Resonance Diagnosis: Natural Frequencies, Bump Tests and Run-Up/Coast-Down Analysis

From Mechanical Maintenance to Vibration Analysis - Part 8

In Part 7 - Gearbox Faults, we saw that gear-mesh vibration can be amplified when a forcing frequency approaches a structural natural frequency. This is resonance: a condition that can make a modest forcing force produce severe vibration.

Resonance is easily misdiagnosed. A large 1X peak may be blamed on extreme unbalance, a blade-pass peak on a fan defect, or gear-mesh vibration on damaged teeth. The forcing frequency is real, but the structure may be multiplying its response.

A natural frequency belongs to the structure. Resonance occurs only when a forcing frequency excites that natural frequency.

Natural frequency and resonance are not the same

Every shaft, bearing housing, baseplate, foundation, pipe and support has natural frequencies. They are properties of the system's mass, stiffness and damping. A structure can have many natural frequencies, each associated with a particular pattern of movement called a mode shape.

A natural frequency may remain quiet for years. Resonance begins when a periodic force approaches it closely enough to excite the mode. Common forcing frequencies include:

• Shaft running speed and its harmonics.
• Fan blade-pass and pump vane-pass frequencies.
• Gear-mesh frequency and its harmonics.
• Reciprocating forces, electrical frequencies and flow pulsation.
• Impacts, looseness and forces transmitted from nearby equipment.

The response does not need an exact frequency match. The width of the resonant region depends strongly on damping. A lightly damped structure has a narrow, sharp response with high amplification. Greater damping normally lowers the peak and spreads the response over a wider frequency band.

Mass, stiffness and damping control the response

For a simple mass-spring system, natural frequency increases with stiffness and decreases with mass. The practical relationships are:

• More mass: generally lowers natural frequency.
• Less mass: generally raises natural frequency.
• More stiffness: generally raises natural frequency.
• Less stiffness: generally lowers natural frequency.
• More damping: generally reduces resonant amplification.

These relationships guide corrections, but real machines have multiple coupled modes. A brace, support or added mass can solve one resonance and move another mode into a forcing-frequency range. Structural changes therefore require engineering review and post-modification testing.

Clues that should make you suspect resonance

Observation	Why resonance is possible	Next test
One unusually large spectral peak	A normal forcing frequency may be amplified	Identify the forcing frequency, then perform a resonance test
High vibration in one direction but much lower in another	Structural stiffness and mode shape are directional	Map amplitude and phase across the structure
Amplitude rises sharply only in a narrow speed range	A speed-related order may be crossing a natural frequency	Run-up or coast-down with a tachometer
A broad hump or raised noise floor surrounds peaks	Several components may be amplified within a resonant band	Bump test or frequency-response measurement
Repeated cracked welds, pipes or supports without another clear cause	Amplified cyclic stress may be driving fatigue	Inspect, map motion and test the suspected structure

These observations justify a test; they do not prove resonance. Unbalance, looseness, misalignment, soft foot, hydraulic excitation and poor measurement technique can produce similar clues.

Amplitude and phase through resonance

As a speed-related forcing frequency approaches a natural frequency, amplitude rises. At the resonant region it reaches a maximum, then falls as the forcing frequency moves above the mode.

Phase provides the stronger confirmation. In a simple single-mode response, phase changes progressively by approximately 180 degrees while passing through resonance, with approximately 90 degrees of lag near the natural frequency. Actual plant data can be distorted by other modes, measurement location, phase wrapping, speed changes and poor tachometer signals, so interpret the complete amplitude-and-phase trend rather than one phase reading.

A Bode plot displays amplitude and phase against speed or frequency. A resonant peak combined with the expected phase transition is much stronger evidence than amplitude alone.

Test 1: the bump or impact test

A bump test introduces a short impact into a stationary structure and measures the frequencies at which it rings. The impact contains energy over a range of frequencies; the structure responds most strongly near its natural frequencies.

Safety comes first. Perform the test only under an approved site procedure. Isolate equipment where required, confirm that stored energy and process hazards are controlled, and never strike rotating, hot, pressurized, fragile or safety-critical components. Select a safe impact point and a suitable hammer or soft mallet that will not damage the surface.

Practical collection sequence

1. Define the forcing frequency and the suspected direction of movement.
2. Mount an accelerometer firmly on the structure in that direction.
3. Select an Fmax high enough to include the suspected mode and use a rectangular/uniform window where the instrument procedure requires it.
4. Use peak-hold averaging or a triggered impact setup. Low line resolution can help capture a short event quickly; refine the test later if nearby modes must be separated.
5. Make practice impacts to set the gain without clipping, then collect several consistent single impacts.
6. Repeat in other directions and at other positions. Avoid judging the structure from a nodal point, where the mode may show little movement.
7. Compare the response peaks with actual forcing frequencies and with historical tests.

