static deflection and operating transmissibility.

The central engineering question was:

Is the floor vibrating because the fan is generating excessive force, or because the support system is amplifying ordinary 1x force?

The evidence pointed to support-system amplification.

Initial Data

Use these simplified investigation values.

Quantity	Symbol	Value
supported fan skid mass	m	1600\ \text{kg}
number of mounts		4
installed stiffness per mount	k_m	3.2\ \text{MN/m}
total vertical stiffness	k	12.8\ \text{MN/m}
estimated damping ratio	\zeta	0.08
operating speed		900\ \text{rpm}
floor vibration limit		2.0\ \text{mm/s RMS}
measured floor vibration		4.8\ \text{mm/s RMS}
measured fan casing vibration		5.5\ \text{mm/s RMS}

The vibration spectrum showed a dominant 1x component at the operating speed. Phase was stable. Bearing fault bands and blade-passing components were not dominant. That made imbalance possible, but the high floor response relative to casing response suggested a support transmissibility problem.

Step 1: Forcing Frequency

Convert running speed to forcing frequency:

For a rotating machine, a 1x force at shaft speed is common. It can come from residual imbalance, eccentricity, pulley runout, aerodynamic asymmetry, or rotating assembly tolerances. The engineering question is whether the support system attenuates or amplifies that force.

Step 2: Installed Natural Frequency

For a simplified single-degree-of-freedom mounted skid:

Substitute:

The operating forcing frequency was:

So the speed ratio was:

Engineering Comment

This is too close to resonance. For isolation, the forcing frequency should normally be well above the mounted natural frequency. If r is near 1, the isolator system can amplify motion and transmitted force.

Step 3: Force Transmissibility

For a damped single-degree-of-freedom isolator, a common force transmissibility estimate is:

Using:

gives:

Numerator:

Denominator:

Therefore:

The installed mounts were not isolating the 1x force. They were amplifying transmitted force by roughly a factor of five in the simplified model.

Engineering Comment

The number should not be treated as exact, because real skids have frame modes, uneven mount loads, lateral stiffness, duct connections, and floor flexibility. It is still decisive: the selected mount stiffness placed the system in the amplification region.

Step 4: Static Deflection Check

Static deflection is:

Substitute:

So:

That deflection is small for a machine expected to be isolated at 15\ \text{Hz}. Stiff mounts can carry the load, but load capacity alone does not imply isolation performance.

Step 5: Corrected Mount Target

A practical target was to move the mounted natural frequency below:

That gives a speed ratio:

Required total stiffness:

Required stiffness per mount:

This is much softer than the installed:

mounts.

New static deflection:

So:

Engineering Comment

The corrected design requires more static deflection. That is not a flaw by itself, but it must be checked against alignment, belt tension, guards, seismic restraints, pipe flexibility, startup motion, and maintenance clearance.

Step 6: Corrected Transmissibility Estimate

With:

the transmissibility is:

So the corrected mount selection should transmit only about:

of the dynamic force in the simplified model.

The improvement ratio compared with the installed condition is:

In an ideal single-degree-of-freedom model, transmitted 1x force would fall to about 3% of the previous value. In the real installation, parallel paths through ductwork, pipework, electrical conduit, frame flexibility, and floor modes limit the achievable reduction.

Step 7: Short-Circuit Path Check

The investigation found that a rigid discharge duct and a tightly clamped drain line were bypassing part of the isolator motion. This matters because a vibration isolator works only if the machine can move slightly relative to the receiver structure.

The corrective package therefore included:

• flexible duct connector with correct slack and no hard contact at the frame;
• flexible drain section with strain relief;
• conduit loop with clearance through the expected static and dynamic motion;
• snubbers adjusted with clearance so they do not preload the skid in normal operation;
• alignment check after the new static deflection settled.

Without these checks, softer mounts could still fail because another stiff path would carry force into the floor.

Validation Results

After installing the corrected mounts and flexible connections, the team repeated startup, steady operation, and shutdown measurements.

Metric	Before correction	After correction	Acceptance
mounted natural frequency from bump test	14.2\ \text{Hz}	5.3\ \text{Hz}	below 5.5\ \text{Hz}
static deflection	1.2\ \text{mm}	9.4\ \text{mm}	within clearance plan
floor vibration at 900 rpm	4.8\ \text{mm/s RMS}	0.9\ \text{mm/s RMS}	below 2.0\ \text{mm/s RMS}
fan casing 1x vibration	5.5\ \text{mm/s RMS}	4.7\ \text{mm/s RMS}	no new machine fault indicated
duct connector contact	intermittent hard contact	none observed	pass
startup resonance dwell	strong floor response	brief controlled passage	pass

The measured reduction was smaller than the ideal transmissibility ratio because the real structure had residual parallel paths and floor response. It still met the engineering requirement.

Failure Mode Diagnosis

Evidence	Interpretation
dominant 1x frequency	rotating force was exciting the support system
stable phase	consistent forcing, not random looseness
natural frequency near running speed	mount system was near resonance
low static deflection	installed mounts were too stiff for isolation
floor vibration high relative to casing vibration	transmitted force, not only machine health, controlled the complaint
improvement after softer mounts and flexible connections	support transmissibility was the root cause

The diagnosis did not clear the machine forever. It showed that this event was primarily an isolation design and installation problem rather than a bearing or balance failure.

Risk and Maintenance Controls

The team updated the maintenance plan:

1. replacement mounts must be specified by stiffness, load range, static deflection, damping, temperature, and chemical compatibility;
2. speed changes must be checked against mounted natural frequency;
3. flexible connectors must be inspected after maintenance;
4. vibration acceptance must include both machine casing and receiver structure measurements;
5. bump-test natural frequency must be recorded after mount replacement or skid modification.

The simplified RPN changed from:

to:

Severity did not change because excessive floor vibration could still affect occupants, instruments, and fatigue-sensitive supports. Occurrence and detection improved because the new specification and validation checks directly target the failure mode.

Engineering Lessons

1. A mount selected only by static load can put the machine near resonance.
2. Isolation requires a speed ratio well above the mounted natural frequency, not simply a compliant material.
3. Static deflection is a useful quick check because it reflects stiffness.
4. Ducts, pipes, conduits, snubbers, and frames can short-circuit isolators.
5. Validation should measure source vibration and receiver vibration; one number cannot diagnose the path.

The transferable lesson is that vibration isolation is a system property. The mount, machine, forcing frequency, floor, attached services, and acceptance measurement must be reviewed together.