Rotor unbalance: what it is and why it is dangerous

A fan starts humming after the impeller gets cleaned, an extractor fan's bearing starts running hot, a spindle starts leaving waviness on the workpiece. In all three cases, the first suspect is the same: rotor unbalance. Below we go through what this phenomenon actually is physically, why doubling the speed quadruples the force, the types of unbalance there are, where it comes from on a running machine, and exactly what it destroys.

Updated 27 August 2026 · by AXILINE · Vila Nova de Gaia

Unbalance is a mismatch between the mass axis and the axis of rotation

A rotor is a body that rotates in bearing supports and transmits forces to them through its journals. In a perfectly balanced rotor, the mass is distributed symmetrically about the axis of rotation: every element of mass has a matching one lying directly opposite it. As the rotor turns, each element experiences a centrifugal force directed radially, that is, perpendicular to the axis. The paired forces are equal in size and opposite in direction, so they cancel each other out. The resultant is zero, and the rotor is balanced.

Now break the symmetry. Say an extra 10 g turns up at a radius of 200 mm: a gusset got welded on, dirt built up, a piece of blade tore away. That 10 g has no matching partner. Its centrifugal force stays uncompensated and rotates along with the rotor, sweeping around the support once every turn. It is exactly this force that loads the bearings and cyclically deforms the supports along with the foundation. What you call vibration is the structure's response to this rotating force.

The rigorous definition is given in terms of axes. Every body has a principal central axis of inertia, around which the mass is balanced. Unbalance is a mismatch between that axis and the axis of rotation set by the bearings. Balancing brings the two axes together. In practice this is done by adding or removing mass in the correction planes: welding on weights, bolting them on, drilling or milling metal away. There is a second route too — machining the shaft journals to match the actual axis of inertia — but it is almost never used in service.

That leads to a conclusion that saves a lot of arguments on site. Unbalance is a property of the rotor: it is measured in g·mm and does not depend on what the rotor is sitting on. Vibration is the response of the rotor-bearings-frame-foundation system: it is measured in mm/s and depends on stiffness, mass and damping. The same unbalance on a rigid foundation gives modest mm/s figures alongside a substantial load on the bearings, while on a flexible frame it is the other way round: the numbers on screen look alarming while the load on the bearing stays moderate.

That is why "normal in mm/s" and "within tolerance in g·mm" are two different statements, and one does not stand in for the other. We cover the three separate tolerances used in balancing in a dedicated article.

Centrifugal force grows as the square of speed

The magnitude of unbalance U is the product of the unbalanced mass m and the radius r it sits at. Centrifugal force is worked out simply as F = U·ω², where ω is the angular speed in rad/s, that is, 2π·n/60 for n in RPM.

The square in the formula means this. Double the speed, and the force quadruples. Triple it, and the force goes up ninefold. This is the single most practical idea in the whole article, and it explains most sudden vibration problems.

Take the same 10 g at a radius of 200 mm. That is a 2000 g·mm unbalance. Let's work out the force at different speeds.

• At 500 RPM, nobody will notice an extra 10 g: half a kilogram of force gets lost in the weight of the rotor itself.
• At 3000 RPM, that same bit of dirt turns into 20 kgf, circling continuously around the shaft.
• At 6000 RPM, it is already around 80 kgf — the weight of an adult person hanging off the shaft journal and spinning along with the rotor.
• That force is not constant, though — it rotates. The bearing's outer ring gets one full load cycle every turn. At 3000 RPM that is 50 cycles a second, 180,000 cycles an hour, around 1.4 million over an eight-hour shift. Metal fatigue counts cycles, not hours of operation.

Two practical conclusions follow. First: on a high-speed machine, the permissible unbalanced mass is many times smaller than on a slow one, and you can no longer judge it by eye. Second: if vibration during start-up grows faster than the square of speed, or shows a narrow peak over a specific range, you are not looking at plain unbalance — you are looking at resonance, where the speed coincides with a natural frequency of the structure. How to recognise and detune it is covered separately.

