How to Select an Isolator From the Disturbing Frequency

Why this matters

Isolators get picked off a chart by equipment type, and then the tenant below still feels the fan. The chart was not wrong, it was answering a different question. An isolator does exactly one thing: it puts a soft element between a machine and a structure so that the ratio of the machine's lowest disturbing frequency to the mounted assembly's own natural frequency is large. Everything else on the selection sheet - the spring, the pad, the housing, the restraint - is a means of hitting a deflection. This card fills in that sheet field by field, and the field most often filled in wrong is the deflection, because the catalogue prints a rated one and the mount delivers an actual one.

The sheet has six fields, and they are filled in this order

Field 1: the lowest disturbing frequency, in Hz, with the operating condition that produced it. For rotating equipment this is shaft speed. A motor's nameplate speed is its speed at rated load; slip falls as load falls, so a lightly loaded machine turns faster than nameplate. Take the lowest speed in the operating range, because a lower disturbing frequency gives a smaller frequency ratio and less isolation, and a rounding that asks for more is the only kind allowed here.

Field 2: the target transmissibility at that frequency. Transmissibility is the fraction of the exciting force that reaches the structure. Isolation efficiency is one minus that, as a percentage. Ninety-five percent is a common design intent for mechanical equipment over occupied space; a slab on grade in a warehouse rarely needs it and a recording space needs more. The number belongs to the project, not to the equipment.

Field 3: the required natural frequency, from the ratio.

Field 4: the required static deflection, from the natural frequency.

Field 5: the actual load at each mount, from the equipment manufacturer's weight distribution, not from total weight divided by the mount count.

Field 6: the isolator whose ACTUAL deflection under that actual load matches field 4 - which is not the same as the isolator whose rated deflection matches field 4.

The two relationships, each with what it holds constant

Natural frequency from deflection. For a single mass on a linear spring, moving in the vertical mode only, on a support that is rigid relative to the mount, and lightly damped, the mounted natural frequency in Hz is about 3.13 divided by the square root of the static deflection in inches. One inch gives about 3.13 Hz, two inches about 2.21 Hz, four inches about 1.56 Hz. The constant 3.13 already contains gravity in inches per second squared, so it is an inch formula and does not survive a switch to millimetres.

Notice what is absent from that expression: mass. Two machines of very different weight sitting at the same static deflection have the same natural frequency. This is the single most useful fact in isolator selection and it is the reason a sibling card on inertia bases exists.

Transmissibility from the frequency ratio. With r as the disturbing frequency divided by the mounted natural frequency, and with light damping and a rigid support, transmissibility is approximately one over the quantity r squared minus one, for r above the square root of 2. Below that ratio the same relationship returns a value greater than one, meaning amplification, and that region is owned by a sibling card rather than re-derived here. Damping reduces the peak at resonance and slightly worsens transmissibility at high ratios; a lightly damped steel spring outperforms a heavily damped elastomer once you are well up the ratio, which is why the damping question is decided after the ratio, not before.

Worked selection: a fan over a tenant space

Say the schedule gives a centrifugal fan on a welded steel frame, operating weight 1,850 lb, direct drive on a four-pole motor with a nameplate speed of 1,160 rpm at rated load, sitting on a slab on grade with an occupied tenant space adjacent rather than below.

Field 1. The lowest disturbing frequency is shaft rotation at rated load: 1,160 rpm divided by 60 is 19.3 Hz. Lightly loaded the shaft turns nearer 1,190 rpm, or 19.8 Hz. Use 19.3 Hz, the lower figure, because it produces the smaller ratio.

Field 2. Target 95 percent isolation at 19.3 Hz, so transmissibility 0.05.

Field 3. One over the quantity r squared minus one equals 0.05, so r squared minus one equals 20, r squared equals 21, r equals 4.58. Required natural frequency is 19.3 divided by 4.58, which is 4.21 Hz.

Field 4. Static deflection is 3.13 divided by 4.21, squared: 0.744 squared, or 0.55 in.

Field 5, printed as its own correction line. Total weight 1,850 lb over four mounts is 462 lb nominal. The manufacturer's weight distribution gives 620 lb at each of the two motor-end mounts and 305 lb at each of the other two. Check: two at 620 plus two at 305 is 1,850. The nominal 462 lb figure is now discarded; it never described any mount on this machine.

Field 6, printed as its own correction line. A spring rated 1.00 in deflection at 700 lb capacity is not a 1.00 in spring at 620 lb. It is a linear element, so actual deflection is 620 over 700 times 1.00, which is 0.886 in. Rated deflection is a point on the spring's curve at its rated load, and selecting against it rather than against actual load is the most common error on this sheet.

