Rotor Rubbing and Thermal Bow: Why Balancing Won't Converge

You did everything by the book. Initial run, trial weight, calculation, correction. And the verification run showed not the 0.8 mm/s the software promised, but 3.5 mm/s at a completely different angle. The problem is often neither an angle-reading error nor the weights: the machine is changing while it runs, and the weight calculation loses its meaning. The two most common causes of this kind of instability are rotor rubbing against stationary parts and thermal bow.

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

Why Unstable Vibration Breaks the Weight Calculation

Influence-coefficient balancing rests on a single equation. The vibration vector at the bearing is the sum of the response to the original imbalance and the response to the added mass. The instrument measures the original vector, you install a trial weight of known mass at a known radius, the instrument measures the new vector, and the software attributes the entire difference between them to the weight. From that difference comes the influence coefficient, and from that, the correction mass and angle.

Two conditions are hidden inside that equation, and people usually don't think about them. First: the system is linear, meaning a twice-as-large force produces a twice-as-large response, and the supports' stiffness doesn't depend on amplitude. Second: the system doesn't change between runs, meaning the rotor's geometry, the clearances, and the temperature stay the same. Rubbing violates the first condition. Thermal bow violates the second.

Work through what happens to the numbers. This example is calculated for illustration, not a report on real work. The initial run gives 4.0 mm/s at 30°. The trial run gives 6.0 mm/s at 70°, and the software assumes the weight produced the entire shift of the vector. But over the twelve minutes it took to stop, install the weight, and come back up to speed, the machine warmed up, and the thermal component added its own 1.2 mm/s at 150°. The influence coefficient comes out wrong in both magnitude and phase. The software promises a residual of 0.5 mm/s; the verification run shows 3.5 mm/s at the wrong angle.

From there it gets worse. You add more weights, but the drift continues, and every new iteration is calculated from data that's already corrupted. That's how the familiar picture emerges: three or four runs, vibration jumping up and down, and the machine never settling within tolerance. The instrument has nothing to do with it. You're solving an equation whose coefficients keep changing.

The criterion for whether the data is usable is simple and checked with one extra run. Stop the machine and start it again, changing nothing. The 1x amplitude (the running-speed component — vibration at the rotor's rotation frequency) should repeat within about 10%, and the phase within a few degrees. If the phase has diverged by tens of degrees, taking influence coefficients is pointless, no matter how careful the rest of the work is.

Rubbing: A Contact That Lives in the Spectrum and the Time Waveform

Rubbing is contact between a rotating rotor and a stationary part. The candidates are few, and all of them are predictable: a labyrinth or brush seal, a fan shroud, an inlet cone, a diffuser, a guard, an oil slinger, a bearing cap, a broken-off piece of insulation. Sometimes the contact isn't created by the rotor itself but by a layer of product built up on the wheel that's grown into the clearance.

The mechanics of the contact explain the entire picture on the screen. As long as the rotor isn't touching the casing, the system has one stiffness. At the moment of contact, the stiffness of the stop gets added in, and only in one direction, and only for part of the revolution. The response comes out asymmetric and clipped, and harmonics appear in the spectrum — components that are multiples of running speed: 2x, 3x, 4x, and further up, often with a raised noise floor.

Partial rubbing, where contact happens once per revolution, produces this comb-like spectrum and impacts in the time waveform with a period of one revolution. Full annular rubbing, where the rotor seats against a seal around the entire circumference, behaves differently: friction spins up a reverse precession — the rotor starts rolling around inside the seal in the direction opposite to rotation — and stable subharmonics appear in the spectrum at 1/2x, 1/3x, 1/4x. This is already an emergency condition, not a reason to keep taking measurements.

There's also a trap that runs the other way. The contact braces the rotor, raises the system's effective stiffness, and sometimes lowers the 1x amplitude. You look at the overall vibration, see that things have gotten "better," and don't notice that the harmonics have grown and the 1x phase has stopped repeating. That's exactly why you should always look at the time waveform, not just the spectrum.