Three types of unbalance: static, couple and dynamic

The types of unbalance are told apart by how the unbalanced mass sits along the rotor's length. The easiest way to see this is by looking at how the two axes sit relative to each other: the principal central axis of inertia and the axis of rotation. This is not an academic distinction. It decides whether you fit one weight or two. The table below uses the notation 1x — the name for the vibration component at the rotor's running speed — and its phase, the angle showing at what point in the turn the push arrives; the instrument gives you both numbers.

Static unbalance. The axis of inertia is shifted parallel to the axis of rotation. The centre of mass has moved sideways, and you can spot this on a stopped machine: a rotor set on prisms or roller rests will turn itself until the heavy point sits at the bottom. Rotation produces a single uncompensated force. One weight in one correction plane cancels it out. This is how narrow, disc-shaped rotors behave: a grinding wheel, a circular saw blade, a thin pulley, a flywheel, a brake disc.

Couple unbalance. The axis of inertia is tilted and crosses the axis of rotation at the centre of mass. Picture two equal masses in different planes along the rotor's length, sitting on opposite sides of the axis. At rest, gravity balances them out, the rotor sits still on the prisms, and no static check will ever find it. Spin the rotor up, and the centrifugal forces from these two masses turn out equal and opposite, but applied at different points along the shaft. They do not lie on the same line, so they do not cancel. Instead they form a couple — a moment — that rocks the rotor around its centre of mass: one bearing support moves up while the other moves down at the same instant.

A single weight is powerless here, because it creates a force, not a couple. Place it to calm the first support, and the second one gets worse: you have simply pushed the vibration from one end of the rotor to the other. A moment can only be cancelled by another moment, which means you need two weights in two separated planes, pointing in different directions.

Dynamic unbalance. Two unbalanced masses are almost never equal, so in real life you get a mixture of static and couple unbalance. Here the two axes skew: they are neither parallel nor intersecting. This is the ordinary real-world case, and it is exactly the one you correct on site. For a rotor that stays rigid at its operating speed, it can be shown that two correction weights, spaced apart along the rotor's length, are enough to remove the unbalance completely, and in the general case you cannot do it with fewer. The weights do not have to sit opposite the original masses or match them in size. All that matters is that together they cancel both the force and the moment.

Keep the difference between a rigid and a flexible rotor separately in mind. The same rotor behaves as rigid at low speed and as flexible at high speed: it bends noticeably under its own centrifugal forces, the radius of the heavy point grows along with the mass, and the linear model stops working. A flexible rotor needs modal balancing across several mode shapes and a different measurement system. How to choose the number of correction planes from the L/D ratio is covered in a separate article.

Sources: ISO 21940-11:2016 · ISO 21940-12:2016

How unbalance is measured: g·mm, g·mm/kg and micrometres

Three quantities cover almost every conversation about unbalance, and people mix them up constantly.

Unbalance U in g·mm. The product of the unbalanced mass and the radius. 10 g at a radius of 200 mm and 20 g at a radius of 100 mm give the same 2000 g·mm and the same force. So a weight's mass on its own means nothing without the radius: always record the mounting radius, and fit the correction mass at the same radius as the trial weight wherever you can.

Specific unbalance in g·mm/kg. This is U divided by the rotor's mass. You need this quantity because a single tolerance cannot fit both a 3 kg wheel and a 300 kg drum. A convenient feature: g·mm/kg is numerically equal to the eccentricity of the centre of mass in micrometres. 40 g·mm/kg means the centre of mass sits 40 μm off the axis of rotation — four hundredths of a millimetre. That is the actual scale you are working at when you hang weights on an impeller.

Balance quality grade G. The grade number is the specific unbalance multiplied by the angular speed — the product e·ω in mm/s. This reveals the key point: the same grade demands a different manufacturing precision at different speeds. Take G 6.3. At 1500 RPM the permissible eccentricity works out at around 40 μm; at 3000 RPM, around 20 μm. For a 50 kg rotor, that is roughly 2000 and 1000 g·mm in total, and that figure still has to be split between the two correction planes.

