How gear mesh frequency varies with input speed and load
Gear mesh frequency is the rate at which gear teeth enter and leave contact. In a power-reduction gearbox, it links rotational speed directly to vibration, bearing loads and tooth fatigue. For geared aircraft engines, it helps engineers decide whether a change in a test trace comes from the shaft, the gear pair or another component. The key distinction is between a genuine frequency shift and a load-related change in amplitude, phase or sideband strength.
For a fixed tooth count, mesh frequency rises in direct proportion to shaft speed. If a pinion has (z) teeth and turns at (n) rpm, its mesh frequency is (f_m = z n / 60). A 24-tooth pinion at 1,200 rpm produces 480 Hz; at 1,800 rpm it produces 720 Hz. Load does not alter that ideal calculation at a steady commanded speed. It can slightly alter actual shaft speed and usually changes the vibration around the mesh peak.
That distinction matters because test engineers often use “frequency” loosely. The fundamental mesh peak may stay locked to shaft speed while load can increase vibration amplitude, broaden a resonance or introduce stronger sidebands. Under a speed ramp, the peak moves continuously; during a load step, it may shift only if the drivetrain slows, surges or changes effective stiffness. A reliable guide must separate these behaviours rather than treating every load change as a new mesh frequency.
Australian conditions make this practical. Hot, dusty ramp environments around Perth and Alice Springs can raise oil and housing temperatures and introduce contamination, while regional routes and mining or agricultural aircraft spend long periods away from suitable maintenance bases. In Australia’s maintenance, repair and overhaul market, imported engines and long-lead replacement parts make premature failures expensive, and airworthiness evidence must meet Civil Aviation Safety Authority (CASA) expectations. The OPTIMIZE Project responds to these pressures through design-of-experiments methods, simulation, tolerance analysis and physical testing for power-reduction gearboxes.
Why mesh frequency follows shaft speed
Every gear stage has its own mesh frequency because it has its own input speed and tooth count. For the first stage, use pinion speed; for a later stage, first apply the preceding reduction ratio. An external pair meshes at one frequency even though its two gears rotate at different speeds: (f_m = z_p n_p / 60 = z_g n_g / 60). Helical teeth, profile shift and contact ratio alter the force waveform, not this counting relationship.
This relationship remains useful near the design point. A 20% rise in pinion speed gives a 20% rise in mesh frequency, while a 20% rise in load leaves the theoretical frequency unchanged. If a speed-controlled test shows the mesh peak moving from 600 to 720 Hz, the ratio is a straightforward 1.2 times change. The same movement during a load increase points first to a small speed droop or changing speed reference, so verify shaft speed before blaming tooth geometry.
Load still determines the severity of the event. Increasing contact force can raise tooth-root bending, contact stress, lubricant-film demands and bearing reactions. It can also change transmission error, gear deflection and damping, making the mesh line brighter, wider or flanked by stronger shaft-order sidebands. In a hyperstatic arrangement, the surrounding structure restrains small geometric changes, so measured response can differ from that of an unloaded laboratory gear. Mesh frequency identifies where the action occurs; the load-dependent spectrum shows how hard the gears are working there.
Reading harmonics, sidebands and thermal effects
A practical spectrum is rarely a single line. The mesh frequency and its integer harmonics appear alongside lower shaft-related orders, while amplitude modulation creates sidebands such as (f_m \pm f_{rot}) and (f_m \pm 2f_{rot}). At steady speed, the centre frequency and harmonic spacing remain tied to geometry and speed. As load rises, the carrier may remain fixed while sidebands and nearby resonance amplitudes grow, making a rising trace easy to mistake for a drifting fundamental.
High operating speed also changes what the accelerometer sees. Structural modes can amplify one mesh harmonic, filters can shape the result, and bearing defects can add frequencies that overlap the gear family. Lubrication conditions matter just as much: viscosity and aeration influence damping and contact behaviour. At altitude, reduced pressure can promote aeration and oil foaming; the project’s discussion of oil foaming at altitude explains why bearing lubrication can deteriorate even when commanded shaft speed is unchanged.
For Australian testing, the surrounding environment belongs in the analysis. A gearbox tested after a hot day may enter the test with different oil viscosity and housing temperature from one tested early in a cool morning. Dust near regional airports can load filters and contaminate components, while changing pressure and temperature during operation can alter lubricant flow. These effects belong beside speed and load in the test record because they change response even when the ideal mesh frequency does not move.
