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Roller Chain Defect Frequency Calculator
Calculate tooth meshing frequency, chain link frequency, driven speed, and harmonics for roller chain drive systems.
Results
Tooth Meshing Harmonics
| Harmonic | Frequency (Hz) | CPM | Note |
|---|
Tooth Meshing Frequency
The tooth meshing frequency (TMF) is the rate at which chain links engage with sprocket teeth:
- Z₁ — number of teeth on driving sprocket
- n₁ — driver shaft speed (RPM)
Chain Link Frequency
The chain link frequency represents one complete revolution of the chain loop:
- Nlinks — total number of chain links
Driven Speed
Vibration Indicators
| Frequency | Source | Indication |
|---|---|---|
| 1× TMF | Tooth engagement | Normal chain operation, polygonal effect |
| 2×, 3× TMF | Harmonics | Chain wear, worn sprocket teeth, excessive slack |
| 1× chain link freq | Chain revolution | Single defective link, tight link |
| Sidebands around TMF | Modulation | Worn/elongated chain, misalignment |
Given: Z₁ = 17, Z₂ = 51, Links = 120, n₁ = 1450 RPM
TMF = 17 × 1450 / 60 = 410.83 Hz
Chain freq = 17 × 1450 / (60 × 120) = 3.42 Hz
Driven speed = 1450 × 17/51 = 483.3 RPM
Speed ratio = 17/51 = 0.333
⚠️ Note: For sprockets with fewer than 21 teeth, the polygonal (chordal) effect becomes significant, producing higher TMF harmonics even in healthy chain drives. Use 21+ teeth sprockets when smooth operation is critical.
Tooth meshing frequency (TMF) is the rate at which chain links engage with sprocket teeth. It equals the number of teeth on the driving sprocket multiplied by the shaft rotational frequency: TMF = Z₁ × RPM / 60.
This frequency is a dominant vibration source in chain drives and its amplitude increases with worn or damaged teeth.
Chain link frequency is the rate at which one complete revolution of the chain loop occurs. It equals the tooth meshing frequency divided by the total number of links:
fchain = Z₁ × RPM / (60 × Nlinks)
A defect on a single chain link (tight link, damaged roller) will produce vibration at this frequency.
Chain wear typically increases the amplitude of tooth meshing frequency and its harmonics (2×, 3×, 4× TMF). Key indicators:
- Rising TMF harmonics — chain elongation, worn sprocket teeth
- Sidebands around TMF at chain link frequency — modulation from chain defects
- Broadband noise increase — severe wear, loose chain
- 1× chain frequency peak — single defective or tight link
Common causes include:
- Chain wear and elongation (pitch growth)
- Misaligned sprockets
- Improper chain tension (too tight or too loose)
- Worn sprocket teeth (hooked teeth profile)
- Damaged or stiff chain links
- Polygonal (chordal) effect — inherent to chain drives
The polygonal (chordal) effect occurs because a chain wraps around a sprocket as a polygon rather than a smooth circle. This causes periodic speed variation at the tooth meshing frequency.
The effect is more pronounced with fewer teeth on the sprocket. Using sprockets with 21 or more teeth significantly reduces the chordal action. The speed variation is approximately ±(1 − cos(180°/Z)) × 100%.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional vibration analysis instruments and software. Diagnose chain drive issues on-site. Used in 50+ countries.
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.
