Rotating Machinery Imbalance Vibration Diagnosis Case Study

This case study follows a common rotating-machinery problem: a variable-speed fan develops high radial vibration after maintenance, and the evidence points toward rotor imbalance rather than bearing damage, misalignment, looseness, or resonance. The useful engineering work is not only identifying a large 1x peak. It is deciding whether the machine can keep running, whether field balancing is justified, how much correction mass to install, and which evidence is needed before releasing the machine.

The case is realistic rather than tied to a specific plant. It shows how vibration spectra, phase, speed reference, trial-weight response, bearing condition, and operating limits should support one engineering decision.

The central question is:

Is the dominant vibration caused by correctable rotor imbalance, or is balancing only masking a different fault?

The answer is that imbalance is the leading diagnosis, but only after resonance, misalignment, measurement error, looseness, and process excitation are checked.

Case Context

A belt-driven industrial fan is returned to service after impeller cleaning and minor weld repair. During commissioning, the outboard bearing vibration is higher than the site action level. The machine is needed for production, but continued operation could damage bearings, loosen the base, or accumulate fatigue in the impeller and support frame.

Item	Field value
Operating speed	1785\ \text{rpm}
Shaft rotational frequency	29.75\ \text{Hz}
Main radial vibration at outboard bearing	8.0\ \text{mm/s RMS}
Site action level for this bearing location	7.1\ \text{mm/s RMS}
Dominant spectral component	1x shaft speed
2x shaft-speed component	1.1\ \text{mm/s RMS}
Axial vibration	1.3\ \text{mm/s RMS}
Measured structural mode near running speed	34\ \text{Hz}
Phase reference	optical tachometer on shaft keyway mark

The high 1x radial vibration, stable phase, low axial vibration, and low 2x component make imbalance plausible. They do not prove it by themselves. The repair history, runout check, bearing condition, speed sweep, and trial-weight response must agree.

Frequency and Resonance Check

The shaft rotational frequency is:

With:

the result is:

A bump test and coast-down data show a nearby structural mode at:

The separation from running speed is:

This is not a large separation. It does not rule out imbalance, but it warns that a residual unbalance force may be amplified by support flexibility. A balance correction can reduce forcing, while a support modification may still be needed if the machine must operate closer to the mode in the future.

Diagnostic Evidence

The diagnostic review compares likely faults.

Possible fault	Evidence for	Evidence against
Rotor imbalance	Dominant 1x radial vibration, stable phase, recent impeller repair, low axial vibration.	Needs trial-weight response to confirm.
Misalignment	Can produce 1x and 2x vibration.	2x is small, axial vibration is low, coupling temperature is normal.
Bearing defect	Bearing can raise vibration and temperature.	No bearing defect frequencies, no temperature rise, oil debris normal.
Looseness	Can produce harmonics and unstable phase.	Phase is stable, higher harmonics are low, hold-down bolts checked.
Resonance	Mode at 34 Hz is close enough to amplify response.	Coast-down peak is not exactly at running speed; phase follows trial weight.
Measurement-chain error	Sensor or tachometer error can distort diagnosis.	Tachometer is stable, sensor mounting verified, repeat measurement agrees.

The case remains a diagnosis until the trial weight changes the 1x vector in a predictable way.

Trial Weight Calculation

A trial weight is installed at a known radius and angular reference. Use:

The trial unbalance is:

The measured 1x vibration vector before the trial weight is:

After installing the trial weight at the zero-degree mark:

The change caused by the trial weight is:

Using vector subtraction:

The influence coefficient is:

with phase:

The correction unbalance that cancels the original vibration is:

so:

At the same correction radius:

The engineering instruction is therefore to install about 25\ \text{g} at a radius of 180\ \text{mm} and at 78.6^\circ from the trial-weight reference, using the same tachometer and angular convention. In field work, the sign convention, rotation direction, angle reference, and whether the trial weight remains installed must be controlled before any mass is added or removed.

Force Significance

The correction unbalance is not trivial. Convert:

The angular speed is:

The corresponding rotating force magnitude is:

This force rotates at shaft speed and is applied continuously. It is large enough to matter for bearing load variation, support motion, looseness growth, and fatigue exposure. The force calculation also explains why balance quality becomes more critical as speed increases: unbalance force scales with speed squared.

