Roller Chain Drive (`roller-chains`)

Check	IND	US	EU	ISO
Power capacity utilization	implemented	—	—	—
Estimated chain life	implemented	—	—	—

Purpose

Size roller chain drives by computing sprocket geometry, chain speed, transmitted power, tension, and estimated service life. Supports strand selection and power capacity screening for industrial machinery drives.

Physics & theory

Roller chains transmit power through sprocket tooth engagement. Chain pitch $p$ and number of teeth $N$ define pitch diameter $D = p / sin (π / N)$ . Chain speed $v = π D n /60$ . Power $P = F v$ relates to chain tension $F$ , which includes centrifugal and chordal action effects at high speeds.

Chain life depends on lubrication, alignment, load spectrum, and pitch selection. ANSI/ISO power rating tables provide allowable power vs speed for each chain number; the module applies service factors and strand count to estimate utilization and life cycles.

Power transmission elements operate under cyclic tension, bending, and contact stresses. Service factors account for driver type (motor vs engine), daily operating hours, and shock loading. Belt slip occurs when required friction capacity exceeds available wrap; chain drives depend on proper lubrication and sprocket tooth count for rated life.

Center distance adjustment affects belt length and wrap angle simultaneously — the solver uses the standard open-drive length formula assuming coplanar shafts and parallel pulley grooves.

Governing equations

D = \frac{p}{sin ( π / N )}, v = \frac{π D n}{60}

F = \frac{1000 P}{v}, i = \frac{N _{2}}{N _{1}}

L = \frac{p}{2} (2 C / p + N_{1} + N_{2} + f (N_{1}, N_{2}, C))

Numerical method

Closed-form sprocket and length equations with tabulated power ratings per chain size. Life estimate from load ratio relative to catalog rating, adjusted by lubrication and service factors. Multi-strand capacity scales approximately linearly with strand count.

Inputs

Parameter	Description
Chain number / pitch	ANSI chain designation
Sprocket teeth (driver, driven)	Tooth counts
`centerDistance`	Center distance
`speedDriver`, `power`	Operating conditions
Strands, lubrication type	Capacity multipliers

Outputs

Pitch diameters, chain speed, chain tension, power utilization, estimated chain life, length in pitches.

Design codes & checks

Indicative: Power capacity utilization, chain life estimate
US: ANSI/ASME B29.1 roller chain standards
ISO: ISO 606 short-pitch precision roller chains

Assumptions & limitations

Steady power transmission; shock loads require additional service factor.
Horizontal or near-horizontal drives; vertical lifts need tension adjustment.
Catalog ratings assume adequate lubrication and sprocket tooth count ≥ 17 (recommended).
Does not analyze silent (inverted tooth) or leaf chains.

References

Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 17.
ANSI/ASME B29.1-2011. Precision Power Transmission Roller Chains.
ISO 606:2015. Short-pitch transmission precision roller chains.
Renold. The Complete Guide to Chain.
PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.

Roller Chain Drive

Assumptions

Limitations

Engineering checks