What is tooth meshing frequency in a chain drive?

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 increases with worn or damaged teeth.

What is chain link frequency?

Chain link frequency is the rate at which one complete revolution of the chain occurs. It equals the tooth meshing frequency divided by the total number of links: f_chain = Z1 × RPM / (60 × N_links). A defect on a single chain link will produce vibration at this frequency.

How do I diagnose chain wear from vibration?

Chain wear typically increases the amplitude of tooth meshing frequency and its harmonics. A worn or elongated chain may also produce sidebands around TMF spaced at chain link frequency. Impact-type vibration from loose chains produces broadband noise with elevated TMF harmonics.

What causes chain drive vibration?

Common causes include chain wear and elongation, misaligned sprockets, improper chain tension, worn sprocket teeth, damaged or stiff chain links, and chordal action (polygonal effect). The polygonal effect is inherent to chain drives and produces vibration at tooth meshing frequency.

What is the polygonal effect in 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 and can be reduced by using sprockets with more teeth (≥21).

Free Engineering Tool

Roller Chain Defect Frequency Calculator

Calculate tooth meshing frequency, chain link frequency, driven speed, and harmonics for roller chain drive systems.

Roller Chain Tooth Meshing Chain Link Freq

Results

Tooth Meshing Frequency

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Chain Link Frequency (1 chain revolution)

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Driver Shaft Frequency

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Driven Speed

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Speed Ratio (Z₁/Z₂)

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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:

N_links — 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

Example — 17/51 Chain Drive

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.