# Belt Drive Vibration: Pulley, Tension, and What Gets in the Way of Balancing

> A belt-driven fan has started humming, you put a sensor on the bearing housing and see 7 mm/s. Most of the level sits at running speed, that is, at the shaft's rotation frequency — so, imbalance? Don't reach for the weights just yet. An eccentric pulley, worn grooves, and an over-tensioned belt produce vibration at exactly the same frequency, and the belt also adds its own lines below running speed — subsynchronous ones — that a standard measurement won't show at all.

**In short:** A belt drive produces two groups of components. First: the subsynchronous (below running speed) belt frequency f_belt = π · D_pulley · f_pulley / L_belt and its harmonics, with the second harmonic often higher than the first. Second: vibration exactly at the shaft's running speed from pulley runout, fit eccentricity, and uneven groove wear — and it's this one that gets mistaken for rotor imbalance. So the work sequence runs opposite to the usual habit: geometry and pulley fit first, replacing the belts with a matched set, aligning the pulleys and setting tension per the manufacturer's method, and only then balancing.

Source: https://axiline.pt/en/articles/belt-drive-vibration/  
Publisher: AXILINE · Vila Nova de Gaia, Portugal · +351 931 831 229 · axilinegeral@gmail.com

## A Belt Drive: Two Groups of Frequencies and One Constant Force

A belt drive looks like a simple assembly: two pulleys and a belt. For vibration diagnostics it's a separate kinematic chain with its own frequencies, its own stiffness, and its own constant load on the bearings.

The first consequence: you have two shafts running at different speeds. The driven shaft's speed is tied to the motor's speed through the pulley diameters. If you've stuck the reflective tape mark on the motor shaft while balancing the fan impeller, the instrument will extract the motor's running-speed component, not the impeller's. From there everything goes wrong, and the software won't tell you about it.

Second: a third frequency appears, one that belongs to the belt itself. It isn't a multiple of either running speed, always sits below both of them, and is easy to calculate from the kinematics.

Third: tension appears. This is a constant radial force that loads the bearings on both shafts, slightly bends the shafts, and sets the stiffness of the "pulley, shaft, support" system. On its own it isn't vibration. But it changes the conditions under which you measure and balance. An influence coefficient — the relationship "installed a trial weight, got this change in vibration" that the entire balancing calculation is built on — taken at one tension no longer holds at another.

So the drive interferes twice: it creates vibration on its own, and it distorts the picture you're basing your decision on.

- Motor running frequency f1 = n1 / 60, Hz
- Driven-shaft running frequency f2 = f1 · D1 / D2, where D1 and D2 are the pitch diameters of the pulleys. This is exactly the one the instrument looks for when balancing the impeller
- Belt frequency f_belt. Always lower than the running frequency of either pulley
- Natural frequency of the free belt span. A tensioned span behaves like a string and can resonate
- Constant tension force. Not vibration, but it affects the bearings, shaft deflection, and every influence coefficient

## Belt Frequency and Its Harmonics

It's calculated as follows: f_belt = π · D_pulley · f_pulley / L_belt, where L_belt is the belt length. The meaning is transparent. The belt's linear speed equals π · D · f. Divide that by the belt length and you get how many times per second the same point on the belt returns to where it started.

The ratio f_belt / f_pulley equals π · D / L_belt and is always less than one, because the belt length is noticeably greater than the length of the pulley's half-circumference. Hence the working rule: belt frequency is subsynchronous. A stable line below running speed, not a multiple of it, is the first thing to check on a belt drive.

A defective section of the belt — a splice, a transverse crack, a torn-out chunk, a local thick spot — passes through the pulleys twice per belt revolution. That's why the spectrum (the breakdown of vibration by frequency) is often dominated not by the first harmonic but by the second, 2× the belt frequency. Harmonics up to the fourth and fifth on a worn belt are a common picture.

An illustrative example, typical of a fan installation. Motor at 1470 rpm, that is 24.5 Hz. Motor pulley 150 mm. Belt 2000 mm. That gives f_belt = π · 0.15 · 24.5 / 2 ≈ 5.8 Hz. Expect lines around 5.8 and 11.6 Hz, with the second likely to be the higher of the two. The numbers here are illustrative — calculate from your own kinematics: measure the diameters, take the belt length from its marking.

