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No. 40 roller-chain drive, 5 hp at 1,750 rev/min on 17 and 51 teeth: chain length, centre distance, power rating and chain loads
| Tool | Chain Drives |
| Source | American Chain Association (2001). Improved Power Ratings for Single Strand Roller Chain. American Chain Association, Naples, FL. Tables 1 and 2 (service and multiple-strand factors) and the No. 40 rating table, against which the rating constants were fitted and checked. |
| Level | Professional |
Problem
An electric motor at 1,750 rev/min drives a machine with moderate shock through a single strand of No. 40 roller chain (pitch 0.5 in) on sprockets of 17 and 51 teeth with the shafts about 20 in apart; the machine takes 5 hp. Find the chain length in pitches, the centre distance that length gives, the wrap and chordal action of the small sprocket, the power rating and its margin at the service factor, the lubrication type, and the chain and shaft loads.
Inputs to Enter
- No. 40 chain: pitch 0.5 in, one strand (factor 1.0); roller diameter, weight and tensile strength left blank (estimates 5/8 p = 0.3125 in, 1.7 p² = 0.425 lb/ft, 12,500 p² = 3,125 lb)
- Power 5 hp, small sprocket 1,750 rev/min, N_1 = 17, N_2 = 51, intended centre distance 20 in, slack-strand sag 2 % of the span, service factor 1.3 (moderate shock, electric motor)
- Rating constants (2001 ratings): K_s 0.0044, tooth exponent 1.00, speed exponent 0.96, link-plate factor 1.0, K_r 17; Type B lubrication from 180 rev/min, Type C from 1,600 rev/min; galling speed estimated
Answers
- Pitch diameters 2.7211 in and 8.1220 in; ratio 3; large sprocket 583.3 rev/min; chain speed 20.66 ft/s (1,239.6 ft/min)
- Length for 20 in centres 114.73 pitches, rounded up to 116 pitches (4.833 ft); centre distance for 116 pitches 20.3199 in by the closed approximation and 20.3196 in by the tangent-line root (40.64 pitches)
- Wrap on the small sprocket 164.7°, 7.78 teeth in the wrap; chordal speed variation 1.703 % at 17 teeth and 0.190 % at 51 teeth; outside diameters 2.9748 in and 8.4066 in
- H_1 = 0.0044 · 17 · 1750^0.96 · 0.5^2.965 = 12.44 hp; H_2 = 1000 · 17 · 17^1.5 · 0.5^0.8 / 1750^1.5 = 9.348 hp; rating 9.348 hp (roller and bushing impact governs; the 2001 table prints 8.96 hp at 1,800 rev/min); peak of the curve at 1,558 rev/min; galling speed about 6,545 rev/min
- Design power 1.3 · 5 = 6.5 hp; M.S. = 9.348 / 6.5 − 1 = +0.44; Type C (oil stream) lubrication
- Chain pull 133.1 lb, centrifugal tension 5.638 lb, sag tension 4.472 lb; tight strand 143.2 lb, slack strand 10.11 lb, shaft load 141.9 lb; static factor on 3,125 lb 21.8
Notes
The tool's default inputs are this drive; press Submit. The case is illustrative, not a printed example. The rating constants are a fit to the American Chain Association tables of 2001, which the equations reproduce in 5,223 of 5,224 standard-series cells away from the galling limit (test_chain_drives.php, 6,696 checks, with an independent numpy and scipy script for the geometry and loads). The weight, tensile strength and roller diameter are estimates recalled by the builder and labelled so on the page; enter the maker's values.