Measuring speed and load without chasing artefacts
Start with a synchronised measurement chain. Use a shaft tachometer or encoder to define revolutions, accelerometers close to the relevant bearing housings for response, and a torque transducer to verify applied load. Record oil and component temperatures, lubricant pressure and flow where available. Order tracking is especially useful because it maps a changing mesh line against the actual shaft reference, while a conventional FFT remains useful for stable points. Preserve the raw time signal so the team can revisit transient events.
Build the campaign in repeatable blocks: establish a no-load baseline, apply graduated torque at fixed speed, hold each condition until temperature stabilises, then repeat while sweeping speed. Include load steps and a controlled run-down because they reveal hysteresis, speed droop and transient overshoot. Use a sampling rate and anti-alias filter that cover the highest mesh harmonic of interest, and check accelerometer mounting resonances before attributing a large peak to the gear.
Compare repeated runs rather than a single trace. Calibrate the tachometer, confirm tooth-count inputs, and inspect the unfiltered signal for impacts, electrical interference or bearing-generated frequencies. Before an Australian workshop declares a rig “good to go”, calibration and repeatability should be settled; plain shop-floor shorthand should not replace documented evidence. If an analyst uses a generic gear vibration reference to label a mesh family, check that its definitions match the rig convention. The project’s raw data, calibration record and uncertainty budget should remain the authority for an aircraft decision.
Converting observations into gearbox design choices
A sound test programme connects measured response to design variables. In the OPTIMIZE approach, design-of-experiments can separate speed, torque, tooth geometry, material, lubrication and manufacturing variation without running every possible combination. Simulation then tests whether a candidate preserves efficiency, durability, weight and power density across the measured operating envelope. Tolerance analysis remains essential because a nominal mesh frequency can be correct while tooth spacing, profile, alignment or backlash changes the actual response and fatigue margin.
Housing material is one variable that can separate frequency from response. Aluminium and steel differ in stiffness, mass and thermal distortion; the project’s housing material comparison examines those consequences for gearbox weight and dimensional stability. If a hot test shifts a resonance or changes the phase of a mesh harmonic without moving its frequency, a housing change may be more effective than chasing the speed controller. If the carrier moves with shaft speed, the kinematic design remains the priority.
The same spectrum can guide contact-ratio, profile-shift, alignment, surface-finish and lubrication choices, provided manufacturing variation is included rather than treated as an afterthought. A useful comparison separates the signatures most often encountered during a controlled speed–load campaign.
| Operating condition | Expected frequency behaviour | Companion evidence | Engineering interpretation |
|---|---|---|---|
| Fixed speed, rising load | Mesh centre normally stays fixed; amplitude and sidebands change | Torque, shaft speed, oil pressure, temperature | Confirm there is no actual speed droop |
| Increasing input speed | Mesh frequency and harmonics move proportionally | Tachometer reference, FFT or order tracking | Kinematic shift rather than load effect |
| Load step or transient | Movement occurs only if actual speed changes | Time history, tachometer, torque | Droop, surge, resonance or impact |
| High temperature or low pressure | Carrier remains unchanged; damping and lubrication response may alter | Oil temperature, pressure, viscosity and flow | Thermal or aeration effect |
| Tooth or manufacturing variation | Average frequency remains unchanged; phasing and sidebands change | Metrology and profile measurements | Tolerance or backup-ratio issue |
Practical recommendations for the next test campaign
Use the first run to establish the measurement chain, not to chase a dramatic result. Document tooth counts, stage ratios, sensor locations, calibration, sampling settings and the speed reference. A useful design cross-check is tooth geometry: the project’s tooth backup ratio study shows how backup ratio changes bending and contact fatigue, helping explain why load can raise selected harmonics even when the mesh carrier stays fixed.
The following actions give an Australian test team a practical way to produce evidence that can survive engineering review and operational scrutiny:
- Hold speed and load separately. Establish a stable baseline at fixed rpm, then apply measured torque increments without changing the speed command.
- Prove the reference. Pair tachometer data with the tooth-count calculation, and use order tracking to confirm that the identified peak follows the expected mesh order.
- Log thermal and lubrication state. Oil temperature, flow, pressure and ambient conditions can change amplitudes and damping even when mesh frequency is unchanged.
- Repeat points after thermal soak and inspect the spread. A repeatable mean with a sensible uncertainty band is more useful than one spectacular trace.
- Preserve traces and assumptions. Archive raw time data, FFT or order-tracking settings, calibration files and test notes so another engineer can reproduce the result.
Bring the completed speed–load map, spectral traces and tolerance findings into the next gearbox design review. Use the OPTIMIZE Project’s videos, objectives and methodology to plan the next physical test around the specific frequency, load or thermal question exposed by the data.