• A comb of harmonics at 1x, 2x, 3x, and higher, with a raised noise floor
• Stable subharmonics at 1/2x, 1/3x, 1/4x, if the contact has become annular
• The time waveform is clipped on one side, or clearly asymmetric about zero
• Impacts in the signal with a period of exactly one revolution
• The picture changes as the machine warms up: the clearance shifts, and the contact comes and goes
• A localized hot spot on the casing at the contact zone: a thermal camera, or simply a hand on the guard
• Marks on the metal: a shiny polished band, temper colours, metal dust, worn-off paint
• The 1x phase doesn't repeat from run to run, and the amplitude jumps around for no apparent reason
• A characteristic sound: a dry rustle or squeal that changes with speed

To see the harmonics and subharmonics, the band used for the overall assessment isn't enough. Set Fmax (the spectrum's upper frequency limit) to roughly 10–20 times running speed — for a machine at 1450 rpm that's about 250–500 Hz — and no fewer than 1600 lines. There's a separate article on measurement settings with more detail on choosing Fmax, the number of lines, and recording time.

Thermal Bow: the Rotor Changes Geometry Under Heat

Thermal bow is a bend in the rotor caused by uneven heating or uneven cooling. One side of the shaft or wheel heats up more than the other, the metal expands asymmetrically, the axis curves, and the centre of mass moves off the line of the supports. You end up with a genuine running-speed force that wasn't there on the cold machine.

It's worth keeping the causes as a list, because they have to be found by eye, not by instrument. Uneven cooling: clogged cooling channels, half the intake grille blocked, a directed flow of hot air onto one side of the casing, exhaust recirculating back to the inlet. Uneven internal heating: a localized short circuit in the winding, damaged rotor bars, an uneven flow of hot process fluid through the wheel. Residual bow from standing idle: a heavy rotor that's sat in one position for many hours sags under its own weight, and in the first minutes after starting you see vibration that won't be there later.

The link between bow and rubbing deserves special mention. The contact heats the rotor at a single point, the hot spot causes a bend toward the contact, and the bend intensifies the contact. The system enters a slow, self-sustaining process in which the 1x phase keeps rotating continuously and the amplitude rises and falls over a period of tens of minutes. On a polar plot (a graph where the vibration vector is shown as amplitude and angle), the tip of the vector traces not a point but a spiral. This is a classic sign: not "measurement noise," but physics.

There's also a variant that lives inside sleeve bearings. On an overhung rotor with high shaft eccentricity, the oil in the clearance heats unevenly around the circumference, the journal warms asymmetrically, and the shaft picks up thermal bow from the bearing itself. The practical takeaway is the same: as long as the thermal process is underway, the 1x vector isn't a characteristic of imbalance.

It's important not to confuse thermal bow with thermal growth of the casings. Growth of the casings and supports raises the shafts relative to each other and produces induced misalignment, and that's fixed by shaft alignment with preset cold offsets. Bow changes the rotor's own geometry. The signs look alike, because both phenomena are tied to warm-up, but the fixes are different.

• 1x amplitude rises monotonically for the first 20–60 minutes at constant speed
• 1x phase slowly drifts in one direction, rather than oscillating around an average
• The scenario repeats almost identically from run to run, following the same curve
• After shutdown and cooling, a cold start gives the same low vibration as before
• A temperature difference across the casing or the flanges is visible with a thermal camera
• Sometimes the vector traces a spiral instead of a point on the polar plot

A warmed-up, bowed rotor behaves like a flexible rotor: its imbalance is distributed along its length and depends on the shape of the bend, so two correction planes may not capture the whole picture. Assessment and balancing of flexible rotors is covered by ISO 21940-12; check the applicable part and edition for your machine.

Sources: ISO 21940-12:2016

The Single-Warm-Up Test: Separating Time from Speed

One idea helps separate the causes. Resonance is a function of speed. Rubbing and thermal bow are functions of time and temperature. So you need to change the speed once, and track time once. The entire check fits into one warm-up and one shutdown — roughly an hour of running time.

