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.