Belt & Pulley — validation & limitations

What it calculates

• V-belt drive design on ISO 4184 / DIN 7753 sections, plus flat and synchronous (timing) belt drives by capstan and vendor methods
• Tension ratio and wrap angle via the Euler–Eytelwein capstan equation (open, crossed and tensioner configurations)
• Belt fatigue life estimation combining tensile and bending stress (engineering estimate — Wöhler heuristic)
• Synchronous belt tooth shear load, teeth-in-mesh count and shear safety factor
• Service-factor-adjusted design power with ISO 4184 section selection guide
• Belt slip safety margin versus wrap angle (interactive chart)

Standards this tool applies

• ISO 4184 — V-belt, flat belt and synchronous drive calculation — wrap angle, belt length, tight/slack-side tensions (Euler–Eytelwein) and a power-range section guide. ISO 4184 / DIN 7753 section designations are reference data; no power rating (ISO 5292) or datum-length selection.

Validation evidence — independent reference cases (1)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• V-belt geometry and belt tensions against a worked example

  Agrees

  Source: Shigley's Mechanical Engineering Design (Budynas & Nisbett), 9th/10th ed., §17-3, Example 17-4; Eq. 17-1, 17-16b, 17-19 to 17-21, Table 17-16

  Inputs: 1750 rpm, sheaves 7.4 in / 11 in, C 42.41 in, 13 hp over 3 belts (Ks 1.3), Kc 0.965, f 0.5123

  Quantity	Reference value	Tolerance
  Belt tension F1	286.50 N (64.4 lbf)	1e-5 vs hand; 0.5 % vs printed
  Belt tension F2	98.881 N (22.2 lbf)	1e-5 vs hand; 0.5 % vs printed
  Wrap angle	3.0567 rad	1e-9 relative
  Centrifugal tension Fc	49.339 N (11.1 lbf)	1e-6 vs hand; 0.5 % vs printed

  tests/golden/REF-belts-vbelt-tensions.golden.test.ts

Limitations

Not checked by this tool

• V-belt power rating per belt and the number of belts — Not computed (ISO 5292 / maker tables); confirm the rating and belt count with the belt manufacturer
• Synchronous-belt rated tooth / tension capacity for the chosen width — Not computed; confirm with the belt manufacturer's rating tables
• Standard (stock) belt length and the resulting centre distance — The computed length is not rounded to a stock length; pick it from the maker's list and recheck wrap and tensions
• Temperature, oil and environment derating of the belt — Only the service factor Ks is applied; apply the belt maker's derating factors
• Pulley misalignment and belt tracking — Not modelled; keep within the belt maker's alignment limits
• Sheave rim-speed rating and the pulley hub / key connection — Belt speed is checked against the belt's limit only; check the sheave maker's rating and the hub with /keys
• Shaft and bearing sizing for the belt pull — The shaft load is reported; size the shaft with /shaft and the bearings with /bearings