In the time waveform, a belt defect shows up as an impact repeating with a period of 1 / f_belt. For the example above that's 0.17 s, and to avoid losing that impact you need to record for a second or longer.

> Belt-frequency harmonics are easy to confuse with subsynchronous phenomena of a different origin: oil whirl in sleeve bearings around 0.42–0.48× running speed, flow separation phenomena, rubbing. The distinction is simple. Belt frequency is fixed rigidly by the kinematics and doesn't move when the operating condition changes. Whirl is tied to a fraction of running speed and shifts along with load.

Sources: [ISO 13373-3:2015](https://www.iso.org/standard/40840.html)

## Pulley: Runout, Eccentricity, and Groove Wear Produce Vibration Right at 1x

This is where the main trap of a belt drive lies. Anything that makes a pulley's rotation geometrically uneven creates a force once per revolution and lands exactly on the spectral line where imbalance lives — at 1x, the running-speed component.

Eccentricity. The centre of the outer diameter doesn't coincide with the axis of rotation. Once per revolution the belt tensions harder, then slacker. The force changes in magnitude, not just direction, so the vibration ends up directional: along the line between the pulleys it's usually noticeably higher than across it. Pure imbalance gives a different picture: the horizontal and vertical amplitudes at the bearing are comparable, with the phases roughly 90° apart.

Radial runout of the fit. The pulley sits on a worn hub, a tilted taper bushing, or a key with play. A dial indicator finds this in two minutes on a stopped machine, and it's fixed by repairing the fit, not with a weight.

Face runout. The pulley wobbles like a figure eight. The belt picks up axial sway, axial vibration rises, and the groove sidewalls wear on one side.

Uneven groove depth and wear. On a multi-groove drive, the belts sit at different depths in their grooves and work on different effective diameters. One belt pulls, the others just ride along. The load distribution changes every revolution, tension pulsates, and both 1x and the belt frequency grow in the spectrum.

A visible sign of a worn groove: a shiny bottom. A V-belt should work on its sidewalls and shouldn't touch the bottom. Shine on the bottom means the belt has sunk down, the drive has already lost grip capacity, and any measurements you take are being taken on a faulty assembly.

- [x] Radial and face runout of both pulleys with a dial indicator, on a stopped and locked-out machine
- [x] Play in the key and the condition of the keyway, the taper bushing's fit, the hub's tightness
- [x] Groove profile with the manufacturer's gauge: rounded edges, a shiny bottom, uneven wear across the grooves
- [x] Signs of slippage: glossy streaks on the belt sidewalls, black rubber dust under the drive, the smell of burnt rubber
- [x] Vibration directionality: compare the level along the line between the pulleys and across it — the difference gives away the drive's geometry

## Tension: Both Too Loose and Too Tight Spoil the Measurement

### Under-Tensioning and Slippage

The belt slips, and the driven shaft's speed stops being rigidly tied to the motor's speed. It drifts along with the load. Lines blur in the spectrum, and the 1x phase doesn't repeat from run to run. Balancing under these conditions doesn't converge: every run describes a slightly different machine, and the influence coefficient comes out unreliable. Along the way, the belt heats up, the rubber ages, and the grooves wear faster.

### Over-Tensioning

The constant radial force on both shafts' bearings grows. For ball bearings, life falls off roughly as the third power of the equivalent load, so the margin taken "to be sure it doesn't slip" eats into bearing life noticeably faster than it seems. The ISO 281 life calculation shows this directly if you feed it the actual tension force. The shaft bends slightly, 1x rises, and the pulley fit suffers. An over-tensioned drive is often exactly the cause of the vibration people are trying to remove with weights.

### Span Resonance

A free belt span behaves like a string. Its natural frequency is roughly (1 / 2·L_span) · √(T / m'), where L_span is the span length, T is the tension, and m' is the mass per metre of belt. If it lands on running speed or on the belt frequency, the span starts flapping and rocking the pulleys. Fixed by changing the tension, shortening the span with an idler, or switching to a different belt.

### How to Set Tension

Not by feel, and not "so it doesn't squeal." Two methods work. Span deflection under a force specified by the manufacturer: a common guideline is about 16 mm of deflection per metre of span, but get the exact figure and force from the belt manufacturer. And the frequency method: pluck the span, measure its natural frequency, and calculate the tension by running the same formula in reverse, T = 4 · m' · L_span² · f². The second method is more accurate and repeatable, which is why it's convenient for the logbook.

