Why an Isolator Can Make Vibration Worse
Why this matters
A shop replaces hard mounts with springs and the complaint gets louder. The customer concludes the springs are defective and the shop concludes the customer is difficult, and neither is right. An isolator is not a damper and it is not a sponge. It is a spring that moves the assembly's natural frequency, and there is a band of disturbing frequencies where a spring delivers MORE force to the structure than a rigid mount does. Inside that band the correct product, correctly installed, correctly deflected, makes the problem worse by design. This card states the gate that separates the two regions and runs one machine through it at two speeds, where it resolves opposite ways.
The gate, stated once
An isolator isolates only where both of these hold, at every speed the machine is permitted to run:
- The frequency ratio exceeds the square root of 2. The ratio is the disturbing frequency divided by the mounted natural frequency, both in Hz. Below that value the isolator amplifies. At exactly that value it transmits the full force and buys nothing.
- The support is stiff relative to the mount. In practice, the isolator's static deflection under the load is large compared with the support structure's own deflection under the same load, a factor of about ten being the common working figure. Where it is not, the termination the arithmetic assumes does not exist.
Both conditions belong to the relationship the arithmetic comes from. For a single mass on a linear spring, moving vertically, lightly damped, on a rigid support, transmissibility is one over the absolute value of the quantity r squared minus one. Above the square root of 2 that returns a fraction, which is isolation. Below 1 it returns a number greater than one, which is amplification. Neither condition is a detail; each one on its own can invert the answer.
What amplification actually costs
At a ratio of 1.0 the undamped expression goes to infinity, which is the mathematics telling you that only damping and non-linearity limit the peak. Manufacturers' own data for a lightly damped steel spring commonly shows resonant amplification of roughly an order of magnitude; an elastomeric mount, which carries far more internal damping, peaks lower and broader. The specific figure belongs to the mount's published dynamic data, not to a rule of thumb, and the direction is what matters here: less damping means better isolation at high ratios and a worse peak at resonance. That trade is the whole reason snubbers and restrained mounts exist.
The practical consequence is that a machine sitting near its mounted resonance is not merely un-isolated. It is a force multiplier bolted to the customer's structure.
One machine, two speeds, two outcomes
Say a two-speed cooling tower fan, full speed 350 rpm and low speed 175 rpm, on a steel dunnage frame over a slab, mounted on spring isolators whose actual deflection under the actual load share is 1.00 in. Deflection of 1.00 in gives a mounted natural frequency of about 3.13 Hz, using the inch form of the deflection relationship, which holds for a single mass on a linear spring in the vertical mode on a rigid support.
High speed. Shaft rotation is 350 divided by 60, or 5.83 Hz. Ratio is 5.83 over 3.13, which is 1.86. That clears the square root of 2, so the gate's first condition passes. Transmissibility is one over the quantity 3.46 minus 1, which is 0.41. That is 59 percent isolation - poor, but genuinely isolation, and the direction of the effect is correct.
Low speed. Shaft rotation is 175 divided by 60, or 2.92 Hz. Ratio is 2.92 over 3.13, which is 0.93. That is below 1, so the gate's first condition fails. Transmissibility is one over the absolute value of 0.87 minus 1, which is one over 0.13, or 7.7. Undamped, the mount delivers roughly 7.7 times the exciting force to the dunnage. The building gets a low-frequency thump on low speed that it did not get on high speed, on the same hardware, with nothing broken.
Support condition, checked rather than assumed. The frame plus slab deflects a small fraction of an inch under the tower's weight, against 1.00 in at the isolator, so the second condition passes at both speeds. That check is what lets the transmissibility figures above stand at all; on a long-span framed floor it would not pass and the arithmetic would not apply.
Sibling-rule check. The isolator-selection card states that field one of the selection sheet is the LOWEST disturbing frequency in the permitted operating range. This example is exactly that rule being violated: the mount was selected against 5.83 Hz, and the machine is permitted to run at 2.92 Hz. Nothing here contradicts the selection card, it demonstrates the cost of skipping its first field. No transmissibility figure below a ratio of the square root of 2 has been reported as isolation anywhere above.
The correction, and its honest limit
Reselect against 2.92 Hz. A ratio of 3 at that frequency needs a mounted natural frequency of 0.97 Hz, which needs a static deflection of about 10.4 in. That is not a practical steel spring for this application, and saying so is more useful than pretending otherwise.
