What a Vibration Isolator Has to Be Tuned To

Why this matters

An isolator is tuned, and the two things it is tuned to are the lowest forcing frequency the machine will ever produce in service and the load that lands on that individual mount. Both get missed the same way: the selection is made against the nameplate speed and against total weight divided by the number of mounts. In the machine below, that shortcut put two corners at a frequency ratio of 1.24, which is inside the amplifying region, so those two mounts delivered 1.86 times the force a solid steel block would have. The set was not underperforming. Two of its four mounts were making the problem, and the set is governed by its worst mount, not its average.

Before you release or reset a mount

A loaded spring isolator holds stored mechanical energy. Take the machine's weight on rigging or jacks and set cribbing under it before releasing any mount, stay clear of the plane a spring would travel in, and isolate and lock the machine under 29 CFR 1910.147 before starting.

Where a running measurement is needed to confirm a selection, keep every guard in place as 29 CFR 1910.212 requires, work from outside the rotating plane, secure sleeves and lanyards, and wear hearing protection wherever the space is at or above the 85 dB A-weighted eight-hour time-weighted average action level in 29 CFR 1910.95(c).

What the isolator is tuned to

Two relationships do the work, and both belong to the vibration-isolating-connection article, which derives them in full. They are stated here because everything below uses them.

Natural frequency. For an isolated machine treated as a mass on a spring, the natural frequency in Hz is about 3.13 divided by the square root of the isolator's static deflection in inches. That expression assumes an undamped single-degree-of-freedom system, the deflection measured under the load actually carried by that mount, and a supporting structure much stiffer than the isolator.

Transmissibility. Undamped, the fraction of force reaching the structure is 1 divided by the absolute value of (the frequency ratio squared, minus 1), where the frequency ratio is forcing frequency divided by natural frequency. Below a ratio of 1.41 the fraction exceeds 1 and the mount amplifies. At a ratio of 1 it is resonance.

What it is not tuned to. Airborne noise, which is a different path. The machine's own vibration amplitude, which softer mounting increases rather than decreases. And anything happening on a parallel rigid path, which the rigid-connection article covers and which sets a floor no selection can beat.

The selection input sheet, field by field

Every field here exists because a set has been installed wrong for want of it.

• Operating weight, in service. With water in the coils, refrigerant charged, oil at level, filters loaded. Not shipping weight.
• Load per mount, from the centre of gravity. Not total divided by count. The equipment submittal usually publishes corner loads; ask for them if it does not.
• Lowest forcing frequency in service. The lowest speed the machine will actually run at, including drive turndown, and any forcing component that sits below shaft speed such as a belt-pass frequency on a belt drive or a sub-synchronous order on a reciprocating machine.
• Required transmissibility at that frequency, from the specification. State it as a fraction and say at which frequency.
• Required static deflection, derived from the two above and rounded up to the next available mount, never down.
• Supporting structure and its own deflection at the mount location under the machine load.
• Restraint requirements and the snubber gap from the restraint submittal.
• Bypass paths identified, and how each is broken.
• Installed deflection, measured after the machine is running at operating weight.

The sheet, filled in

Machine. Rooftop air handler, operating weight 4,000 lb, four mounts, driven by a variable frequency drive.

Load per mount. The equipment submittal gives corner loads of 1,400 lb at the two mounts nearest the fan section and 600 lb at the other two. Two times 1,400 plus two times 600 is 4,000 lb, which checks against the operating weight.

Lowest forcing frequency in service. Design fan speed 900 rpm, drive minimum speed 300 rpm. The forcing frequency of interest is the once-per-revolution imbalance at the lowest speed the machine will run: 300 rpm is 5 Hz. The selection is made at 5 Hz, not at 15 Hz.

What the shortcut produced. Four identical mounts specified at total weight divided by four, so 1,000 lb each, at a rated 1.0 in deflection at 1,000 lb, giving a stiffness of 1,000 lb per inch.

• Heavy corners. 1,400 lb on 1,000 lb per inch is 1.4 in deflection. Natural frequency 3.13 divided by the square root of 1.4, which is 2.65 Hz. Frequency ratio 5 divided by 2.65 is 1.89. Transmissibility 1 divided by (1.89 squared minus 1), which is 1 divided by 2.57, which is 0.389.
• Light corners. 600 lb on 1,000 lb per inch is 0.6 in deflection. Natural frequency 3.13 divided by the square root of 0.6, which is 4.04 Hz. Frequency ratio 5 divided by 4.04 is 1.24, which is below 1.41. Transmissibility 1 divided by the absolute value of (1.24 squared minus 1), which is 1 divided by 0.538, which is 1.86.

Correction printed, which mount governs. The set does not average. The two light corners transmit 1.86 times the force a rigid mount would pass, and they are the path with the highest natural frequency and therefore the worst frequency ratio. The governing figure for the installation is the 4.04 Hz corner, not the 2.65 Hz one and not an average of the two. Reporting this set as "1 inch deflection mounts, natural frequency 3.13 Hz" would have been three separate errors in one line.