> After tensioning the belt, re-measure vibration from scratch. Tension changes the static load and the support's stiffness, and the influence coefficients along with them. Balancing done before retensioning the belt will partly come undone afterward, and you'll get a call back within a week.

Sources: [ISO 281:2007](https://www.iso.org/standard/38102.html)

## Pulley Misalignment, Mismatched Belt Lengths, Aging

On the shop floor, one word gets used for three different geometric defects, and each is corrected differently.

Parallel offset: the shaft axes are parallel, but the pulleys are shifted relative to each other along the axis. The belt enters the groove at an angle, and the sidewall wears on one side.

Angular tilt: the shaft axes aren't parallel. The belt sits skewed in the groove and pulls unevenly across its width.

A tilt of the pulley itself relative to the shaft is really face runout — a fit defect, not an installation one. Moving the motor won't help; the pulley has to come off.

Checked with a string or straightedge across the pulleys' outer faces, a cord along the grooves, or a laser pulley-alignment tool. While you're at it, check the motor for soft foot: a shim under one foot tilts the frame, the shaft, and the pulley all at once. The terminology matters here: misalignment is the cause, and shaft alignment or pulley alignment is the corrective action.

In vibration terms, pulley misalignment produces 1x with a noticeable axial component, sometimes 2x, and always accelerated belt wear with hot sidewalls. A weight on the pulley or the impeller won't remove it.

Mismatched belt lengths within a set. Even belts of the same designation from different batches differ in actual length. The short one pulls, the long one just rides along. Load wanders, tension pulsates, vibration is unstable from run to run, and balancing on a drive like this won't repeat. Hence the rule that gets broken most often: install a matched set from one manufacturer and replace all the belts at once. A new belt next to three stretched ones ends up working alone and dies within weeks.

Aging. The rubber loses elasticity, and transverse cracks and stiff patches appear on the inner surface. A stiff patch passes over the pulley with an impact, and that's exactly the excitation you'll later see at the belt frequency and its harmonics.

## What Gets Confused with What in the Spectrum

| What You See | What Produces It on a Belt Drive | How to Tell It Apart from Imbalance |
| --- | --- | --- |
| A dominant peak exactly at the driven shaft's 1x | Pulley eccentricity, fit runout, uneven groove wear, over-tensioning | Dial indicator on the pulley before any weights. Compare the level along the line of the pulleys and across it. Check whether 1x changes after correct tensioning |
| A stable line below running speed, not a multiple of it | Belt frequency, often with a dominant second harmonic | Calculate f_belt from the kinematics and compare it against the line. Imbalance never produces subsynchronous lines at all |
| 1x plus increased axial vibration | Pulley misalignment, pulley face runout | String or laser tool across the pulley faces. On an overhung impeller, axial vibration can also come from imbalance, so check the geometry regardless |
| Lines are blurred, 1x phase jumps from run to run | Slippage and unstable speed | Look at the speed spread between runs. With imbalance the phase is stable and repeats |
| A hum at one frequency, the belt span visibly flapping | Free-span resonance | Change the tension by 10–15% and repeat the measurement. Resonance will shift; imbalance will stay put |
| The level came back a few weeks after a successful balancing job | Groove wear and belt stretch are still progressing | Compare the before and after spectra. If it's specifically 1x that has risen with unchanged kinematics, look for drive geometry, not a new imbalance |

Sources: [ISO 13373-3:2015](https://www.iso.org/standard/40840.html)

## Work Sequence on a Belt Drive

1. **Pulley Geometry and Fit** — Stop and lock out the drive. Dial indicator on both pulleys: radial and face runout. Play in the hub, key, taper bushing. Groove profile against a gauge. Everything found here gets corrected by repair, not by weights.
2. **Replace the Belts as a Set** — A matched set from one manufacturer, all the belts at once. Don't buy just one to add to worn ones. Clean the grooves of rubber dust and residue before installation.
3. **Aligning the Pulleys** — String or straightedge across the faces, a cord along the grooves, a laser tool. At the same time check the motor for soft foot and the slide rails for tightness: a twisted frame undoes any alignment work.
4. **Tension per the Manufacturer's Method** — Deflection under a specified force, or the frequency method. Record the value in the logbook. After a 20–30 minute break-in period, check the tension again: a new belt seats and stretches during the first few hours.
5. **Verification Measurement** — Overall vibration (the total level across the entire frequency band) and 1x at both bearing housings, in the radial and axial directions, plus the spectrum and recorded speed. Some work orders get closed right here: the level is already normal, and there's nothing left to balance.
6. **Balancing, If 1x Is Still High** — Now the influence coefficients relate to a properly working drive and repeat from run to run. Put the tape mark and the laser phase sensor on the shaft of whichever rotor you're balancing. Two to three runs, a weight on the available correction plane, a verification run.

