How to Work Out Whether You Are Near a Critical Speed

Why this matters

"Critical speed" gets used loosely for any speed a machine misbehaves at, and the looseness costs money, because the two things it can mean have completely different fixes. A rotor critical speed is the shaft and its rotor bending as a beam, and you change it by changing the shaft, the bearing span, or the rotor mass. A support resonance is the housing, base, curb or duct ringing, and you change it by changing the structure. Both produce a speed the machine hates. If you stiffen the base to cure a shaft problem you will spend the money and get nothing, and the reverse is worse, because a shop that replaces a shaft to cure a curb problem has now put a customer through a shutdown for no result. This procedure separates them with tools a service truck already carries, and ends with a margin you can put on a report.

Step 1: Make the machine safe for both kinds of test

Two of the tests below happen on a stopped machine and one happens on a coasting one, and the protections differ.

For the impact test and any indicator work, open the disconnect, apply your own lock and tag, and confirm the rotor has stopped rather than merely slowed before a hand or a hammer goes near the assembly, which is the energy-control and verification requirement of 29 CFR 1910.147. A large fan wheel on good bearings holds usable spin for minutes.

For the coast-down, the machine is turning, so the reading is taken from outside an intact guard with a magnetic-base sensor on a stationary bearing housing, never with a panel lifted, because 29 CFR 1910.219 covers a decelerating drive the same as a running one. No gloves and no loose sleeves near the shaft line.

If any part of the work takes you into the starter, the motor terminal box or a drive enclosure, that is electrical work under 29 CFR 1910.333(b)(2) rather than 1910.147, which excludes electric utilization installations at 1910.147(a)(1)(ii)(C); prove the conductors dead with the live-dead-live sequence in NFPA 70E-2021, 120.5, and on a variable-frequency drive wait out the manufacturer's stated DC-bus discharge time and verify absence of voltage at the bus before touching the terminals.

One operating rule throughout: do not park the machine at a speed where it is peaking to get a better reading. Dwelling at a resonance accumulates high-stress fatigue cycles quickly on whatever is resonating. Pass through it and read on the way.

Step 2: Write down every speed the machine actually runs at

Nameplate speed is not enough. Record the driver's full-load speed, the driven speed after the sheave ratio, and the full range if there is a drive. A two-speed or variable machine has to clear the margin at every speed it holds, not just at design.

Skipping this is how a shop clears a machine at 1,750 rpm and gets called back for the 1,150 rpm setting that was never tested.

Step 3: Get the published rotor critical if one exists

Fan shaft assemblies and pump manufacturers commonly publish a first critical speed or a maximum operating speed derived from it, because it is a function of the shaft diameter, the bearing span, the overhang and the rotor mass, all of which the manufacturer knows and you do not. Ask for it before you estimate it.

If nothing is published, you can bound it. For a shaft carrying a rotor, natural frequency in cycles per minute is roughly 187.8 divided by the square root of the static deflection in inches at the rotor under its own load. That relationship is derived for a lumped mass on a linear spring with rigid supports, so applied to a real shaft in real bearings it is an approximation that is optimistic: soft bearing pedestals lower the actual critical below what the shaft alone predicts. Use it to decide whether you are anywhere near the neighbourhood, not to certify a margin.

The practical reassurance: the large majority of field-service machinery, meaning direct-drive fans, pumps, blowers and compressors at two-pole and four-pole speeds, runs as a rigid rotor well below its first critical. Where you get close is long belt-driven fan shafts with a wide bearing span, and vertical pump shafting.

Step 4: Impact test with the rotor stopped, in two directions

With the machine locked out and stopped, strike each bearing housing and the base with a soft-face hammer and record where the structure rings, striking both horizontally and vertically at each point. Support modes are usually strongly directional, often 20 percent or more apart between the two directions, so a single-direction test finds half the picture.

What this test does and does not see. It excites the structure: housings, pedestals, rails, curb, ductwork. It does not excite the rotor's own bending mode in any useful way, because that mode only matters while the rotor is turning and being forced by its own unbalance. That asymmetry is what makes the next step diagnostic.

Step 5: Take a coast-down and record the speed at every amplitude peak

Open the disconnect and watch the reading fall, noting the speed at which amplitude spikes. Every resonance the machine passes through on the way down shows as a peak, and the good ones are unmistakable: amplitude climbs several-fold over a narrow speed band and collapses again.

Record the speed, not just the fact of a peak. The speed is what you compare against step 4.

Step 6: Match the peaks against the impact results, allowing for multiples

This is where the diagnosis actually happens, and it has one trap in it.

• A coast-down peak whose speed matches a frequency you found by impact is a support resonance excited by running speed. Fix the structure.
• A coast-down peak that does not appear in the impact test at any direction is a candidate rotor critical. Confirm against the published figure from step 3 before you act on it.
• Before you conclude "rotor", multiply the peak speed by 2, and by the blade or vane count, and check those against the impact results too. A peak at some speed can be a mode at twice that frequency being driven by a twice-per-revolution excitation. This is the trap, and it sends people after shafts that are innocent.

