Fixed-axis pair kinematics — candidate spectral positions only
Gear-Mesh Kinematic Frequency Calculator
Calculate the mesh frequency of one simple fixed-axis gear pair,derived driven-shaft speed,a selected mesh harmonic and arithmetic candidate sideband positions. The result does not diagnose a fault or apply an ISO vibration limit.
Kinematic frequencies
Arithmetic candidate sidebands around h·fm
| n | Spacing n·f₁ | Lower hfm−n f₁ | Upper hfm+n f₁ | Spacing n·f₂ | Lower hfm−n f₂ | Upper hfm+n f₂ |
|---|
Implemented fixed-axis pair equations
f₂=f₁N₁/N₂
fm=N₁f₁=N₂f₂
fc=hfm
candidate positions=fc±n f₁ and fc±n f₂
N₁ and N₂ are positive integer tooth counts;for a worm pair,N₁ is the number of starts. Frequencies are magnitudes in hertz. Direction,backlash,transmission error,load,amplitude and phase are not calculated. Planetary and moving-carrier systems require their own relative-speed kinematics.
Published technical basis
NASA/TM—2013-216617 describes gear-mesh frequency as tooth count multiplied by rotational speed and reports sidebands at integer shaft-speed offsets in its tested gear set. It uses measured sideband amplitudes in a particular condition indicator;this page uses only the frequency-position kinematics.
NASA TM112207 explains that sidebands arise from rotational modulation and notes that normal tooth-load fluctuations can occur at gear-mesh sidebands without being connected to a fault. Therefore calculated positions alone cannot identify a cracked tooth,eccentricity or a particular wheel.
Current ISO scope—not a formula source
ISO20816-9:2020,edition1 covers measurement and evaluation of broad-band housing/shaft vibration for specified enclosed gear units and operating ranges. Its official scope says specialist techniques for evaluating gear condition are outside the document. It supplies no universal GMF/sideband fault threshold to this calculator.
ISO13373-3:2015,edition1 remains confirmed and provides general structured vibration-diagnosis procedures. It is not the source of the elementary mesh-frequency equation and does not make an isolated sideband position a diagnosis.
Removed obsolete/unrelated references
The former related-link labels invoked ISO10816 and ISO1940 without applying a specific current part or scope. Gear-unit vibration evaluation is now referenced to ISO20816-9:2020. ISO1940-1:2003 is withdrawn and replaced by ISO21940-11:2016 with Amendment1:2022 for rigid-rotor balancing;that balancing standard is not a gear-mesh-frequency formula.
No automatic diagnosis
No line in this page means “healthy”,“worn”,“cracked” or “severe”. Diagnosis requires actual spectra and waveforms,stable operating conditions,adequate frequency resolution,trend/baseline evidence and corroborating features. A lower algebraic candidate at0Hz is labelled DC;negative algebraic positions are not displayed as physical negative frequencies in a one-sided spectrum.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