Result at the heavy end. Deflection 0.886 in gives 3.13 over the square root of 0.886, which is 3.33 Hz. Ratio is 19.3 over 3.33, or 5.80. Transmissibility is one over 32.6, or 0.031, so 96.9 percent isolation. Comfortably past target.

Result at the light end if the same spring is used. At 305 lb that spring deflects 305 over 700 times 1.00, or 0.436 in. Natural frequency is 3.13 over 0.660, or 4.74 Hz. Ratio is 4.07, transmissibility is one over 15.6, or 0.064, which is 93.6 percent. Below the 95 percent this project asked for, on the same machine, with the same catalogue part, because the load share differed.

The correction that fixes it. Select for equal deflection, not equal spring. A spring rated 1.00 in at 350 lb, loaded to 305 lb, deflects 0.871 in, giving 3.35 Hz, a ratio of 5.75, transmissibility 0.031, and 96.9 percent. Both ends now sit at essentially the same natural frequency, which also keeps the frame level and stops the assembly rocking about its short axis.

Structure check, printed because the transmissibility relationship depends on it. Slab on grade, no measurable deflection under the unit's weight, so the rigid-support condition the relationship was derived under holds at this site. On a long-span framed floor it would not, and the sibling card on amplification governs instead.

Sibling-rule check. Every frequency here is stated in Hz with the operating condition that produced it. Nameplate speed is treated as the speed at rated load and the lightly loaded case is faster, consistent with the motor cards. The natural frequency comes from actual deflection under actual load, never from mass, consistent with the inertia-base card. No transmissibility figure below a ratio of the square root of 2 is quoted as isolation. The one rounding choice made, 19.3 rather than 19.8 Hz, runs in the conservative direction.

Getting the machine onto the mounts without hurting anyone

A loaded spring mount is a stored-energy device. Keep the rigging attached and load-bearing until the full weight is on all mounts and the leveling bolts are backed off in sequence, keep hands out of the closing gap between the equipment rail and the mount housing while the load transfers, and back the shipping restraints off in the order the isolator manufacturer's instruction sheet gives rather than cutting them. Where the machine is lifted, the rigging plan and the load path are their own subject; do not improvise one to save a trip. If the unit is on a roof or a platform, fall protection under 29 CFR 1910.28 applies to the whole of the work, including the part where you are lying down reading a gap with a scale.

How to verify the selection after it is installed

Measure, do not assume. Three checks, each of which can fail independently.

Free height minus installed height, at every mount, with a scale. That difference is the actual static deflection. Compare it against the figure you computed in field 6. A mount reading materially less than computed is carrying less load than the distribution said, which usually means the frame is bridging or the mount is bottomed against its housing.

Level and rock. Push the assembly by hand at the top and let it settle. It should return without a rocking mode that persists. A pronounced rock means the mounts are not at matched deflection or the centre of gravity is high relative to the mount spacing.

Nothing else touching. Walk the machine and confirm no conduit, no drain line, no duct connection and no hanger rod bypasses the mounts to the structure. A single rigid conduit whip returns most of what the springs bought, and it is the most common reason a correct selection measures as a failed one. The connector and hanger side of this is covered by its own cards.

Then, if the complaint that started the job was a level rather than a feel, re-measure that level with the same quantity, weighting, bandwidth, time basis and position as the original reading, or you have no comparison.

What would change this selection

If the lowest disturbing frequency is not shaft speed, the whole sheet moves. A fan with a blade-pass tone at blade count times shaft speed still has shaft speed as its LOWEST disturbing frequency, so field 1 is unchanged, but a reciprocating machine with a half-order component runs lower than shaft speed and field 1 must follow it down. If the machine is variable speed, field 1 is the lowest speed it is permitted to run, not the design speed, and a drive that can be turned down after handover has quietly moved the selection. If the equipment is on a framed floor rather than a slab, the deflection you need is set by the floor's own natural frequency rather than by the ratio arithmetic here.

References

• ASHRAE Handbook chapters on sound and vibration control, for the transmissibility and deflection relationships and their stated assumptions
• Isolator manufacturer's published load-deflection data for the specific mount, which owns the actual deflection at actual load
• Equipment manufacturer's weight distribution drawing, which owns the per-mount load
• 29 CFR 1910.28, fall protection duties where the work is on a roof or elevated platform
• See related: Why an Isolator Can Make Vibration Worse; What an Inertia Base Adds Beyond Mass; What a Flexible Connector Does and Does Not Break