EngineeringMechanical EngineeringPart 04 of 15
Vee and Wedge Belt Drive Design
A belt drive is the most forgiving power transmission element available and the easiest to specify badly. The design is a loop: choose pulleys, close the geometry, count the belts, then discover the bush bore forces you back to the start.
- 16-step procedure
- Belt length and centre distance
- Correction factors
- Worked example
Executive summary
Vee belts have been largely superseded by wedge belts — a deeper profile that costs a little more and carries substantially more power for the same pulley. The two run on interchangeable pulleys, and the generic term "vee belt" is still used loosely for both.
Designing the drive means converting a running power into a design power through a service factor, choosing a belt section and a pulley pair that hold the required speed ratio, closing the belt length and centre distance geometry against standard belt lengths, and then correcting the published power per belt for arc of contact and belt length before dividing to get the belt count.
Belt families and what each is for
| Type | Character | Typical use |
|---|---|---|
| Vee | The original profile. Largely superseded for new designs. | Replacement on existing drives. |
| Wedge | Deeper profile, higher power rating per belt, slightly higher cost. Same pulleys as vee. | The default choice for new industrial drives. |
| Banded | Several belts joined across the top to form a composite. | Eliminates belt twist, whip and turnover on long or shock-loaded drives. |
| Multi-pull | Similar construction to banded belts with a different profile. | As for banded belts. |
| Link | Built from linked reinforced urethane elastomer sections; any length can be assembled on site. | High heat, oil or chemical exposure; awkward centre distances; emergency replacement. |
| Cogged raw edge | Cogged on the face opposite the vee, allowing tighter bending. | Small pulleys and high-speed drives, including automotive. |
| Synchronous | Flat belt with a tooth profile meshing with toothed pulleys. | Where slip cannot be tolerated. Lower power capacity than vee or wedge. |
There is no Australian Standard for vee or wedge belts. Reputable products comply with the relevant British and ISO standards, and pulleys are commonly supplied to the taper lock pattern — which means a complete specification names both the pulley and the bush.
Establishing the design power
Normal running power is the maximum power at the driver end, excluding shock loading and hard-start effects. Those belong in the service factor, not in the duty.
- Service factor
- Read against the character of the prime mover, the class of driven machine and the hours per day of operation.
- Speed increasing
- For a step-up drive, an additional multiplier is applied to the service factor, rising with the speed ratio.
Service factor tables are organised on three axes. Understanding the axes matters more than memorising the numbers, because they tell you what the factor is actually protecting against.
Prime mover character
Soft starts — star-delta motors, shunt-wound DC, engines of four or more cylinders, and anything fitted with a centrifugal clutch, fluid coupling or electronic soft starter. Heavy starts — direct-on-line motors, series and compound DC, engines under four cylinders, and prime movers with no soft-start device.
Driven machine class
From light duty (uniform-density agitators, small fans, centrifugal pumps, uniformly loaded belt conveyors) through medium and heavy duty to extra heavy duty (gyratory, jaw and roll crushers; ball, rod and tube mills).
Hours per day
Banded as up to 10 hours, 10 to 16 hours, and over 16 hours. A drive that runs three shifts is a different design problem from one that runs a day shift.
The design procedure
- Determine the service factorIncluding the speed-increasing multiplier if the drive steps up.
- Calculate design powerRunning power multiplied by the service factor.
- Select the belt sectionTwo or three sections may suit. As a general rule take the larger section, which gives fewer belts.
- Establish the speed ratioFaster shaft speed divided by slower shaft speed. Calculate the driven speed tolerance band if one applies. About 6:1 is the practical maximum for a single pulley pair.
- Find the minimum pulley diameterGoverned by the speed of the faster shaft and the power. Take the next larger size for intermediate values.
- Trial a set of pulley pairsStart at the minimum diameter and step up through the available pitch diameters. Multiply each small pulley by the speed ratio, choose the nearest available large pulley, and recalculate the actual driven speed. Discard pairs outside the tolerance band.
