How to Work Out a Drive Ratio From What Is on the Machine

Why this matters

Nobody hands you the drive ratio. The submittal is gone, the sheave markings are a part number, and the last tech changed something without writing it down. So you work it out from the machine, and the trap is that there are four ways to do it, each one gives a slightly different number, and each one is blind to a different thing. A tech who takes one route and trusts it will confidently report a ratio that is off by the exact amount of whatever that route cannot see. The method is not to pick the best route. It is to take two, and let their disagreement tell you what is wrong with the drive.

Isolate first, and know which readings need it

Three of the four routes are hands-on and every one of them happens with the motor locked out and tagged at its disconnect. A wheel or impeller holds rotational energy after the power is off, which is stored mechanical energy under 29 CFR 1910.147, so verify zero rotation by eye and block the wheel or close and secure the damper before reaching past the guard, because a windmilling wheel back-drives the sheave. Wear cut-resistant gloves when running a tape around a cast sheave rim, and when barring the drive over by hand, grip the rim and keep fingers clear of the point where the belt enters the groove. The one running route is taken from outside a closed guard, standing out of the plane of rotation because a failed belt or sheave fragment leaves along that plane, with hearing protection under a program per 29 CFR 1910.95 where the space is at or above the 85 dBA action level. Opening an electrical enclosure to reach the disconnect is electrical work under 29 CFR 1910.333(b)(2), proved live-dead-live per NFPA 70E-2021, 120.5, and the guard goes back on before restart under 29 CFR 1910.219 in general industry or 29 CFR 1926.300(b) on a construction site.

Route 1: read the markings

Fastest and least trustworthy. Look on the sheave rim, hub face and bushing.

What it cannot see: whether the number is a diameter at all. Cast digits are frequently a pattern or catalog number, a bushing marking identifies the bore taper and not the sheave, and a variable-pitch sheave's stamped size is its nominal setting rather than where its flanges sit today. Markings also cannot know about groove wear, and they are silent about which of several grooves is in use.

Use route 1 to narrow the section and the family. Do not use it to compute anything.

Route 2: measure and correct to pitch diameter

Measure the outside diameter of each sheave with a caliper across the rim, or run a tape around the rim and divide the circumference by pi, which is more accurate on a large sheave than trying to find a true diameter by hand. Then subtract the section's published outside-to-pitch correction, which every belt and sheave maker publishes by section, to get pitch diameter. That correction exists because the belt's tensile cords sit below the rim, and the ratio is defined at the cords.

What it cannot see: wear. Route 2 gives you the geometry the sheave was made with, and the belt runs on the geometry the sheave has now. It also cannot see a belt of the wrong section sitting high or low in the groove.

Route 2 is the number you need if you are selecting a replacement sheave, because catalogs are written in pitch diameters.

Route 3: tach both shafts under load

An optical tachometer with a reflective target on each shaft, both read at the same running condition, through the guard's sight opening with the guard closed. Never hold a contact tachometer against a running shaft on a belt drive; the reach puts your hand inside the plane of the rotating parts.

delivered ratio = motor rpm / driven rpm

What it cannot see: the difference between geometry and slip. Route 3 measures what the machine is actually doing, which is the truth about performance and a lie about the drive's design. It also cannot be trusted if the two readings were taken at different loads.

Route 3 is the number you need if the question is why the driven machine is not making its output.

Route 4: count revolutions with the drive barred by hand

Mark both sheaves with a chalk line across the rim. Bar the drive over by hand from the sheave rim, turning the driven sheave a whole number of revolutions and counting the driver's revolutions, reading its final partial turn to the nearest eighth. Turning the driven sheave gives you the higher count on the driver, which is where your resolution lives: ten driven revolutions on a ratio near 2.5 puts about 25 driver revolutions on the clock, so reading to an eighth of a turn resolves the ratio to roughly half a percent.

What it cannot see: nothing about the belt path, which is the point. At hand-barring torque there is no gross slip, so route 4 returns the effective ratio, meaning the ratio at the diameters the belt is actually riding at today.

What it costs: on a drive with a large wheel or an awkward reach, twenty-five revolutions by hand is a real job, and on some equipment you cannot get a hand to the rim at all.

Reconciling them is the actual method

Each pair of routes isolates a different fault, and this is the whole reason to take more than one.