ISO 21940-11 sets the G grades and the permissible residual unbalance. The numbers above are given as working guidance on the order of magnitude: check which part and edition of the standard applies to your specific machine, and for contractual acceptance, record the grade, the rotor mass, the speed, the radii and the number of planes. And remember the distinction: the G grade describes the rotor's residual unbalance, not the permissible vibration velocity of the casing. These are different tolerances under different standards.

Sources: ISO 21940-11:2016 · ISO 20816-1:2016

Where unbalance comes from on a running machine

A new rotor is never perfect, and a running one keeps changing. It is worth keeping this list of causes in mind: it almost always points to what to check first.

• What was done to the machine shortly before the vibration appeared: cleaning, a wheel replacement, a bearing repair, rewinding, work on the foundation?
• Did the vibration jump suddenly or build up gradually? A sudden jump means something broke off — a piece of build-up, a snapped blade, or a lost weight. Gradual growth means wear, build-up, or loosening fasteners.
• Does the vibration change as the machine warms up, and does it go away once it cools?
• Are there signs of previously fitted weights on the rotor, and are they all still in place?
• Do the readings repeat after stopping and restarting? Drifting values often mean a mass that is shifting around, or rubbing.

Check separately whether the operating speed has changed. Switching the machine to a VFD and running it at a new speed can push it into resonance, and unbalance has nothing to do with that. In that case, weights will not help, however many you fit.

Why unbalance is dangerous: what it actually destroys

Unbalance rarely breaks a machine outright. It works differently: every turn adds one load cycle to every joint in the machine, and parts fail through fatigue. So "it shakes, but it still runs" is not an argument — it is a delay.

Bearings take the hit first. Their calculated life is painfully sensitive to load. Under ISO 281, it depends on the ratio of dynamic load rating to equivalent dynamic load, raised to the power of 3 for ball bearings and 10/3 for roller bearings. In practical terms: doubling the equivalent dynamic load cuts the calculated life by roughly 8 to 10 times. In a real machine the drop will be gentler, because the equivalent load also includes a constant component from the rotor's weight and belt tension, not just the force from unbalance. But the order of the effect is exactly that: not "a bit less," but "several times less."

From there, the load spreads through the whole structure.

• The extreme case is also worth keeping in mind, because it accelerates as it goes. Rising vibration loosens the mounting; a loosened mounting raises the vibration further. Eventually a blade or a weight tears off, unbalance jumps up by a large factor instantly, and the rotor starts rubbing against the casing. On a high-speed machine, that is a failure with parts flying apart, not just a repair job.

Look at the trend, not just the absolute figure. A doubling of the level from a baseline taken on a healthy machine is worth investigating even while it is still inside the permissible zone in mm/s. The limit answers the question "is this acceptable." The trend answers the question "what is happening."

Sources: ISO 281:2007 · ISO 20816-1:2016

How to confirm it is unbalance, and not something else

Unbalance is the most common cause of elevated vibration, but nowhere near the only one. Fitting weights without checking first is an expensive habit: you lose a shift, and in the worst case you make things worse. There is a short set of signs that give unbalance away. You will need the spectrum — the breakdown of vibration by frequency that the instrument produces.

• A noticeable 2x and a rise in axial vibration. This is usually shaft misalignment, and the fix is shaft alignment, not weights.
• A comb of harmonics — 1x, 2x, 3x (peaks at frequencies that are multiples of running speed) — half-order harmonics like 0.5x, and a raised noise floor. Look at the fasteners, soft foot, cracks, rubbing.
• High-frequency peaks that are not multiples of running speed, noise in the envelope — the analysis that isolates bearing frequencies. This means bearings, and balancing does not substitute for replacing them.
• A sharp, narrow peak over a specific speed range, with a phase shift of around 180° near it. This is resonance: a balancing result will not hold there.
• Overall vibration is several times higher than 1x. Something else is producing most of it, and weights will not remove that part.