What is achievable: a 4.00 in actual deflection mount gives a natural frequency of about 1.56 Hz. At low speed the ratio becomes 1.87, transmissibility 0.40, so 60 percent isolation - essentially the performance the original mount gave at high speed, and critically, on the isolating side of the gate rather than the amplifying side. At high speed the ratio becomes 3.73, transmissibility 0.078, so 92 percent. One reselection turns an amplifier into a modest isolator across the whole range.
Where deflection runs out, the remaining moves are not isolation moves at all. Restrict the drive so the machine cannot dwell in the band around resonance, address the exciting force at source by balancing the rotating assembly, or accept a stiffer mount and treat the structure. Choosing between those is a design decision, not a field one.
If the correction is a drive setting, treat it as an instruction that changes the machine. Setting a skip band or a minimum speed in a drive is work inside energized control equipment: de-energize and follow 29 CFR 1910.333(b)(2) for the electrical hazard where you are opening the drive enclosure, and confirm with the equipment manufacturer that the new minimum speed does not starve a bearing, a seal flush or a motor's own cooling before you commit it. A speed limit that protects the structure and cooks a motor is not a fix.
The other three routes into the amplifying region
The two-speed case is the obvious one. Three quieter routes reach the same place.
Every start and every stop. A machine coasting up or down passes through its mounted resonance. That is unavoidable and normally harmless because the dwell is short, but on a machine that starts many times an hour, or one whose coast-down is long, the resonant excursion is what breaks flexible connections and loosens fasteners. This is where mount damping and travel-limiting snubbers earn their place, and it is the one condition where an elastomeric mount can beat a spring.
Variable speed added after handover. A drive retrofitted to a constant-speed machine, or a setpoint turned down for energy savings, silently moves field one of the original selection. Nobody re-runs the arithmetic because nobody thinks of a setpoint as a mechanical change.
A soft support. Where the structure's deflection under load is comparable to the isolator's, the assumed rigid termination is gone and the floor participates in the motion. The symptom is a complaint that moves around the floor plate rather than sitting under the machine, and it is diagnosed by measuring the floor's own response, not the machine's. That case is a structural engineering question and should be routed to one rather than solved with a bigger spring.
How to tell amplification from a plain un-isolated installation
Both feel like a machine that is not isolated. They are distinguished by how the level behaves when something changes.
Change speed and watch the direction. An un-isolated machine gets worse as speed rises. A machine sitting near mounted resonance gets BETTER as speed rises away from the resonance, and worse as speed falls toward it. That reversal is the fingerprint, and it is the reason the two-speed case above is worth carrying whole: at 5.83 Hz the same hardware is doing its job and at 2.92 Hz it is doing the opposite.
Compare the machine's motion with the structure's. On a working installation the machine moves visibly more than the structure does. Near resonance both move and the phase relationship between them is what a sibling card on reading a vibration signature exists to interpret; use it there rather than guessing from amplitude alone.
Measure the deflection rather than trusting the schedule. Free height minus installed height at each mount, with a scale. A mount reading half the deflection you expected has a natural frequency about 1.4 times higher than you expected, because natural frequency goes with the inverse square root of deflection at constant support stiffness, and that shift alone can drag a marginal selection down into the amplifying band.
Where the machine is running for any of these checks, hearing protection and guarding are not optional accessories to the measurement: keep every belt and coupling guard in place while the machine turns, and where the measurement position sits at or above the 29 CFR 1910.95 action level for your own exposure time, wear the protection the program specifies for that position.
References
- ASHRAE Handbook chapters on sound and vibration control, for the transmissibility relationship and the assumptions it is derived under
- Isolator manufacturer's published dynamic data, which owns the resonant amplification figure for a specific mount and its damping
- 29 CFR 1910.333(b)(2), electrical safe work practices where a drive enclosure is opened to change a speed limit
- 29 CFR 1910.95, occupational noise exposure, where measurement positions put a technician in the exposure
- See related: What a Vibration Isolating Connection Can and Cannot Do, which follows one rooftop unit whose isolators became amplifiers after a drive retrofit; How to Select an Isolator From the Disturbing Frequency; What an Inertia Base Adds Beyond Mass; Reading a Vibration or Sound Signature as Its Own Diagnostic Method