- Choose the pulley pairSmall pulleys give a compact drive and low belt speed; large pulleys give a higher power rating per belt and therefore fewer belts. Space constraints may decide it.
- Check belt speedBelt speed must not exceed about 40 m/s. If it does, use smaller pulleys.
- Set a trial centre distanceWhere not specified, a sound starting rule is a centre distance equal to the sum of the two pitch diameters.
- Calculate the required belt pitch lengthUsing the pitch length formula below.
- Round to a standard belt lengthGenerally take the next larger standard length rather than the next smaller.
- Recalculate the exact centre distanceFor the standard belt length actually chosen.
- Read the basic power rating per beltFormed as rated power plus additional power. Interpolate linearly for intermediate speeds.
- Apply the correction factorThe combined arc of contact and belt length factor, giving corrected power per belt.
- Calculate the number of beltsDesign power divided by corrected power per belt, rounded to a whole number.
- Specify pulleys and bushesConfirm the pulley is available with the required number of grooves and that the bush maximum bore accepts the shaft.
- L
- belt pitch length, mm
- C
- centre distance, mm — trial value in the first formula, exact value from the second
- D
- pitch diameter of the larger pulley, mm
- d
- pitch diameter of the smaller pulley, mm
Rounding the belt count
Dividing design power by corrected power per belt rarely returns a whole number, and the rounding decision carries real consequence. A widely used design rule is to round down when the fractional part is below 0.3 and up when it is above.
| Calculated | Usual decision | What should influence it |
|---|---|---|
| 2.8 | Use 3 belts. | Unambiguous. |
| 2.3 | Judgement call. | Accuracy of the duty data, the safety factor already embedded in the service factor, and the required life. |
| 2.05 | Use 2 belts. | Confirm the duty data is reliable before accepting the marginal case. |
If a shaft diameter exceeds the maximum bore of the bush suited to the chosen pulley, a larger bush is required — which forces larger pulleys, which changes the belt length, the centre distance and the power rating. The design then repeats from the pulley selection step. Check bore capacity before committing to a pulley pair, not after.
Worked example
A six-cylinder diesel engine governed to 1050 rev/min drives a reciprocating gas compressor required to run at 650 rev/min within three per cent. Maximum power is 50 kW, the drive runs more than sixteen hours per day, the engine shaft is 70 mm and the compressor shaft is 80 mm.
Stepping through the available pitch diameters from the minimum upward and pairing each against the nearest standard driven pulley produces several combinations inside the speed tolerance. Choosing a 315 mm driver against a 500 mm driven pulley gives 661.5 rev/min — inside the band, with the larger pulleys carrying a higher rating per belt.
Closing the geometry
With a basic rating of roughly 29.1 kW per belt at this speed and pulley size, and a combined correction factor of 0.9, the corrected rating is about 26.2 kW per belt. Dividing the 70 kW design power gives 2.67 belts, so the drive is specified with three belts. Both 70 mm and 80 mm shafts fall inside the bush bore range for the pulleys chosen, so the loop closes without iteration.
Design checklist
- Running power stated free of shock and starting allowances.
- Service factor selected on prime mover, driven class and hours per day, with the speed-increasing multiplier if applicable.
- Belt section chosen deliberately, with the larger section preferred where two suit.
- Speed ratio within about 6:1 for a single pulley pair.
- Driven speed inside the specified tolerance band for the pulley pair actually chosen.
- Belt speed below 40 m/s.
- Belt pitch length rounded to a standard length, generally upward.
- Exact centre distance recalculated for the standard belt length.
- Power per belt corrected for arc of contact and belt length before dividing.
- Belt count rounded with the fractional-part rule and the duty data quality considered.
- Pulley groove count available and bush maximum bore greater than the shaft diameter.
- Both pulley and taper lock bush designations recorded in the specification.