Operating Decision

Before correction, the recommended operating decision is restricted service, not unrestricted production. The reason is not only that vibration exceeds a limit. The reason is that the fault is correctable, but the nearby structural mode, recent repair, and elevated bearing vibration make continued operation a poor reliability choice.

The decision package is:

1. Keep the machine available only at reduced speed if process demand requires short operation.
2. Do not cross the speed range near the 34 Hz mode slowly during ramp-up or coast-down.
3. Install the calculated correction mass after confirming trial-weight convention.
4. Repeat the measurement at the same speed, load, sensor location, filter settings, and tachometer reference.
5. If residual 1x remains high or phase becomes unstable, stop balancing and inspect runout, looseness, support stiffness, bearing fits, and repair geometry.

Balancing is an engineering intervention, not a ritual. If the trial weight does not create a coherent vector response, adding more correction mass can hide the true failure mode.

Validation After Correction

After installing the correction weight and removing the trial weight, the commissioning team repeats the test.

Evidence item	Before correction	After correction	Acceptance intent
1x radial vibration at outboard bearing	8.0\ \text{mm/s RMS}	2.1\ \text{mm/s RMS}	below site action level
2x vibration	1.1\ \text{mm/s RMS}	0.8\ \text{mm/s RMS}	no new misalignment signature
Phase at 1x	stable at 35^\circ	stable after correction	coherent balance response
Bearing temperature rise	normal	normal	no secondary bearing distress
Runout check	within limit	unchanged	balance did not hide bent shaft/runout issue
Speed sweep near 34 Hz mode	elevated response	reduced response but still visible	mode recorded for future speed limits
Repeatability after restart	not yet proven	repeat measurement agrees within 10\%	correction is not transient

The residual vibration is not zero, and it does not need to be zero. The machine is acceptable because the dominant 1x component falls below the site action level, phase remains stable, bearing evidence is normal, and the nearby mode is documented for future operation.

Failure Mode Controls

The permanent corrective actions are:

• preserve the balancing record with correction mass, radius, angle, rotation direction, trial-weight data, and sensor locations;
• add a repeat balance check after the next impeller cleaning or weld repair;
• require runout measurement after impeller removal and reinstallation;
• trend 1x amplitude and phase at the same speed and load;
• maintain a speed-sweep record so the 34 Hz mode is not forgotten during future drive changes;
• inspect bearings during the next planned outage if temperature, oil debris, or vibration trend changes;
• review repair procedure so weld mass, cleaning residue, and coating thickness are controlled around the rotor.

These controls make the event useful beyond the immediate repair. The plant now has a better maintenance rule for similar rotating equipment.

Transferable Lessons

The main lessons are:

• A high 1x peak suggests imbalance, but phase stability, trial-weight response, and exclusion of other faults make the diagnosis credible.
• Balancing near a structural mode can work, but the mode remains a design and operating constraint.
• Trial weights should be large enough to produce a measurable vector change but small enough to avoid unsafe vibration.
• Vibration acceptance should match speed, load, process state, sensor location, and filtering.
• A successful balance correction should be validated by spectrum, phase, bearing evidence, repeatability, and operating history.
• If the response is nonlinear, unstable, or inconsistent with the trial weight, stop balancing and inspect the machine.

Engineering Closeout

A defensible closeout statement is:

The elevated fan vibration was caused primarily by rotor imbalance after impeller maintenance. The diagnosis is supported by dominant 1x radial vibration, stable phase, low axial and 2x components, acceptable bearing evidence, a coherent trial-weight vector response, and a successful influence-coefficient correction. A 25\ \text{g} correction at the documented radius and angle reduced vibration from 8.0 to 2.1\ \text{mm/s RMS}. The nearby 34 Hz structural mode remains documented as an operating and future modification constraint.

This is the useful engineering conclusion: the machine did not simply need a lower vibration number. It needed a traceable diagnosis, a controlled balance correction, and validation evidence that the corrected rotor can operate reliably in its real speed and load range.