Step 7: State the margin as a percentage of running speed, and decide

Rotating-machinery practice keeps running speed at least 15 to 20 percent away from any natural frequency it can excite, tighter where damping is low and the excitation is strong. Compute it both ways and write it on the report.

Be honest about what a margin buys. At a 15 percent separation with 5 percent of critical damping, a common assumption for a bolted steel assembly and one almost never measured, the amplification is still around 3, whether you are 15 percent below the frequency or 15 percent above it. A separation margin gets you off the peak. It does not get you to 1.0, and a machine cleared at exactly 15 percent is still amplifying its own unbalance threefold.

Worked example: the belt-driven plenum fan at 1,150 rpm

A plenum fan, wheel between bearings, belt-driven at 1,150 rpm, complaint of a shake that the customer says has been there since a re-sheave two years ago.

Step 3. The shaft assembly manufacturer publishes a first critical of 1,850 rpm for this shaft diameter and bearing span. Running speed is 1,150, a ratio of 0.62, so the rotor sits 38 percent below its own critical. The shaft is not the story, and that is established before anyone quotes one.

Step 4. Locked out and stopped, impact testing gives 1,070 cpm horizontally at the drive-end bearing housing and 1,390 cpm at the motor pedestal across the rails. Vertical strikes ring much higher at both points.

Step 5. The coast-down peaks twice: strongly at about 1,060 rpm and more mildly at about 690 rpm.

Step 6. The 1,060 peak matches the 1,070 cpm impact result within 1 percent. That is the base and housing mode, excited by running speed. The 690 peak matches nothing in the impact list, which looks like a rotor mode until you apply the multiple check: 690 x 2 = 1,380, which is within 1 percent of the 1,390 cpm motor pedestal mode. So the second peak is the pedestal being driven at twice running speed, not a rotor critical. Both peaks are structural, and the shaft quote is now formally off the table.

Step 7. Running speed 1,150 against the 1,070 cpm mode is a ratio of 1.075, so the machine runs 7.5 percent above a resonance it excites directly. That fails the 15 percent rule, and the amplification at that ratio with 5 percent damping works out near 5.3. Every ounce-inch of residual unbalance on that wheel is being multiplied more than fivefold, which is exactly what the customer feels.

Choosing the fix, with the arithmetic. Two ways out.

Move the frequency. To clear 1,150 rpm by 15 percent, the mode has to reach 1,150 x 1.15 = 1,323 cpm. Going from 1,070 to 1,323 is a 24 percent rise in frequency, and because frequency rises with the square root of stiffness, that needs stiffness up by 1.24 x 1.24, or about 53 percent. That number is the argument against the reflexive fix. Bolting one more angle alongside an existing rail does not add half the stiffness of the assembly; shortening the unsupported span between supports does, which is why the gusset goes where the span is longest rather than where there is room to work. If that gusset is welded, treat the fume as the hazard it is: welding on zinc-coated or galvanized rail releases zinc oxide fume and welding on stainless releases hexavalent chromium, so the work needs local exhaust plus respiratory protection under a written 29 CFR 1910.134 program, with 29 CFR 1910.1026 applying wherever chromium-bearing metal is in the joint, and a hot-work fire watch if the work is on a roof or near combustibles.

Move the speed. To sit 15 percent below 1,070 cpm the fan has to come down to about 910 rpm. Flow falls roughly in proportion to speed, so that is about 79 percent of the current airflow, which on a fan sized for a space is usually not available. On this job it was not, so the fix was structural.

The failure mode this avoids. Without step 6's multiple check, the 690 rpm peak reads as an unexplained rotor resonance, and the natural next move is a shaft and bearing assembly. That is a shutdown, a shaft, two bearings, a re-alignment and a re-tension, after which the machine still shakes at 1,150 rpm because the 1,070 cpm mode was never touched. The check that prevents it costs one multiplication.

How to verify the fix actually worked

Re-run the coast-down after the change and confirm the peak moved, not merely that the overall reading dropped. A reading can fall for reasons that have nothing to do with the mode: a belt re-tensioned during the work, a fastener torqued, a sensor placed slightly differently. The peak's speed is the only number that proves the structure changed.

Then re-run the impact test at the same points and confirm the new frequency is where you calculated it should be. If the frequency moved much less than the stiffness change predicted, the stiffness was added in a place the mode does not care about, which is the usual outcome of bracing at a node rather than at the point of maximum motion.

References

• 29 CFR 1910.147 for isolation, lock and tag, and stopped-rotor verification before impact testing or indicator work
• 29 CFR 1910.219 for guarding during a coast-down measurement on a turning machine
• 29 CFR 1910.333(b)(2) and NFPA 70E-2021, 120.5 for the electrical fork at the starter, terminal box or drive enclosure
• 29 CFR 1910.134 and 29 CFR 1910.1026 for respiratory protection and hexavalent chromium exposure where a stiffening gusset is welded onto coated or chromium-bearing steel
• Fan shaft and pump manufacturer documentation for published first critical speed and maximum operating speed
• See related: What Resonance Is and Why It Finds Your Machine; Why a Machine Is Worse at One Speed Than at a Higher One; How a Base and a Foundation Change the Machine on Them