A roller-chain sprocket must match the chain pitch and tooth system. This calculator determines ideal pitch-circle diameters and tooth-count ratios from selected pitch and tooth counts. It does not size a chain drive or predict capacity, efficiency, service life, wear or safety.
Sprocket Pair · Selected Pitch-Geometry Ledger
Explore ideal pitch-circle diameters, selected tooth-count ratio and ideal speed factor.
Equation Used
- P is the selected common chain and sprocket pitch.
- N1 and N2 are selected integer tooth counts.
- Pitch diameter uses ideal equal chord spacing.
- The speed factor assumes synchronized pitch engagement and no shaft or coupling slip.
- Tooth form, chain series, centre distance, wrap, load, lubrication, wear and safety are excluded.
Former reduction and driven-speed wording is narrowed to a selected tooth-count ratio and ideal speed factor.
Selected pitch-geometry ledger
For N equally spaced chain pins on a pitch circle, the selected chain pitch P is the chord between adjacent pin centres, giving D=P/sin(pi/N). A selected driver/driven tooth-count pair gives the ideal angular-speed factor N1/N2.
What the calculator determines
Use it to compare ideal pitch diameters and tooth-count ratios. A real drive also requires matching chain series and width, centre distance, wrap, chain length, lubrication, alignment, speed, shock and load checks.
Exact selected relationships
D1=P/sin(pi/N1); D2=P/sin(pi/N2); selected tooth-count ratio=N2/N1; ideal driven-speed factor=N1/N2.
Selected-input example
At P=12.7 mm, N1=12 and N2=20, the ideal pitch diameters are approximately 49.1 mm and 81.2 mm, the selected tooth-count ratio is 1.67 and the ideal driven-speed factor is 0.60.
Not a drive design
The model excludes tooth form, roller diameter, chain width, centre distance, wrap angle, chordal speed variation, chain length, tension, lubrication, wear, alignment, power, torque and manufacturer limits.
Questions
Is N2/N1 always a reduction?
No. It is labelled as a tooth-count ratio because it can be below, equal to or above one.
Does the speed factor include losses or slip?
No. It is ideal synchronized pitch engagement.
Can these numbers select a chain?
No. Use current manufacturer engineering data for the full drive.
References & Further Reading
- Wikipedia contributors. Sprocket. Wikipedia
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