Conveyor Belt — validation & limitations

What it calculates

• ISO 5048 bulk material capacity in t/h and m³/h for three-roll troughed idler geometry (DIN 22101 equal-roll cross-section)
• Drive power and motor selection: main resistance F_H, secondary resistance F_N (with the ISO 5048 length factor C), incline/decline lift resistance F_St
• Belt tensions (tight side T₁, slack side T₂) using Euler's belt-friction formula, minimum sag tension and belt-strength utilisation
• Idler load on the most-loaded roll (estimate — centre-roll share of the cross-section), carry-run belt sag percentage and the DIN 22101/CEMA 1.5 % sag limit check
• Take-up travel and recommended take-up range from belt elongation (ISO 9856 per-unit-width modulus)
• Discharge trajectory off the head pulley — departure angle, landing distance and maximum height

Standards this tool applies

• ISO 5048 — ISO 5048 resistance-method power and tensions: bulk capacity (t/h, m³/h), main resistance, length factor C, shaft power, belt tensions T₁/T₂, sag check, take-up travel and discharge trajectory.

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.

• Overhauling (regenerative) decline threshold

  Conservative

  Source: Hand derivation from ISO 5048 / DIN 22101 motional resistance, F_U = C·F_H + F_S + F_St and the DIN 22101 load section

  Inputs: Sand 1600 kg/m3, B 1000 mm, trough 35 deg, v 2.5 m/s, L 150 m, f 0.020, q_B 6.5 kg/m, C 1.58; H -4.9 m and -5.1 m

  Quantity	Reference value	Tolerance
  Load q_G	215.37 kg/m	1e-5 relative
  F_U lower bound, H -4.9 m	+260.77 N (not overhauling)	1e-4 relative
  F_U lower bound, H -5.1 m	-162.26 N (overhauling)	1e-4 relative
  Plain ISO F_U, H -5.1 m	+1231.37 N	1e-4 relative

  Conservative simplification: The engine screens on a lower-bound driving force that omits idler rotating mass, so it flags an overhauling decline about 0.66 m of lift earlier than the plain ISO 5048 force does.

  tests/golden/REF-conveyor-overhauling-decline.golden.test.ts

Limitations

Conservative simplifications

• Overhauling (regenerative) decline threshold — The engine screens on a lower-bound driving force that omits idler rotating mass, so it flags an overhauling decline about 0.66 m of lift earlier than the plain ISO 5048 force does.

Not checked by this tool

• Pulley shaft, bearings and pulley shell strength — Only a rule-of-thumb pulley diameter is suggested; size pulleys per DIN 22101 / the supplier and shafts with /shaft
• Idler rating and idler bearing life for the roll load — Compare the roll load with the idler maker's rating
• Brake / backstop sizing and stopping tensions — Stopping and surge loads are not modelled; size the brake or holdback for the decline and coast-down
• Belt splice strength — The belt safety factor covers the carcass; check the splice efficiency with the belt supplier
• Troughing transition distance and belt edge stresses — Not checked; set the transition length per DIN 22101 or CEMA
• Convex and concave vertical curves — A straight profile is assumed; calculate the curve radii per DIN 22101 or CEMA