> The sequence can't be reordered. Every step changes the conditions for the next one: a new belt changes the static load, tension changes the support's stiffness, aligning the pulleys changes the direction of the force. Balancing comes last, otherwise you're locking in with weights a condition that won't exist an hour later.

## Why Balancing a Pulley on Worn Belts Is Pointless

The reason isn't pedantry, it's arithmetic. Vibration at 1x is a vector sum of two contributions: genuine mass imbalance and geometric excitation from runout, eccentricity, and uneven grooves. A weight removes only the first contribution. The second stays, and the residual level hits it like a floor. You'll make four runs, bring 7 mm/s down to 4 mm/s, and get stuck there, while the software honestly reports that you haven't reached tolerance.

Worse, the second contribution isn't stable. The groove keeps wearing, the belt keeps stretching, tension drops, slippage grows. A month later the geometry is different, but the weights are still sitting where the old calculation put them. Hence the classic complaint: we balanced it, it was quiet for two weeks, then it all came back. There's a separate article with more detail on this scenario, on why vibration returns after balancing.

And third. The moment you install a new set of belts, you change the very system the influence coefficients were calculated for. The right weights for the old drive aren't the right weights for the new one. Balancing before replacing the belts means doing the work twice.

The reverse situation also happens: the pulley itself genuinely needs balancing. A large-diameter cast pulley, a pulley whose fit bore has been rebored, a pulley with a welded-on hub. There are two paths here. On site, together with the rotor and in the machine's own bearings, once the drive geometry has been sorted out. Or in the shop, on an arbor, in which case the arbor's own eccentricity is removed by index balancing: the rotor is repositioned on the arbor by 180°, the instrument takes a second measurement, and subtracts the arbor's contribution from the result.

A thin, disc-shaped pulley, with L/D below 0.5, usually only needs one correction plane. There's a separate breakdown on choosing the number of planes and the L/D rule, and for the residual-imbalance tolerance by G class see the article on choosing an accuracy class.

Sources: [ISO 21940-11:2016](https://www.iso.org/standard/54074.html) · [Balanset-1A manufacturer specification](https://vibromera.eu/product/balanset-1/)

## Fans and Induced-Draft Fans: Measuring on a Drive with Slip

Belt drives show up most often exactly where vibration is already a headache: centrifugal fans, induced-draft fans, dust extraction, crushers, mulchers. Speed is low, the wheel is large, the air is dirty. There are two measurement quirks here that let the drive slip past your reading.

The first: subsynchronous components fall below the filter's cutoff. Machine condition is assessed by mm/s RMS (the root-mean-square value of vibration velocity) over the 10–1000 Hz band. On a slow-running drive, the belt frequency is often below 10 Hz — 5.8 Hz in the example above. A high-pass filter simply cuts it off. You get a decent-looking overall number and never see the cause. So for drive diagnostics, take a separate spectrum with a lower limit below the belt frequency and enough resolution to separate 5.8 Hz from running speed. Resolution costs recording time: Δf = 1 / T, and to get lines spaced 0.25 Hz apart you need a 4-second recording. There's a separate article on choosing Fmax and the number of lines.

Keep the ISO 20816 acceptance measurement in the standard band, though: comparison against the zones only makes sense under the stated measurement conditions. Check the applicable part and edition of the standard for your machine — there are exceptions by power, speed, and unit type. The diagnostic spectrum and the acceptance measurement are two different measurements with different settings, and it's worth keeping them separate in the report.

The second quirk: speed. A drive with slip doesn't hold running frequency as rigidly as a direct coupling. If speed drifts by a few percent between runs, the 1x amplitude and phase change on their own, with no weight involved, and a trial run gives you a false influence coefficient. On a fan this gets compounded by the damper and gas temperature: a warmed-up belt pulls differently than a cold one.

