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V-belt drive design

Enter power, speeds, belt section and pulleys to get the belt length, how many belts to run and the force to tension them at installation.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizing
Drive
Belt and pulleys

With the driven pulley at 0, its diameter comes from the speed ratio. Belt length is rounded to the nearest stock size (ISO 4184 R40 series for narrow belts; belt number in inches for classical belts) and the center distance is recalculated.

—Belts required
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Number of belts versus driver pulley diameter

Same ratio, section and service factor. Larger pulleys raise belt speed and power per belt.

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Power per belt by section

Basic rating plus speed-ratio addition at this pulley and speed, corrected for arc of contact. Sections whose minimum diameter exceeds the pulley are left empty.

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Method, assumptions and references

Equations used

Ratio: i = n1 ÷ n2 = D ÷ d; exact length: L = 2C·cos β + π(D + d)/2 + β(D − d), sin β = (D − d) ÷ (2C); C recalculated for the stock length by bisection
Arc: θ = 180° − 2β; Cθ = 1.25 · (1 − 5^(−θ/180)); length: CL = (L ÷ Lref)^k
Basic rating (RMA/ISO 5292 form): P = x · [K1 − K2/d − K3 · x² − K4 · log x], x = d · n ÷ 1000 (d in inches, P in hp); plus speed-ratio addition
Belts: z = ⌈P · fs ÷ (P1 · Cθ · CL)⌉; static tension: T = 500 · (2.5 − Cθ)/Cθ · P/(z · v) + m · v²; deflection: F = T/16 to 1.5·T/16 to deflect span/64

Assumptions and limits

  • Classical A, B and C: RMA constants K1 to K4 (Machinery’s Handbook). Narrow sections: constants fitted by least squares to catalog 3V, 5V and 8V rating tables (typical error 2%, maximum 10%); SPZ ≈ 3V and SPB ≈ 5V; SPA and SPC by geometric similarity of the section. Values for standard belts; premium belts carry 20% to 40% more.
  • Slip of 1% to 2% ignored in speed. Deflection force excludes the belt stiffness term (add about 10% for new belts). Confirm the result in the belt maker’s catalog.

Standards and technical documents

  • ISO 4184: Belt drives — Classical and narrow V-belts — Lengths in datum system
  • ISO 4183: Belt drives — Classical and narrow V-belts — Grooved pulleys (system based on datum width)
  • ISO 5292: Belt drives — V-belts and V-ribbed belts — Calculation of power ratings
  • ARPM (RMA) IP-20: Specifications for drives using classical V-belts and sheaves; IP-22: narrow multiple V-belts
  • Machinery’s Handbook, 31st ed.: V-belt horsepower rating formulas
  • Bando: V-Belt Design Manual (rating tables 3V, 5V, 8V)

U.S. regulations

  • OSHA 29 CFR 1910.219: mechanical power-transmission apparatus (belt and pulley guarding)
  • ASME B15.1: Safety Standard for Mechanical Power Transmission Apparatus

Frequently asked questions

How do I calculate V-belt length?

Use L = 2C·cos β + π(D + d)/2 + β(D − d). For 6 in and 12 in pulleys at 20 in centers, L = 68.7 in pitch; the nearest belt is a B-67 (68.8 in pitch), and centers barely change.

How many belts do I need?

Divide design power (power × service factor) by the corrected rating of one belt. With 20 hp, a 1.2 factor and B belts on a 6 in sheave at 1750 rpm (about 7.5 hp each before corrections), you need 4 belts.

How do I tension a V-belt?

Push the middle of the span until the belt deflects 1/64 in per inch of span and read the force. It should sit between T/16 and 1.5·T/16, where T is the calculated static tension. Retension after 24 hours of running.

Narrow or classical belts?

Narrow belts (3V, 5V, 8V, or SPZ, SPA, SPB, SPC) carry more power with fewer belts and smaller sheaves. Classical A, B and C belts are still common as replacements and on older machines.