The Mobius Category II manual offers example starting settings such as peak-hold averaging, about 400 lines or fewer, multiple averages and pre-triggering where available. These are instrument-dependent setup guides, not universal requirements. A calibrated impact hammer and frequency-response function provide better control because both input force and structural response are measured.

Test 2: run-up and coast-down analysis

During a controlled run-up or coast-down, shaft speed changes and the machine's orders sweep through a range of frequencies. If an order crosses a natural frequency, the response increases and then decreases. A waterfall plot shows the moving order as a diagonal ridge and the resonant region as a high-amplitude zone near a fixed frequency.

Use a reliable tachometer and collect spectra quickly enough to capture the transition. Order tracking can extract 1X or another order while speed changes and display amplitude and phase on a Bode or polar plot. This is especially useful when the machine starts or stops slowly enough for the mode to respond.

Run-up and coast-down tests must follow the machine manufacturer's limits and site operating procedure. Do not hold a machine near a suspected critical speed merely to improve the plot. Some flexible-rotor machines are designed to pass through critical speeds rapidly.

ODS and modal analysis answer different questions

An operating deflection shape (ODS) uses amplitude and phase measured while the machine operates to animate its motion at a selected frequency. It shows how the machine is moving under the present forces. It does not automatically identify every natural mode.

Modal analysis uses a measured input from an instrumented hammer or shaker and measures the structural response, normally with the machine stopped. It identifies natural frequencies, damping and mode shapes more directly. For complex structures or high-consequence modifications, specialist modal testing or finite-element analysis may be required.

Worked diagnosis: fan vibration near running speed

A belt-driven fan operates at 1,490 rpm, or 24.8 Hz. The fan outboard bearing measures 9.2 mm/s horizontally but only 1.8 mm/s vertically. The spectrum is dominated by 1X. Balancing reduces the calculated unbalance force but the vibration remains high.

The analyst records these findings:

• A stationary bump test shows a strong horizontal response at 25.4 Hz.
• A controlled coast-down shows the 1X amplitude rising sharply near 25 Hz and falling below it.
• The 1X phase changes progressively through the high-amplitude region.
• Movement mapping shows the fan base swaying horizontally, with the largest response near the unsupported side.

Conclusion: fan 1X is exciting a horizontal structural natural frequency. Residual unbalance supplies the forcing force, but structural flexibility supplies the amplification.

Action: an engineering review identifies a suitable brace and verifies loads, clearances and foundation condition. After installation, the natural frequency moves away from 1X. The bump test, coast-down and steady-state measurements are repeated under comparable conditions to confirm lower vibration and ensure that no new forcing frequency has been approached.

Correcting resonance without creating another problem

There are four broad strategies:

1. Change the forcing frequency. Adjust operating speed or process pulsation where the machine and process design allow it.
2. Move the natural frequency. Change stiffness or mass through an engineered structural modification.
3. Reduce transmission. Use correctly designed isolation where appropriate.
4. Add damping. Dissipate energy and reduce amplification.

A separation of roughly 15 to 20 percent between a forcing frequency and a natural frequency is commonly used as a screening guide in the reviewed training materials. It is not a universal acceptance limit. Follow the equipment manufacturer's criteria, applicable standards and qualified engineering analysis.

Do not add a brace, mass or isolator simply because it appears convenient. Confirm the mode shape, check structural loads and piping strain, preserve alignment, and test across all operating speeds and important harmonics after the change.

How System 1 and other software help

Condition-monitoring platforms can correlate vibration with speed and load, store run-up and coast-down data, display waterfall and Bode plots, track orders, compare phase, and trend narrow frequency bands. Modal and ODS packages can animate structural movement and calculate frequency-response functions.

Software organizes evidence; it does not make an exact diagnosis automatically. The analyst must verify the tachometer, sensor direction, mounting, operating condition, test repeatability and physical meaning of every peak and phase change.

