Balancing in one or two planes: how to choose the number of correction planes

A fan starts humming after the impeller is cleaned. You've arrived with the instrument, fitted the sensors, and the first real question comes up: balance in one plane, or two? The answer decides how many runs you'll make and whether you get a result at all. Below: the L/D rule, an explanation of couple imbalance, and the signs that tell you one weight won't be enough.

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

Static and couple imbalance: why one mass sometimes can't do the job

Imbalance is classified by how the extra mass sits along the rotor's axis. This isn't an academic distinction. It's exactly what decides whether you fit one mass or two.

You'll see static imbalance on a stopped machine. The center of mass is offset from the rotation axis, and a rotor placed on knife-edges will turn itself until the heavy spot settles at the bottom. When it spins, one uncompensated centrifugal force appears. One weight in one plane cancels it out.

Couple imbalance doesn't show up at rest. Picture two equal masses sitting in different planes along the rotor's length, on opposite sides of the axis. Gravity balances them out, and the rotor sits still on the knife-edges. Spin it up, and the centrifugal forces from these masses turn out equal in magnitude and opposite in direction, but applied at different points along the shaft. They don't lie on the same line, so they don't cancel each other out. Instead they form a couple — a moment. That moment rocks the rotor around its center of mass: bearing 1 moves up while bearing 2 moves down at the same instant.

From there it's simple mechanics. Only a pair of forces creates a moment. A single weight produces one force, not a pair. Fit it to calm the first bearing, and the second one gets worse. You've simply pushed the vibration from one end of the rotor to the other. A moment is cancelled by a moment: two weights, spaced along the rotor's length and pointed in different directions.

In real life, two unbalanced masses are rarely equal, so you almost always end up with a mix of static and couple imbalance. That's what's called dynamic imbalance. For a rotor that stays rigid at operating speed, it's a proven fact: two weights in two spaced-apart planes are always sufficient. One plane is just the special case where there's practically no couple component.

How this looks on the screen. A typical picture of a dominant couple: the bearing on the coupling side shows 7.8 mm/s at a phase of 32°, the opposite bearing 6.9 mm/s at a phase of 211°. The amplitudes are close, the phases are almost 180° apart. If the phases are close and the amplitudes comparable instead, you're looking at a static imbalance. The numbers here are illustrative, but the phase relationship works as a reliable indicator.

The L/D rule: a one-minute calculation

The rotor's shape tells you whether a moment even has a lever arm to work with. A moment is a force multiplied by a distance. A thin disc has almost no distance, so the resulting moment is small. An elongated rotor has a lever arm, and a moment appears from any asymmetry along its length.

Determine two values. L is the rotor's working length — more precisely, the distance between the two planes where you can actually fit a weight. D is the diameter in the zone where the weight is mounted, at the correction radius. Not the shaft diameter. Not the machine housing's overall size. The diameter where the mass will actually sit.

Then divide one by the other and check the table.

The 0.5 threshold is a working guide, not a figure from a standard. ISO 21940 classifies rotors by their behavior and by operating speed relative to critical speeds, not by a single geometric ratio. Check the applicable part and edition of the standard for your machine. Use L/D as a first filter, and make the actual decision from the measured vectors.

Between-bearing and overhung rotors: where to put the planes

The mounting geometry determines where the weight can physically go and how strongly the planes interact with each other.

• Mount 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 surface.
• Keep the measurement direction the same from run to run. Usually horizontal-radial, because the foundation's stiffness is lower in the horizontal direction and the response is larger.
• Two planes need both channels running at once. Aim the laser tachometer at the reflective mark on the shaft; it gives you the speed and the reference phase.
• Keep an eye on the axial direction too. Axial vibration more often points to shaft misalignment than to imbalance. A strong couple imbalance can also produce an axial component, from twisting the frame.

When to use two planes regardless of L/D

The reverse situation happens too. The second plane isn't accessible: it's covered by a guard, potted in, or simply out of reach without a strip-down. In that case, work in one plane, reduce what can be reduced, and record honestly in the report that the couple component remains. Sometimes it helps to recalculate the correction weights onto other, accessible planes — the software has that function. But a recalculation doesn't create a lever arm where none exists.

• Speed is high, or the operating frequency is close to the first critical speed (the speed at which the rotor goes into resonance) or the natural frequency of the supports. The response to the couple component grows with speed faster than the response to the static one.
• After a single-plane correction, the first bearing calmed down but the second stayed at the same level or got worse. That's a direct signature of a couple.
• The 1x phases at the two bearings differ by around 120-180° at comparable amplitudes.
• The rotor is overhung, and the width of the wheel can't be ignored.
• The rotor is mounted at an angle, or the wheel has noticeable face runout.
• Two correction planes are physically accessible, marked out, and you can fasten a weight to them reliably.
• The machine is critical, and you need a report showing residual vibration at both bearings, not just one.

The cost of the question: runs, stoppages, and time

Two-plane balancing follows the three-run method. First you take the baseline vibration reading. Then you fit a trial weight of known mass in plane 1 and make a second run. Then you move the trial weight to plane 2 and make a third run. After that, the software calculates the masses and angles for both planes.