The correct selection. The specification calls for transmissibility of 0.10 or less at the lowest service speed.

• 1 divided by (ratio squared minus 1) equals 0.10 gives ratio squared equals 11, so ratio equals 3.317
• Required natural frequency: 5 divided by 3.317 is 1.507 Hz
• Required static deflection: (3.13 divided by 1.507) squared, which is 2.077 squared, which is 4.31 in

Correction printed, rounding direction. Round up to the next available mount, not to the nearest. The next standard nominal deflection is 5 in. Rounding down to 4 in would have given a natural frequency of 1.565 Hz, a ratio of 3.19 and a transmissibility of 0.109, which fails the specification by a hair while looking like it passes. Rounding on a number where an error costs somebody a complaint runs one way.

Correction printed, per-corner stiffness. Every mount has to reach the same 5 in deflection under its own load, which means two different springs, not one part number.

• Heavy corners: 1,400 lb divided by 5 in is 280 lb per inch
• Light corners: 600 lb divided by 5 in is 120 lb per inch

Correction printed, what happens if the light corners get the heavy spring. Put a 280 lb per inch mount under a 600 lb corner and it deflects 600 divided by 280, which is 2.14 in. Natural frequency 3.13 divided by the square root of 2.14, which is 2.14 Hz. Ratio 5 divided by 2.14 is 2.34. Transmissibility 1 divided by (5.48 minus 1), which is 0.223. Still isolating, and more than twice the specified figure, on a set that would look correct on a submittal review that only checked the part number appeared four times.

Result at the correct selection. Natural frequency 3.13 divided by the square root of 5, which is 1.40 Hz. Ratio at 5 Hz is 3.57. Transmissibility 1 divided by (12.75 minus 1), which is 0.085, inside the 0.10 requirement. At the 900 rpm design speed, 15 Hz, the ratio is 10.7 and transmissibility is about 0.0088.

Supporting structure. The deck's calculated deflection at the mount locations under the machine load is 0.30 in. Published guidance in the ASHRAE Handbook, HVAC Applications, sound and vibration control chapter, in the edition the specification names, is that isolator deflection should be several times the structural deflection at that point, commonly stated as a factor of at least five to ten. Five inches against 0.30 in is a factor of 16.7, so the much-stiffer-support assumption behind the natural frequency expression holds here. Where it does not, the machine and the deck become a two-mass system and the calculated frequency is wrong.

Restraints. Snubber gap per the restraint submittal, checked with a feeler gauge after the machine is at operating weight, because a snubber touching in normal operation is a rigid path.

Bypass paths. Power in a flexible whip with a service loop, condensate through a flexible section with slack, duct connections slack, curb seal compressible and not bearing. Each one is on the sheet with a sign-off, because a correct selection installed beside a rigid conduit produces the floor the rigid-connection article derives, regardless of any of the arithmetic above.

Installed deflection, measured. Free height minus installed height at each of the four mounts, taken after the machine is running at operating weight, recorded per corner. Anything more than a small variation between the two mounts that should match means the load is not where the submittal said it was.

Sibling-rule check. The natural frequency and transmissibility relationships are cited to the article that owns them, with their held-constant conditions restated, and no number in this example was introduced that the general section had not already stated. Both are applied at the lowest service frequency throughout, never at the design speed, and the 1.41 amplification threshold is the same one the sibling states, used in the same direction. The governing mount is named as the least-deflected one, which agrees with the resilient-layer article's rule that a stiffer element in the load path decides the result. Rounding on the required deflection went up, and the consequence of rounding down was printed rather than assumed. The bypass path result is cited rather than re-derived.

Two things that invalidate a correct sheet

A flexible supporting structure. The natural frequency expression assumes a support much stiffer than the isolator. A long-span deck has its own natural frequency, and where that sits near the forcing frequency the deck amplifies whatever reaches it. The field tell is a complaint that is worse at one spot on the floor below rather than directly under the machine, and no isolator selection fixes it.

Spring surge at high frequency. A steel coil spring is not a simple spring above its own internal wave frequencies. It passes high-frequency energy straight through, which is why a spring mount intended for a machine with high-frequency content is normally supplied with an elastomeric pad in series at its base. That pad is part of the selection, not an accessory, and leaving it out of a submittal is a real omission rather than a detail.

References

• 29 CFR 1910.147 for isolating and controlling the stored energy in a loaded isolator; 29 CFR 1910.212 for guarding during running measurements; 29 CFR 1910.95 for the occupational noise action level.
• ASHRAE Handbook, HVAC Applications, sound and vibration control chapter, in the edition the specification names, for isolator selection guidance including the relationship between isolator deflection and structural deflection; it binds by contract rather than as code.
• Isolator and restraint manufacturer submittal data, which owns the rated static deflection at rated load, the available deflection steps, the snubber gap and whether a base pad is supplied.
• Equipment manufacturer submittal data, which owns the operating weight and the published corner loads.
• See related: What a Vibration Isolating Connection Can and Cannot Do; Why a Rigid Connection Defeats an Isolator; What a Resilient Layer Is Actually Doing.