An eight-step resonance diagnosis workflow

1. Identify the forcing frequency. Calculate 1X, harmonics, blade/vane pass, gear mesh, electrical and process frequencies.
2. Confirm the symptom. Compare directions, locations, operating states and historical trends.
3. Check measurement quality. Verify sensor mounting, Fmax, resolution, phase reference and tachometer signal.
4. Form competing hypotheses. Include unbalance, looseness, misalignment, soft foot, hydraulic forces and transmitted vibration.
5. Select a safe test. Use a bump test, speed variation, run-up/coast-down, ODS or modal analysis according to risk and machine availability.
6. Combine amplitude and phase. Look for an amplitude maximum and a progressive phase transition through the suspected mode.
7. Design the correction. Change force, stiffness, mass, isolation or damping only after engineering review.
8. Close the loop. Repeat the special test and normal route measurements across the operating range.

Final takeaway

• Natural frequencies exist in every machine and structure.
• Resonance is the amplified response created when a forcing frequency excites a natural frequency.
• A large spectral peak alone does not prove a severe mechanical fault.
• Directionality, speed sensitivity, bump tests, waterfall plots and phase changes build stronger evidence.
• Structural modifications must be engineered and verified across the complete operating range.

Coming in Part 9

Part 9: Fans and Pumps - Blade Pass, Vane Pass, Cavitation and Flow-Related Vibration. We will connect spectra and waveforms with operating point, pressure, flow, recirculation and mechanical condition.

Discussion question: Have you encountered a machine that was repeatedly balanced or aligned before resonance was identified as the real amplifier?

References and further learning

• Mobius Institute, Vibration Analysis Category II Course Manual, Chapter 17: Natural Frequencies and Resonance.
• Emerson Process Management, Basic Vibration Analysis - Course 2031, Chapter 10: Resonance.

Educational note: The diagnostic patterns and setup examples are learning guidance, not universal alarm limits, test procedures or structural-acceptance criteria. Apply approved site safety procedures, manufacturer requirements and qualified engineering judgement.

Gearbox Faults: Gear Mesh Frequency, Sidebands and Evidence

From Mechanical Maintenance to Vibration Analysis - Part 7

In Part 6 - Rolling-Element Bearing Faults, we learned that a calculated fault frequency is evidence, not an automatic replacement decision.

The same discipline is essential for gearboxes. Gear-mesh vibration exists even when the gears are healthy, its amplitude changes with load, and several shafts may modulate the same mesh frequency. The analyst's job is not simply to find gear mesh frequency. It is to explain what is changing around it.

Gear mesh frequency tells you where tooth contact occurs. Sideband spacing often tells you which shaft is modulating that contact.

Start with a gearbox map, not the spectrum

Before collecting data, sketch the drive train. Record the input, intermediate and output shaft speeds; the number of teeth on every mating gear; the gear type; bearing locations; measurement points; normal load range; lubrication system; and direction of rotation.

This map allows you to calculate each shaft speed and each gear-mesh frequency. Without it, a high-frequency peak may be mistaken for a gear mesh, bearing frequency, motor-bar frequency, blade-pass frequency or structural resonance.

Calculate gear mesh frequency correctly

Gear mesh frequency (GMF) is the rate at which teeth enter mesh:

GMF = number of teeth x rotational frequency of that gear

The same GMF must be obtained from either member of a mating pair. If one result differs, the tooth count, shaft speed or gear pairing is wrong.

Worked calculation

A 24-tooth input pinion rotates at 2,400 rpm, or 40 Hz, and drives a 72-tooth gear.

• Input GMF = 24 x 40 = 960 Hz.
• Output shaft speed = 960 / 72 = 13.33 Hz, or approximately 800 rpm.
• Output GMF check = 72 x 13.33 = approximately 960 Hz.

A multi-stage gearbox has a separate GMF for every mating pair. Work through the train one stage at a time and keep the shaft names consistent.

Why GMF alone is not a defect verdict

Every tooth pair generates a small force variation as contact moves through engagement, rolling and sliding. GMF may therefore appear in a healthy gearbox. Its amplitude is also strongly influenced by transmitted torque, gear design, tooth profile, stiffness, backlash, lubrication, resonance and the sensor transmission path.

A higher GMF amplitude at a higher load does not automatically mean deterioration. Compare measurements at similar speed, load, temperature and process condition. Trend the same point, direction, sensor mounting and acquisition setup.

Observation: GMF increased from 2.0 to 3.5 mm/s.

Question: Did gear condition change, or did torque, speed, alignment, lubrication, resonance or measurement setup change?

Better evidence: comparable operating data plus GMF harmonics, sidebands, waveform impacts, trends and corroborating inspection findings.

Sidebands are modulation evidence

When the amplitude or frequency of a gear-mesh signal changes periodically, the FFT produces peaks on both sides of GMF. If the modulating frequency is f_m, sidebands may appear at:

GMF - f_m, GMF + f_m, GMF - 2f_m, GMF + 2f_m ...

