Ideal average-speed arithmetic
Roller-Chain Kinematic Frequency Calculator
Calculate shaft, tooth-engagement and chain-loop candidate frequencies for an ideal no-slip chain drive. The output locates spectral lines; it does not identify a defect.
Kinematic candidate lines
Arithmetic multiples of engagement rate
| Вишеструко | Учесталост | Cycles/min |
|---|
Multiples are frequency markers only; amplitude, sidebands or a matching line are not a diagnosis by themselves.
Ideal kinematic identities
fₑ is the mean rate at which chain pitches engage sprocket teeth. Dividing by the total pitch count gives the mean loop-circulation frequency: one identified link returns to the same reference position once per loop. The formula does not predict vibration amplitude.
Standards boundary
ISO 606:2015 specifies characteristics of short-pitch precision roller/bush chains and associated sprockets, including dimensions, tolerances, length measurement and strength. It is currently published but under revision. ISO 10823:2004 with Corrigendum 1:2008, confirmed in 2024 and under revision, gives industrial roller-chain drive selection guidance and explicitly notes that loading, environment and maintenance vary and supplier consultation is desirable. Neither official scope turns these candidate frequencies into fault diagnoses.
Tooth-count recommendations are application and product dependent. For example, the Renold Roller Chain Designer Guide recommends 19 teeth as an ideal minimum in its selection method and at least 25 for high speed or impulsive loads. That does not create a universal threshold for all chain drives; use the applicable standard, supplier data and design conditions.
Diagnostic gate: use a verified speed reference and compare measured spectra, orders, time waveforms, modulation/sidebands, trends, load and inspection. A calculated line may contain normal engagement energy, structural response, another source or a defect-related modulation. Do not label wear, slack, misalignment, a tight link or severity from frequency coincidence alone.
Checked example
Z₁=17, Z₂=51, L=120, n₁=1450 rpm gives f₁=24.166667 Hz, fₑ=410.833333 Hz, floop=3.423611 Hz and n₂=483.333333 rpm.
