CourseWiki/Engineering Fundamentals/Power Transmission

Belt Drives

Distinguish friction belts from timing belts, read belt and pulley terminology, and recognize common wear patterns.

Flat and V-belts grip; timing belts engage teeth

Flat belt: A broad, flat band transmits force through friction against a pulley. Useful for smooth, quiet motion and long spans when the drive is designed for them. Tracking and tension matter.
V-belt: A trapezoidal section runs in a matching V-groove. Contact at the sides gives a wedging action that increases grip. The belt should not rely on rubbing the bottom of the groove.
Timing / synchronous belt: Teeth on the belt engage matching grooves in the pulleys. Load is carried by this engagement, so the drive keeps its tooth-count ratio without frictional slip in normal operation.

Flat belt touching a flat pulley surface, V-belt contacting groove sides with bottom clearance, and timing-belt teeth fitting matching pulley grooves. — Contact shape determines how force crosses from pulley to belt. Sketches show the principle, not a manufacturing profile.

Timing does not come from extra tension. It comes from matching teeth. An undertensioned or overloaded timing belt can jump teeth or strip them; that is a fault, not its normal way of transmitting power. A notched V-belt remains a friction belt: relief notches for bending do not make it a timing belt.

Belt contact transfers load at the pulley rim; the pulley still needs a connection to its shaft. For a keyed pulley, follow the torque path through the key and hub. Other pulley mountings use different connections.

Read length, tension and wrap before ordering

Pulley / sheave: The wheel that carries a belt. “Sheave” is commonly used for a grooved belt pulley. A timing pulley has matching tooth grooves.
Pitch and pitch length: Timing-belt pitch is the spacing between adjacent tooth centers along the pitch line. Pitch length is the loop length along that reference line, near the tensile cords. It is not the outside circumference. Match pitch and tooth profile to the pulley.
Tension: The pulling force along the belt. The difference between the loaded and return spans transmits torque. Installation tension keeps the belt seated; too little encourages slip or tooth jumping, and too much loads belts and bearings.
Wrap angle: The angle through which the belt contacts a pulley. Less wrap gives a friction belt less contact and a timing belt fewer teeth in engagement. Check the smaller pulley in particular.

Catalogs may specify inside, outside, datum, effective or pitch lengths. Use the length convention and measuring method for that belt family; do not substitute a tape measurement of the outside for the catalog value.

One-stage reminder: n_out = n_in × D_driver / D_driven using matching effective/pitch diameters and assuming no slip. For timing belts, use tooth counts N in place of diameters. Write the reduction as i:1, where i = input speed / output speed. Follow Gear Ratios for the ratio method and Rotation and Linear Speed for belt linear speed.

Here N means teeth and n means rotational speed. Some class slides use n for teeth and ω for angular speed; check the quantity, not just the letter.

Choose a belt for the load and environment

Belts can span separated shafts, soften vibration and avoid oil at the transmission contact. Flat and V-belts suit jobs where a small speed variation is acceptable. Choose a timing belt when the shafts must stay synchronized. Compare the alternatives in Belt, Chain and Gear Drives.

Check belt section or tooth profile, width, minimum pulley size, available length, wrap, power rating, temperature and chemical compatibility. There is no single maximum speed or temperature range for every belt. Reinforcement cords limit stretch, but the belt still needs correct alignment and installation tension.

Some specially designed flat-belt layouts connect nonparallel shafts. That does not make misalignment acceptable in an ordinary V-belt or timing-belt installation. Frictional slip may soften an overload, but it can also generate heat and destroy the belt; it is not a guaranteed overload-protection device.

Use the wear pattern to find the cause; Practice

Use the wear pattern to find the cause

Fault clues to investigate with the drive safely isolated.
Symptom	Possible cause to check
Squeal, glazing or excess heat on a friction belt	Low tension, overload, contamination or worn pulley grooves can reduce grip.
Frayed edges or the belt tracking to one side	Pulley alignment, damaged flanges and shaft movement.
Cracks or hardening	Age, heat, chemical attack or repeated bending around an unsuitable pulley.
Missing timing-belt teeth or lost timing	Overload, inadequate tension, poor engagement, debris or worn pulleys.

Inspect the pulleys as well as the belt. Replacing the worn part without fixing its cause often repeats the failure. Follow the product's tension and inspection instructions; use Equipment Operating Procedure before touching the drive.

Practice a timing-pulley speed

Manufacturer references for belt geometry and faults

Gates, Preventive Maintenance Manual, “Belt identification,” “Installation,” and “Belt drive problem diagnosis,” supplies the length/profile distinctions and troubleshooting checks. Gates' industrial synchronous-belt guide explains toothed engagement and dry belt contact. Use the exact belt's data for a real selection.

Explore how pulley size and spacing change belt length and wrap; Interactive; Practice

Explore how pulley size and spacing change belt length and wrap

Use pitch diameters D (large) and d (small), and center distance C in one length unit. For an open belt, the approximate pitch length is L ≈ 2C + π(D + d)/2 + (D − d)²/(4C). The last term is the correction for unequal pulleys. Increasing C increases length and brings small-pulley wrap closer to 180°; the no-slip speed ratio stays D/d.

Real belts come in standard lengths from the manufacturer's catalog. Pick the nearest stock length in the correct length convention, then use “Enter L → find C” to estimate the required shaft spacing. These calculations do not set installation tension or replace the manufacturer's selection procedure.

Open belt: D = 200, d = 100 mm; n_small = 1200 r/min
Belt pitch length L (approx., mm)	1277.49
Center distance C (mm)	400
Speed ratio n_small / n_large	2
Large-pulley speed (r/min)	600
Belt speed (m/min)	376.991
Small-pulley wrap (degrees)	165.638
Unequal-pulley correction (mm)	6.25

Less wrap means less grip for a friction belt and fewer teeth engaged for a timing belt. This geometry model does not rate load capacity.

Worked example: D = 200 mm, d = 100 mm, C = 400 mm and n_small = 1200 r/min. L ≈ 800 + 150π + 6.25 = 1277.49 mm. The inverse returns C ≈ 400 mm. Ratio = 2; n_large = 600 r/min; v = π × 100 × 1200 / 1000 ≈ 376.99 m/min; wrap ≈ 165.64°.

Derive the inverse and check speed and wrap

Multiply the length approximation by 4C: 4CL = 8C² + 2π(D + d)C + (D − d)². Set B = 4L − 2π(D + d), giving 8C² − BC + (D − d)² = 0. The quadratic formula gives C = [B + √(B² − 32(D − d)²)]/16. Use this larger root and require C > (D + d)/2 so the pitch circles are separated. An impossible length produces no valid layout.

Assuming no slip, n_small / n_large = D/d and v = πd n_small. With d in mm, divide v by 1000 to get m/min; with d in inches, multiply by 0.0254. Speed n is in r/min; N remains the symbol for teeth.

The tangent-span angle is α = asin((D − d)/(2C)); small-pulley wrap is θ = 180° − 2α, with α expressed in degrees. Less wrap means less grip. The drawing uses circular arcs and tangent spans; the length equation approximates that geometry. Its error grows as (D − d)/(2C) grows, so very unequal, closely spaced pulleys need a more exact calculation for final selection.

Practice the same method:

Belt length Stock-length center distance Driven speed Belt speed Small-pulley wrap

Appears in

Belt, Chain and Gear Drives DET 403 DET