A damaged or eccentric gear rotates once per shaft revolution. Its contact stiffness or tooth load may therefore vary at that shaft's 1X frequency, producing GMF sidebands spaced by that shaft speed.

Measure the spacing; do not judge the cluster by appearance alone. In a gearbox with 40 Hz input speed and 13.33 Hz output speed:

• Sidebands spaced by 40 Hz point toward modulation associated with the input shaft or pinion.
• Sidebands spaced by 13.33 Hz point toward the output shaft or gear.
• Both spacings may indicate that both gears, their alignment, or a shared load path is involved.

The number and amplitude of sidebands often become more useful than the central GMF amplitude. They still do not identify the physical failure mode by themselves; they identify a repeating modulation that must be connected to the machine.

Read the complete pattern

Observed pattern	Possible explanation	Useful next check
Stable GMF with few small sidebands	Normal tooth contact or stable load-related response	Compare with baseline at the same load
GMF sidebands spaced at one shaft speed	Eccentricity, runout, localized tooth damage or load modulation on that shaft	Inspect waveform, phase, gear contact and shaft runout
Higher GMF harmonics with sideband families	Increasing nonlinearity, misalignment, wear, looseness or severe contact disturbance	Check alignment, backlash, mounting, load and oil debris
Once-per-revolution impact in acceleration waveform	Cracked, chipped or broken tooth; localized contact defect	Relate impact period to the responsible shaft and inspect teeth
Broadband high-frequency energy	Impacts, poor lubrication, wear debris, looseness, bearing activity or resonance	Use waveform, oil analysis, envelope data and local comparisons

These are hypothesis patterns, not universal fault rules. Gear geometry, load, transmission path and structural resonance can change the appearance significantly.

Use the acceleration time waveform

Gearbox waveforms are naturally busy because many teeth are engaging. A localized damaged tooth can add a stronger pulse once per revolution of the shaft carrying that tooth. Acceleration usually reveals these short impacts more clearly than velocity.

Set the waveform duration long enough to include several revolutions of the slow shaft. A very short record may show tooth-mesh impacts but hide the slow once-per-revolution modulation. Look for:

• Repeating impacts at the input, intermediate or output shaft period.
• Amplitude beating that agrees with the measured sideband spacing.
• Random bursts that may indicate looseness, debris or intermittent contact.
• Peak-to-peak growth even when the velocity RMS changes little.

Measurement setup can make or break the diagnosis

GMF and its harmonics can be far above the frequency range used for routine motor data. The Emerson course recommends an Fmax of approximately 3.5 x GMF where practical so higher harmonics and adjacent sidebands remain visible. SKF gives a similar practical starting point of about 3.25 x GMF. Treat these as setup guides, not severity limits.

Also consider:

• Resolution: the frequency spacing between lines must be much smaller than the slowest shaft speed you need to separate.
• Sensor: use an accelerometer with adequate high-frequency response.
• Mounting: stud mounting normally preserves high-frequency content better than a hand-held probe or loose magnet.
• Location: measure near each bearing that supports a gear shaft, in relevant radial directions and axial direction for helical gears where appropriate.
• Sampling: avoid aliasing and retain enough waveform samples to capture impacts.
• Operating state: record speed, load, direction, oil temperature and transient events.

A single spectrum may require both a wide frequency view and a high-resolution zoom around GMF. The wide view finds harmonics and resonances; the zoom separates closely spaced sidebands.

Variable speed requires order-based thinking

When speed changes, GMF and shaft-related sidebands move. A fixed-frequency trend can miss the peak or combine different operating states. Use tachometer-referenced orders, speed-synchronous sampling, waterfall plots or narrow speed/load bands where available.

During run-up or coast-down, a gear-mesh harmonic may cross a structural natural frequency and grow dramatically. That amplitude increase may be resonance amplification rather than sudden tooth deterioration. A waterfall plot helps separate a speed-following order from a fixed natural frequency.

Do not confuse gear, bearing and process activity

Several sources can occupy the same high-frequency region:

• Rolling-element bearing frequencies and their harmonics.
• Motor rotor-bar or stator-slot frequencies.
• Fan blade-pass, pump vane-pass or compressor lobe frequencies.
• Variable-frequency-drive switching activity.
• Structural resonance excited by normal gear mesh.
• Impacts from looseness, coupling problems or a nearby machine.

Gear mesh is synchronous with shaft speed and tooth count. Bearing defect frequencies are normally non-integer orders and may include cage- or shaft-related sidebands. Calculate all credible sources before assigning a label.

