Critical Speed Avoidance Band Run-Up Case Study

This case study follows a variable-speed fan that can run safely above a critical-speed crossing only if the controller avoids dwelling near the crossing. The technical issue is not whether a resonance exists. The issue is how measured run-up evidence becomes a defensible operating rule.

The machine is a generic industrial fan driven by a variable-frequency drive. After a support modification, the commissioning team must decide whether the unit can be released for production up to its required operating speed.

Case Context

Item	Field value
Required operating range	900\ \text{rpm} to 1785\ \text{rpm}
Predicted first bending mode	27.0\ \text{Hz}
Dominant excitation	1x shaft speed
Site action level	7.1\ \text{mm/s RMS}
Vibration trip level	12.0\ \text{mm/s RMS}
Initial run-up rate	90\ \text{rpm/s}
Corrected run-up rate through restricted band	240\ \text{rpm/s}
Speed reference	optical once-per-revolution tachometer
Required evidence	order-tracked amplitude and phase, waterfall spectrum, bearing check and repeat run-up

The initial run-up showed a sharp 1x vibration peak near 1625\ \text{rpm}. At the final operating point near 1785\ \text{rpm}, vibration fell back to an acceptable value. That pattern suggests a critical-speed pass-through problem rather than continuous high-speed imbalance.

Failure Signature and Operating Boundary

The failure signature is a speed-localized 1x peak with phase rotation through the peak and recovery after the crossing. That is different from a simple imbalance condition that remains large at operating speed, and different from looseness or rub that may generate harmonics, impacts or broadband energy.

The operating boundary is therefore conditional. The machine may be acceptable above the critical-speed region, but it is not acceptable to dwell inside the avoidance band. Startup, coast-down, auto-restart, process turndown and control-loop hunting must all respect the same restricted range.

Step 1: Calculate the Crossing

For a running speed n in rpm, the 1x excitation frequency is:

The first mode is:

For a 1x crossing:

Substitute the measured mode:

The observed 1x peak near 1625\ \text{rpm} agrees with the predicted crossing closely enough to treat the speed region as a controlled risk.

The separation from the intended high-speed operating point is:

So the operating point is about 10.2\% above the crossing. That does not by itself release the machine, because the machine still crosses the critical region during every start and stop.

Step 2: Define an Avoidance Band

The site uses a temporary \pm5\% avoidance band around the critical speed until longer-term damping and support data are available:

Therefore:

The controller should not dwell between about 1540\ \text{rpm} and 1700\ \text{rpm}. It may pass through the band under a controlled ramp if vibration remains below the trip level.

The band should be implemented in both software and operating procedure. A drawing note or commissioning memo is not enough if the VFD, operator screen or automatic control loop can still command steady operation inside the band.

Step 3: Check Exposure Time

During the original run-up, the time spent inside the avoidance band was:

With \dot{n}=90\ \text{rpm/s}:

The peak vibration during that run was:

Compared with the action level:

The machine exceeded the action level by 52 percent but stayed below the trip level. This is not a clean release. It is evidence for a controlled pass-through rule.

After the drive parameters were changed, the run-up rate through the band was increased to 240\ \text{rpm/s}:

The repeat run-up peak was:

The corrected peak is still above the action level:

but it has more margin to the trip level:

The engineering conclusion is conditional: pass-through is acceptable with the faster ramp and trip protection, but continuous operation inside the band is not approved.

Step 3b: Compare Exposure Before and After Correction

A simple exposure screen multiplies peak vibration by time in the avoidance band:

For the original run-up:

For the corrected ramp:

The exposure screen falls by about 70 percent. This is not a fatigue calculation, but it is useful evidence that the new ramp materially reduces time spent near resonance.

Step 4: Check Damping and Phase Evidence

The waterfall and order-tracked data show that the 1x peak grows through the crossing and then falls after the crossing. The phase changes rapidly through the peak, which supports the critical-speed interpretation.

A half-power estimate from the run-up response gives:

with:

so:

This is moderate damping, not enough to ignore the crossing. A simplified resonance amplification screen at r=1 is:

That number is not used as an exact rotor response prediction. It is used to justify why small forcing near the crossing can produce a large measured response.

Validation Evidence

The release package should include a tachometer-referenced run-up and coast-down, order-tracked 1x amplitude and phase, waterfall spectrum, bearing temperature, vibration sensor location and calibration, VFD ramp parameters, alarm and trip settings, coast-down behavior, and repeatability across at least two starts.

The evidence should also show that the final operating point is not being held by a controller that can drift into the avoidance band under load. If process control can demand intermediate speed, the speed reference, minimum ramp rate and no-dwell rule must be locked into the control configuration.

Coast-down evidence matters because a trip, power loss or controlled shutdown also crosses the critical-speed band. If coast-down is slower than run-up, the machine may spend longer in the restricted range during shutdown than during startup. The release package should therefore state whether coast-down vibration remains below trip limits or whether a controlled stop procedure is required.

Release Decision

The machine is released only with operating restrictions:

• skip or ramp through 1540\ \text{rpm} to 1700\ \text{rpm};
• no automatic control dwell inside the avoidance band;
• minimum ramp rate of 240\ \text{rpm/s} through the band unless a later test approves slower passage;
• vibration alarm at 7.1\ \text{mm/s RMS} and trip at 12.0\ \text{mm/s RMS};
• repeat run-up after bearing replacement, support modification, balancing, impeller repair or drive-parameter change.

Continuous operation near 1785\ \text{rpm} is acceptable because the corrected high-speed vibration is 4.1\ \text{mm/s RMS}, the phase is stable, bearing temperature remains normal and the dominant response falls after the critical-speed crossing.

This is not a blanket release for future hardware states. The avoidance band should be revalidated after balance correction, bearing replacement, support stiffness change, coupling work, foundation repair, impeller fouling, VFD parameter change or any modification that can move the mode or forcing order.

Common Mistakes

Do not release the full speed range only because the final operating point is above the critical speed. Startup and coast-down still matter. Do not treat a speed avoidance band as a drawing note; it must be implemented in the drive, procedure, alarm logic and maintenance record.

Another mistake is calling the peak imbalance without checking phase and speed dependence. Imbalance may be the forcing source, but the release decision here is controlled by critical-speed response, ramp exposure and measured evidence.

Other mistakes include using a fixed-frequency spectrum instead of order tracking during run-up, ignoring coast-down, placing the alarm above the practical trip response time, failing to update operator displays with the avoidance band, and allowing automatic process control to hunt inside the restricted speed range.