That last row is the trap worth naming. Groove wear and slip push the driven speed the same direction. Both make the driven shaft run slower than the pitch diameters predict, so a tech holding only routes 2 and 3 sees a shortfall and has no way to attribute it. Either add route 4, or use the load test below.

Worked example: a pump drive that reads slow

A belt-driven centrifugal pump. Motor nameplate 1750 rpm.

Route 1. The driver sheave carries a bushing marking only. The driven sheave has "12" cast into a spoke, which is tempting and is a pattern number. Nothing usable.

Route 2. Tape around the driven rim reads 40.5 in of circumference, so the outside diameter is 40.5 / pi = 12.9 in. Caliper across the driver rim reads 5.4 in. Say the section table gives an outside-to-pitch correction of 0.4 in for this section; use your own table, this is a placeholder for the arithmetic. Pitch diameters are then 12.5 in and 5.0 in, so the geometric ratio is 12.5 / 5.0 = 2.50.

Route 3. Guard closed, optical tach on both shafts within the same minute at the same load: motor 1742 rpm, pump 672 rpm. Delivered ratio is 1742 / 672 = 2.59. Predicted pump speed from geometry at that motor speed is 1742 x 5.0 / 12.5 = 697 rpm. The pump is 25 rpm short, which is 25 / 697 = 3.6 percent.

Route 4. Locked out, chalk marks on both rims, pump sheave turned ten full revolutions by hand: the driver comes to rest at 25.1 revolutions read to the nearest eighth. Effective ratio 2.51, against a geometric 2.50. The difference is inside the method's own half-percent resolution, so the belt is riding essentially where the pitch diameters say it should. Grooves and belt are not the problem.

What that leaves. Route 4 agrees with route 2 and disagrees with route 3, and the only thing that lives in the gap between a hand-barred ratio and a running ratio is slip. The drive is losing 3.6 percent.

Confirming it with load. Slip is load-dependent and a diameter error is not, so change the load and re-read. On this centrifugal pump the discharge valve was throttled part way, staying above the pump maker's published minimum continuous flow and never approaching a closed valve, because a dead-headed pump turns its shaft power into heat in the casing and can flash the liquid. Do not attempt this at all on a positive-displacement pump, where a closed discharge builds pressure until a seal, a casing or a relief path gives. At the reduced load the shortfall fell to 0.6 percent, which is inside the elastic creep every correctly running belt drive shows. Load-dependent, so slip.

The other outcome, and why it matters. Suppose route 4 had come back at 2.59, matching the running ratio. Then the geometry itself is wrong and there is no slip to find. Working backwards, the implied driver effective diameter would be 12.5 / 2.59 = 4.82 in against a 5.0 in pitch diameter, meaning the belt is riding about (5.0 - 4.82) / 2 = 0.09 in low in the driver groove. Under a tenth of an inch, and it produces the same 3.6 percent shortfall that slip did. That case is a worn groove or a wrong-section belt, and adding tension to it makes things worse rather than better.

Which number to write on the ticket

• Replacing a sheave or specifying a new drive: route 2, pitch diameters, because that is the language of the catalog.
• Explaining a performance shortfall: route 3, and state the load condition it was taken at, because the number is only true at that condition.
• Deciding whether the drive is healthy: route 4 against route 3, because that pair is the one that separates a drive that has lost geometry from one that has lost grip.

Write down all the raw values, not just the ratio: both outside diameters, the correction you applied, both tach readings, the load condition, and the revolution counts. A ratio with no inputs behind it cannot be checked by the next person, and on a drive that has been quietly changed once already, it will be.

References

• 29 CFR 1910.147 for mechanical isolation and stored rotational energy; 29 CFR 1910.333(b)(2) and NFPA 70E-2021, 120.5 for enclosure work and live-dead-live proving
• 29 CFR 1910.219 (general industry) and 29 CFR 1926.300(b) (construction) for guarding of belts, pulleys and sheaves; 29 CFR 1910.95 for the occupational noise program and its 85 dBA action level
• Belt and sheave manufacturer engineering data for outside-to-pitch diameter corrections by section and for published pitch diameters
• Pump and fan manufacturer data for minimum continuous flow and permissible throttling limits
• See related: How Sheave Diameter Sets Speed and Torque; Why a Belt Slips and What It Costs; What a Worn Sheave Groove Does to a New Belt