What an Inertia Base Adds Beyond Mass

Why this matters

An inertia base gets specified because it is heavy, and heavy sounds like it must help. Then the same shop that poured 2,250 lb of concrete under a pump measures the same force going into the slab as before, and cannot explain it to anybody. The explanation is short and it is the most useful thing on this card: mass does not set the mounted natural frequency, deflection does, and if you spend the added weight on stiffer springs you have bought no reduction in transmitted force at all. What the mass genuinely buys is a different list, and this card is mostly that list's negative image - the things people believe an inertia base does, which it does not.

The relationship that decides the argument

For a single mass on a linear spring, moving in the vertical mode, on a support that is rigid relative to the mount, the mounted natural frequency in Hz is about 3.13 divided by the square root of the static deflection in inches. Mass is not in that expression. It is in the deflection, because a heavier machine on the same spring sits lower, but once you state the deflection the mass has already done its work and cannot do it twice.

Well above resonance, two further relationships matter and they behave differently:

• Transmitted force is the exciting force times transmissibility, and transmissibility well above resonance is close to the square of the natural frequency divided by the square of the disturbing frequency. Hold the deflection constant and transmissibility is constant, whatever the mass.
• Motion of the mounted assembly is close to the exciting force divided by the mass times the square of the angular disturbing frequency, holding the exciting force amplitude and frequency constant and staying well above resonance. Mass is in that one, and it is the only place mass appears on its own.

So mass always reduces MOTION. It reduces transmitted FORCE only if you let the springs deflect further.

Worked case: the same base spent two ways

Say an end-suction pump and motor on a fabricated rail base, operating weight 900 lb, motor nameplate 1,740 rpm at rated load, so the lowest disturbing frequency is 29.0 Hz. It sits on four spring mounts on a slab on grade, actual deflection 1.00 in at 225 lb per mount, which is 225 lb per inch each.

Starting point. Deflection 1.00 in gives a natural frequency of 3.13 Hz. The ratio is 29.0 over 3.13, or 9.27. Transmissibility is one over the quantity 85.9 minus 1, which is 0.0118.

Now add a steel-framed concrete inertia base weighing 2,250 lb, which is 2.5 times the equipment weight. Total supported weight becomes 3,150 lb, or 3.5 times the original.

Spend one: keep the same springs. Load per mount rises to 787.5 lb, so deflection rises to 787.5 over 225, which is 3.50 in, provided the mount has that much travel before it goes solid. Natural frequency falls to 3.13 over the square root of 3.50, which is 1.67 Hz. The ratio rises to 17.3, transmissibility falls to one over the quantity 300 minus 1, which is 0.00334. Transmitted force falls to 0.00334 over 0.0118 of what it was, which is 28 percent - a reduction of about 3.5 times, exactly the mass ratio, because well above resonance transmissibility varies inversely with mass at constant spring rate.

Spend two: re-select the springs to hold 1.00 in. Now each mount is 787.5 lb per inch. Deflection is 1.00 in, natural frequency is 3.13 Hz, the ratio is 9.27, transmissibility is 0.0118. That is the number the pump had before the base was poured. The mass bought nothing in transmitted force.

What it bought in both cases. Motion of the assembly at 29.0 Hz falls to one over 3.5 of its previous value, which is 29 percent, in spend one and in spend two alike, holding the residual unbalance force and the speed constant. That is the thing mass reliably delivers, and it is worth having for reasons that have nothing to do with the number going into the slab.

Sibling-rule check. The isolator-selection card states that natural frequency comes from actual deflection under actual load and never from mass; spend two is that rule producing an unwelcome answer rather than a contradiction of it. The amplification card's gate requires the frequency ratio to exceed the square root of 2 at every permitted speed; both spends clear it at 9.27 and 17.3, and the pump is constant speed here, so there is no lower speed to check. The support-stiffness condition is checked rather than assumed: slab on grade, no measurable deflection under the added 2,250 lb, though on a framed floor that added weight is a structural question before it is an acoustic one. No transmissibility figure has been quoted without the deflection that produced it.

What the mass is actually for

Five things, and none of them is the transmitted force at running speed.

It cuts the assembly's own motion. Twenty-nine percent of the previous displacement at the same unbalance force. That is what protects the flexible connections, the conduit whip, the seal faces and the alignment, all of which are damaged by excursion rather than by force.

It holds alignment between two shafts. A fabricated rail base flexes under pipe reaction and under starting torque. The pump end and the motor end move relative to each other, which shows up months later as a coupling and a seal. A rigid platform is the reason a base is specified on close-coupled equipment even where nobody is complaining about noise.