• The spectrum is dominated by a peak at the rotation frequency, 1x. Overall vibration in mm/s RMS sits close to the running-speed component. A practical guideline for when weights will work: the 1x share is above roughly 70–80% of the overall figure.
• The vibration is mainly radial. The axial component is noticeably lower than the radial one.
• Amplitude grows with speed roughly as the square, smoothly, with no narrow peaks and no drop-off after them.
• The 1x phase is stable and repeats from run to run: amplitude within roughly ±5%, phase within roughly ±5°. A drifting phase means you cannot balance yet.
• The picture at the two supports is consistent: close phases point to static unbalance, a difference of around 180° points to couple unbalance.

We cover each of these cases in detail in separate articles: how to read a spectrum by multiples of running speed, how overall vibration, 1x and phase differ, how to recognise and detune resonance, and seven situations where balancing does not help. Here, one rule is enough: measure first, decide after.

Sources: ISO 13373-3:2015 · ISO 13373-5:2020 · ISO 20816-1:2016

What to do next, and how AXILINE can help

Balancing in the machine's own bearings is done on site, with no disassembly and no removal of the rotor. The machine does not go to a balancing machine, the wheel does not get pressed off, and vibration is measured at the operating speed — exactly the condition the machine actually runs in. For fans, extractor fans, crushers, mulchers, spindles and pumps, this is usually the only practical option.

The Balanset-1A is built for exactly this job. The case holds two vibration sensors, a laser phase sensor, a two-channel USB module with preamplifiers, integrators and an ADC, and Windows software. It balances in one and two planes, measures speed, amplitude and phase of vibration velocity (overall and 1x), plots an FFT spectrum and the time waveform, records both channels at once, tells you itself whether the trial weight was a good size, works out the tolerance against the G grades, splits the correction mass across fixed positions and calculates a drilling correction, works out arbor eccentricity, recalculates weights for other correction planes, works from stored influence coefficients, and saves the results to an archive for the report.

If you balance regularly, it is cheaper to keep the instrument on site. If it is a one-off or a disputed case, AXILINE's engineers will come and do it themselves: measure, assess the cause, balance it, and leave you a report. The Balanset instruments are designed and manufactured by the same engineers who use them for on-site balancing, so you get consultation support on choosing planes, fitting sensors, and working through a run that did not go as planned.

• Machine type, operating speed, drive power, rotor mass if known.
• Photos of the rotor from both sides, and photos of where sensors could be fitted.
• What was done to the machine before the vibration appeared, and how it built up: suddenly or gradually.
• If measurements already exist: overall vibration, 1x amplitude and phase at both supports, the spectrum.

1. 01

   Take a measurement you can trust

   Vibration sensors on the bearing housings, as close to the bearing as possible, on a rigid mount: a stud or a magnet on a clean, flat pad. Radial direction, usually horizontal, and the same every time you measure. A laser tachometer aimed at a reflective marker on the shaft. Record the speed, overall vibration, 1x amplitude and phase at both supports, and the spectrum.

2. 02

   Assess whether it is unbalance

   Compare the 1x share of overall vibration, look at the spectrum, check that three runs repeat. If the phase drifts, or overall is several times higher than 1x, stop and look for a different cause. An hour spent checking is cheaper than a shift spent on balancing that does not help.

3. 03

   Check the mechanics before fitting weights

   Torque on the foundation bolts, soft foot, play, the condition of the grout and the frame, bearing clearances, tension and alignment on a belt drive. You balance a machine that is mechanically sound, securely fixed to its foundation, and free of resonance at operating speed. A faulty machine gets repaired first: balancing does not substitute for a repair.

4. 04

   Balance it and confirm the result

   A baseline run, a trial weight, the calculation, fitting the correction weights, a check run, and trim weights added to the existing ones if needed. Record the result against three things at once: residual 1x, overall vibration at both supports, and, if acceptance requires it, residual unbalance in g·mm/kg.

Sources: Balanset-1A manufacturer specification · Balanset-1A operation manual

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