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 ISO1940-1:2003 is withdrawn and replaced by ISO21940-11:2016 with Amendment1:2022 for rigid-rotor balancing;that balancing standard is not a gear-mesh-frequency formula.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.