It lowers the centre of gravity relative to the plane of the mounts. The vertical-mode arithmetic above covers one mode of six. The rocking modes sit at their own, generally lower, natural frequencies and they are excited by starting torque and by pipe reaction. A base that puts mass low, with the mounts spread wide, moves those modes where they do less harm. Where the equipment's centre of gravity is high, the mount plane and the base depth are a manufacturer conversation, not a field adjustment.

It gives pipe and duct reaction something to react against. The load a connected pipe puts on a pump nozzle does not disappear because there is a flexible connector in the line; it is reacted somewhere. On a light rail base it is reacted by the pump casing.

It spreads a point load. Four mount feet on a thin slab or a raised floor become a distributed load through the base.

What it does not do, which is the part that costs money

It does not lower the natural frequency by itself. Spend two above. This is the single most common misunderstanding on the subject, and it is why "we put it on an inertia base" is not an answer to "what deflection are the mounts at."

It does not reduce the exciting force. Residual unbalance, blade pass, gear mesh and hydraulic pulsation all come off the machine unchanged. Balancing the rotating assembly is what reduces the force, and on a machine whose complaint is a once-per-revolution component that is the cheaper fix by a wide margin.

It does not add useful damping to the mounted mode. Concrete in a steel frame is stiff, not lossy. Damping at the mounted resonance belongs to the mount, and choosing it is covered by the amplification card.

It is not a substitute for isolation. A base set directly on a floor transmits everything the machine produces into a larger, better-coupled contact area than the original feet did. This is the failure mode worth naming concretely: an inertia base with the isolators omitted, value-engineered out, or shimmed solid during commissioning and never released, is measurably worse than the machine on its original feet.

It does not close a flanking path. Rigid conduit, a hard-piped drain, a duct connection or a hanger rod that bypasses the mounts returns most of what the springs bought, and the base cannot see any of that.

It does nothing for airborne noise. Casing radiation, discharge noise and motor whine leave the machine through the air and are unaffected by what is underneath it.

Sizing, and who owns the number

Base weight is commonly specified as a multiple of the equipment operating weight, typically in the range of one to two times for general pumping and fan duty and higher where thrust or starting torque is significant. The multiple, the base depth, the mount locations and the reinforcement are the specifying engineer's, and on equipment with a published base recommendation, the manufacturer's. Do not select a multiple from a rule of thumb on a machine whose centre of gravity is high or whose piping is large relative to the pump, because those are precisely the cases where the rule of thumb was never derived.

The structural side is a hard gate rather than a preference: adding 2,250 lb to a roof, a mezzanine or a framed floor is a load question that goes to a structural engineer before anything is poured or set.

Building and setting one without hurting anybody

Where the base is poured on site, wet cement is caustic and causes skin burns through clothing, so wear impervious gloves and boots and rinse any contact immediately with clean water; dry cement, and any later drilling or cutting of the cured base for anchors, releases respirable crystalline silica, which is an inhalation hazard controlled under 29 CFR 1910.1053 in general industry and 29 CFR 1926.1153 in construction, so use the wet method or on-tool extraction the standard's control table specifies for that task rather than a dust mask. Where the base is set as a unit, the rigging plan and the lift points belong to the base manufacturer's drawing, and nobody stands under or reaches beneath a suspended base to guide it.

How to verify a base is doing its job

Measure free height minus installed height at every mount and confirm each matches the deflection the selection called for, because a base whose mounts are still shimmed solid from delivery reads zero and is the failure named above. Then check that the machine and the base move as one: place your hand across the joint between the equipment rail and the base while it runs and feel for relative motion, which means the equipment was fastened to a base that is not stiff enough or the fasteners have worked loose. Then confirm alignment against the coupling manufacturer's tolerance with the system at operating temperature and with the pipe connected, since holding alignment under pipe load is one of the things the base was bought for and the only honest way to check it is with the load present.

References

• ASHRAE Handbook chapters on sound and vibration control, for the deflection and transmissibility relationships and the assumptions behind them
• Equipment and base manufacturer's documentation for base weight multiple, mount locations and lift points
• 29 CFR 1910.1053 (general industry) and 29 CFR 1926.1153 (construction), respirable crystalline silica, for drilling or cutting cured concrete
• See related: How to Select an Isolator From the Disturbing Frequency; Why an Isolator Can Make Vibration Worse; What a Flexible Connector Does and Does Not Break