A collection of lookups and calculations for ANSI standard roller chains.
All ANSI reference values are from manufacturers' catalogues.
The chains' length conversion between inches and pitches is calculated by the folling formula:
$$ L = P \times p $$
where:
$L$ = chain length, inches
$P$ = chain length, pitches
$p$ = chain pitch distance, determined from ANSI values
The weight of the chain is calculated as…
$$ W =\frac {L \times w}{12} $$
where:
$W$ = weight of length of chain, lbs
$w$ = weight of chain, determined from ANSI values, lbs per foot
$L$ = length of chain, inches
Elongation of the chain is determined as follows…
$$ l = \frac {L}{12} \times \frac {T}{k_{elongation}} $$
where:
$l$ = elongation of chain length due to stretch, inches
$L$ = length of chain, inches
$T$ = chain tension, lbf
$k_{elongation}$ = a stretch factor. Interpolated from a data from Tsubaki. This value is determined by the selected chain size.
Calculate the center distance of the two shafts when the chain’s pitch length is given…
$$ C_{dist} = \frac {p}{8} \times \left(2P - N - n \right) + \sqrt{ \left(2P - N - n \right)^2 - \frac {8}{\pi^2} \times (N - n)^2 } $$
where:
$C_{dist}$ = Center-to-center distance of shafts, *inches*
$P$ = chain length, pitches
$p$ = chain pitch distance, determined from ANSI values
$N$ = number of teeth on larger sprocket
$n$ = number of teeth on smaller sprocket
Calculate the pitch length of a chain when the ceter-to-center distance of the two shafts are given…
$$ P = 2 \frac {C_{dist}}{p} + \frac {N+n}{2} + \frac {(\frac {N-n}{2 \pi})^2}{ \frac {C_{dist}}{p}} $$
Calculates properties for a sprocket of user selected size and tooth number…
$$ D_{p} = p \times sin \, t_{no} $$ $$ D_{o} = p \times \left( 0.6 + \frac {1}{tan \, t_{no}} \right) $$ $$ t_{width} = 0.93 c_{width} - 0.006 $$
where:
$p$ = chain pitch distance, determined from ANSI values
$t_{no}$ = number of sprocket teeth
$t_{width}$ = width of sprocket teeth
$D_{p}$ = pitch diameter, *inches*
$D_{o}$ = outside diameter, *inches*