- [x] Put the tape mark and the laser phase sensor on the shaft of whichever rotor you're balancing, not on the motor shaft
- [x] Record the speed on every run and keep the spread between runs within about 1%
- [x] Keep one operating condition: damper position, load, temperature. Warm up the machine before the first measurement
- [x] If the 1x phase drifts by more than 10–15° when you repeat the same run, look for slippage and looseness rather than calculating a correction
- [x] Record the time waveform: an impact with a period of 1 / f_belt gives away a splice or a stiff patch on the belt
- [x] Inspect the wheel before anything else. Buildup and cracks at the blade roots settle the balancing question right away

> A two-channel instrument is a real help on a machine like this: it shows overall vibration and 1x with phase at both bearing housings, speed from the laser sensor, and the full spectrum with the time waveform, all at once. In a single run you see the belt's subsynchronous lines, the stability of the speed, and whether installing weights makes any sense at all. This is exactly how the engineers who design and manufacture Balanset instruments and use them to do field balancing themselves work: measurement and inspection of the drive first, then a decision, and only then correction. If you need help with a specific machine on a belt drive, we'll go through your kinematics and spectrum as part of our consulting support, and on site we'll carry out both the diagnostics and the balancing.

Sources: [ISO 13373-5:2020](https://www.iso.org/standard/62202.html) · [ISO 20816-1:2016](https://www.iso.org/standard/63180.html) · [Balanset-1A manufacturer specification](https://vibromera.eu/product/balanset-1/)

## Frequently asked questions

**How do you calculate belt frequency?**

Using the formula f_belt = π · D_pulley · f_pulley / L_belt, where D_pulley is the pitch diameter of either pulley, f_pulley is its running frequency in hertz, and L_belt is the belt length in the same units as the diameter. The result is always lower than the running frequency of both pulleys, because the factor π · D / L is less than one. Belt defects show up at this frequency and its harmonics, and the second harmonic is often higher than the first: the defective section passes the pulleys twice per belt revolution.

**How do you know vibration is coming from the belt and pulley, not from imbalance?**

Three checks. Calculate the belt frequency and look for its line in a spectrum with a lower limit below 10 Hz — imbalance never produces subsynchronous lines at all. Put a dial indicator on the pulleys and measure radial and face runout — imbalance doesn't produce runout. Compare the vibration level along the line between the pulleys against across it: strong directionality points to the drive, while with imbalance the amplitudes in the two radial directions are comparable, with the phases roughly 90° apart. An additional trick: remove the belt and spin the rotor down in coast-down — if the picture changes qualitatively, the problem is in the drive.

**Does the belt need to be removed for balancing?**

Balancing is usually done with the belt on, at working speed, and in the machine's own bearings, because removing the belt changes both the static load and the support's stiffness. But removing the belt remains a good diagnostic trick: spin the rotor down in coast-down, or drive it without the belt, and compare the spectra. If the subsynchronous lines disappear and 1x drops, you've found the source in the drive. Balancing still needs to be done in the state the machine actually runs in, though.

**What tension counts as correct?**

The one specified by the belt manufacturer for your profile, span length, and transmitted power. Two working methods: span deflection under a specified force (a common guideline is about 16 mm per metre of span, with the exact value and force from the manufacturer), and the frequency method, where you pluck the span and calculate tension from its natural frequency: T = 4 · m' · L_span² · f². The second is repeatable and convenient for the logbook. Never tension by feel: under-tensioning causes slippage and unstable speed, over-tensioning kills bearings and raises 1x on its own.

**Can a single belt from a set be replaced on its own?**

No. Even belts of the same designation from different batches differ in actual length, and the old belts are stretched besides. The new belt will end up shorter than the rest, take on most of the load, and fail quickly, while tension in the drive becomes pulsating — that means unstable vibration and non-reproducible measurements. Install a matched set from one manufacturer as a whole, and check the grooves while you're at it: if the belt was touching the bottom of the groove, the pulley needs replacing too.

**Why did vibration come back a month after balancing a belt-driven fan?**

The most common scenario: the real cause of 1x was drive geometry, not imbalance. The weights removed the share of the level that came from mass, while pulley eccentricity and groove wear stayed and kept progressing. The belt stretched along the way, tension dropped, slippage grew. A second possibility: between the balancing job and the follow-up measurement, someone retensioned the belt or changed the set, and the influence coefficients stopped matching the machine. A third: the wheel picked up buildup again. Start with a dial indicator on the pulleys and the tension logbook, not with fresh trial runs.