One plane takes just two runs before the calculation. The difference of one run looks small on paper, but on site it's measured not in calculation time but in stoppages: coast-down, lockout, removing the guard, repositioning the weight, reassembly, clearance to start. On a machine with a long coast-down, each cycle can easily eat up 20-30 minutes. That's where the cost of the second plane actually hides.

If you service a fleet of identical machines, the three runs are only needed once. The instrument stores the influence coefficients, and on the next identical machine you balance from the saved coefficients with no trial runs at all. Always do a verification run after fitting the weights, and add trim weights (small fine-tuning weights) to the ones already fitted if needed.

How to tell the choice was right

A rough guide for a typical fan on a rigid foundation: a starting level of around 12 mm/s comes down to around 1.5-2 mm/s once the right number of planes has been chosen. This is an expectation, not a guarantee. On a machine with resonance, worn bearings, or a drifting phase, you won't get that result no matter how many planes you use.

• Both bearing housings come within tolerance on overall vibration — the total level across all frequencies, not just 1x. As a guide for measurements on non-rotating parts: mm/s RMS (root mean square) over the 10-1000 Hz band, zone A or B (the machine-condition zones defined by the standard). Record the applicable part of ISO 20816 and the measurement points separately.
• The 1x component has dropped at both bearings, not just moved from one to the other.
• Readings repeat between runs: amplitude within roughly ±5%, phase within roughly ±5°. If the phase is drifting, don't trust the calculation, and it's too early to fit weights.
• Axial vibration hasn't increased.
• Overall vibration hasn't stayed several times higher than 1x. If it has, something else is producing most of the vibration.

If the second bearing got worse after a single-plane correction, don't add a weight at random and don't try to guess an angle. Take fresh baseline vectors at both bearings and move to a full two-plane calculation. Otherwise you'll just be chasing the vibration around the rotor blind.

Where the choice of plane count won't solve anything

Balancing removes vibration caused by an asymmetric mass distribution. It removes nothing else, no matter how many planes you use. Here are the cases where you need to stop and deal with something else instead.

• Resonance. The operating frequency is close to the natural frequency of the rotor, the supports, or the frame. Amplitude shows a sharp peak, the 1x phase swings by about 180° with a small change in speed, influence coefficients don't repeat. First find the natural frequencies from a coast-down or a bump test, then address the stiffness of the supports, the fasteners, or the operating speed.
• A flexible rotor. At high speed the rotor bends, the radius of the heavy spot grows along with the mass, and the linear model stops working. This calls for modal balancing — across several bending modes of the rotor — and a different measurement system.
• Aerodynamic or hydraulic imbalance. A force of this kind is proportional to the angular velocity, while the centrifugal force from a correction weight is proportional to its square. You'll compensate the response at one speed and produce a new error at another. The same applies to electromagnetic forces in electric machines.
• Shaft misalignment. It more often produces 2x and axial vibration. It's fixed with shaft alignment, not weights. If a machine has both misalignment and imbalance, align first, then balance.
• Mechanical looseness, rubbing, bearing defects. Compare the overall vibration with 1x. If the overall level is several times higher, look for a mechanical cause. Balancing doesn't replace a repair.
• A narrow wheel with face runout. The lever arm is short, so large masses are needed for the required moment, and you pick up an additional induced imbalance from the disc's deformation. Fix the fit and the runout first.

Sources: ISO 21940-11:2016 · ISO 21940-12:2016 · ISO 20816-1:2016 · ISO 13373-3:2015 · ISO 13373-5:2020 · ISO 281:2007

What this looks like on site with AXILINE

The procedure is straightforward. We come to the machine, mount two vibration sensors on the bearing housings, aim the laser tachometer at the mark, and take the baseline picture: speed, overall vibration, the amplitude and phase of 1x at both bearings, and the FFT spectrum (vibration broken down by frequency). We decide one plane or two from the phase difference and the L/D ratio. Then come the trial runs, the correction, the verification run, and, if needed, a small trim-weight top-up.

The Balanset-1A handles both one and two planes. It tells you whether the trial weight was adequate, splits the correction mass across fixed positions (blades or holes), calculates drilling when mass is being removed, displays a polar diagram, recalculates weights onto other correction planes, and stores the results in an archive for the report. The kit fits in a case: two accelerometers, a laser phase sensor, a two-channel USB module with preamplifiers and an ADC, and Windows software.

If you balance regularly, it makes sense to keep the instrument on hand rather than booking a site visit every time. If the case is a one-off or unclear, we'll come and do it ourselves. Balanset instruments are designed and manufactured by engineers who use them themselves on site visits, so on choosing planes, mounting sensors, and troubleshooting a failed run, you get consulting support.

• Send us the machine type, speed, drive power, and photos of the rotor from both sides.
• Tell us whether two correction planes are accessible and reachable without a strip-down.
• If you already have readings, include the 1x amplitude and phase at both bearings and the overall vibration.
• Tell us whether anything changed before the vibration appeared: cleaning, a wheel replacement, a bearing repair, work on the foundation.

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

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