Worked diagnosis: two-stage conveyor gearbox

A conveyor gearbox operates at steady production load. The input shaft runs at 29.5 Hz, the intermediate shaft at 8.2 Hz and the output shaft at 1.9 Hz. The first-stage GMF is 590 Hz. The analyst observes:

• GMF remains similar to the historical baseline.
• Sidebands around GMF have increased and are spaced at 8.2 Hz.
• The same spacing appears around 2xGMF.
• The acceleration waveform shows amplitude modulation every 0.122 seconds, approximately one intermediate-shaft revolution.
• Oil debris has increased slightly, while bearing envelope trends remain stable.

Observation: a growing first-stage mesh sideband family is modulated at intermediate-shaft speed.

Leading hypothesis: a developing tooth-contact problem associated with the intermediate-shaft gear, such as localized wear, eccentricity or alignment-related load variation.

Competing explanations: load fluctuation at 8.2 Hz, gear resonance, shaft runout, support-bearing clearance, loose mounting or an incorrect shaft-speed calculation.

Recommended actions: repeat data at comparable load; verify shaft speeds and tooth counts; collect high-resolution spectra and longer acceleration waveforms; check phase and runout where practical; review alignment, backlash and lubrication; inspect oil debris; and schedule a borescope or tooth-contact inspection according to risk.

An eight-step gearbox diagnosis workflow

1. Map the train. Record every shaft speed, tooth count, gear pair, bearing and measurement point.
2. Record operating condition. Capture speed, torque or load, direction, temperature and lubrication state.
3. Calculate all frequencies. Include shaft orders, each GMF, GMF harmonics, bearing frequencies, blade/vane frequencies and relevant electrical components.
4. Verify measurement quality. Confirm sensor, mounting, Fmax, resolution, waveform length and tachometer signal.
5. Read the pattern. Compare GMF, harmonics, sidebands, broadband energy and the acceleration waveform.
6. Measure sideband spacing. Connect the spacing to the input, intermediate or output shaft instead of guessing from peak height.
7. Test competing causes. Review load, alignment, backlash, bearings, resonance, lubrication, looseness, torsional effects and transmitted vibration.
8. Close the loop. Inspect gears and oil, document the actual failure mode, correct the root cause and repeat measurements under comparable conditions.

The damaged gear may not be the root cause

Common contributors to gear distress include incorrect or contaminated lubricant, inadequate oil delivery, water ingress, excessive or cyclic load, shaft misalignment, soft foot, incorrect backlash, bearing clearance or failure, housing distortion, poor installation, overheating and resonance.

Replacing one damaged gear without checking its mating gear and the cause can create a poor contact pattern and repeat failure. Gear-set, bearing and alignment decisions should follow the gearbox manufacturer's guidance and an inspection of the complete load path.

How System 1 and other software help

Condition-monitoring platforms can store gearbox kinematics, calculate shaft and mesh frequencies, place sideband cursors, trend selected bands, create waterfall plots, correlate vibration with speed and load, and alarm on changing patterns.

Software still depends on correct tooth counts, shaft speeds, sensor locations and operating context. It can display a sideband family instantly; the analyst must decide whether the spacing is physically credible and what test will distinguish the leading hypothesis from its competitors.

Final takeaway

• GMF is tooth count multiplied by the rotational frequency of the gear.
• GMF can be present in a healthy gearbox and is strongly affected by load.
• Sideband spacing often identifies the shaft modulating the mesh.
• Harmonics, waveform impacts, trends and oil evidence strengthen the diagnosis.
• Correct Fmax, resolution, waveform duration and sensor mounting are essential.
• A damaged gear is evidence of a failure mechanism, not necessarily its root cause.

Coming in Part 8

Part 8: Resonance and Natural Frequency Testing. We will examine resonance symptoms, impact testing, run-up and coast-down data, phase changes and practical ways to separate a forcing frequency from a structural response.

Discussion question: When you diagnose a gearbox, which evidence has been most useful - GMF trend, sideband spacing, acceleration waveform, oil analysis or visual inspection?

References and further learning

• Emerson Process Management, Basic Vibration Analysis - Course 2031, Section 6: Gear Defects.
• SKF, Spectrum Analysis, Section 10: Gears.
• Fluke Reliability, Condition Monitoring with VibGuard IIoT Helped Two Customers Avoid Over $1.7M in Damage and Downtime.

Educational note: The patterns are simplified learning guidance, not universal fault rules, alarm limits or remaining-life predictions. Apply approved site procedures, gearbox-manufacturer guidance and qualified engineering judgement to real machinery.