1. Step 1

   Record the Warm-Up Curve

   Start the cold machine at running speed and hold it constant. Every 2–3 minutes, record four values: speed, overall vibration, 1x amplitude, and 1x phase. Log the bearing housing temperature alongside them. Don't move the sensor and don't change the measurement direction, otherwise the curve becomes incomparable with itself.

2. Step 2

   Wait for a Steady Thermal State

   Consider the condition steady once the bearing temperature changes by less than 1–2°C over 10 minutes, and the 1x phase holds within a few degrees over the same 10 minutes. For a small fan this takes 20–30 minutes; for a large machine with a hot process fluid, an hour or more. Before that point, any measurements are only good for diagnostics, not for calculating weights.

3. Step 3

   Check Repeatability

   Stop the machine without touching anything, and start it again. Compare the 1x vector at the same point in the warm-up. If it matches within 10% in amplitude and a few degrees in phase, the data is usable. If it doesn't match, look for the cause rather than calculating weights.

4. Step 4

   Change the Speed

   On a machine with a variable-frequency drive, shift the speed by 10–15% and see what happens to the amplitude and phase. A sharp, narrow peak with a phase reversal of roughly 180° points to resonance. If the picture barely depends on speed but depends strongly on running time, it's a thermal phenomenon. If the speed isn't adjustable, record vibration through a coast-down instead.

5. Step 5

   Let the Machine Cool

   Stop the machine, let it cool, and record a cold start. If low vibration and the original phase come back, a thermal origin is confirmed. If high vibration remains after cooling, the cause is mechanical: a worn fit, looseness, a lost weight, a broken blade, or rubbing that's already caused wear.

6. Step 6

   Inspect the Machine While It's Still Hot

   Right after shutdown, sweep a thermal camera across the casing, seals, guard, and flanges. A localized hot spot on the guard in one sector gives away the contact zone. Then remove a cover or inspection hatch and look at the metal: a polished band, gouges, metal dust.

Log everything in a table with timestamps. It's the curve of "phase versus minutes of running" that makes the diagnosis, not any single attractive-looking spectrum. One measurement can't tell thermal bow apart from an operator's mistake; a series of measurements can.

Table: Telling Five Similar Situations Apart

Combinations show up more often than pure cases. Looseness increases the rotor's mobility and provokes rubbing. Rubbing heats the rotor and causes bow. Bow raises vibration and finishes off the clearance. So don't stop at the first sign you find: go through the whole list, or you'll fix the consequence and leave the cause in place.

Sources: ISO 13373-3:2015

Found Rubbing: What to Do

Rubbing belongs to the category of defects that simply can't be compensated with weights. As long as the contact exists, any correction only lasts until the next change in clearance, while the wear keeps progressing. Your job is to find the contact location and restore the clearance.

• Measure the clearances wherever they're accessible: seal, guard, inlet cone, diffuser, covers. Compare against the drawing or the machine's record card
• Remember that clearance differs between the cold and hot machine. If the contact only appears under load, calculate the thermal movements, not just the cold dimensions
• Check whether the rotor has moved toward the casing because of bearing or fit wear. Excess radial clearance in the bearing can create rubbing on its own
• Check for strain from a rigidly connected pipe or duct: it shifts the casing and eats up the clearance on one side
• Check the tightness of the feet and for soft foot. Looseness gives the rotor system extra travel and leads to contact
• Inspect the wheel and impeller: a built-up layer of product, a bent blade edge, a loosened or shifted previously installed weight
• Check whether it's not the rotor itself rubbing but a foreign object: a piece of insulation, a torn scrap of seal, a delaminated guard coating
• Restore the clearance and repeat the measurement before balancing. The harmonics and subharmonics should disappear, and the 1x phase should start repeating

Handing out weights blindly while rubbing is present isn't dangerous only because it wastes time. The contact heats the metal, damages the seal, and lowers efficiency, and on a machine with sleeve bearings, annular rubbing can drive the rotor into instability within minutes. If subharmonics at 1/2x and 1/3x are pronounced and growing, the machine gets shut down — it doesn't get "pushed through to the end of the shift."

Thermal Bow: What to Do and How to Work with a Warmed-Up Machine

Here the approach is different. Thermal bow isn't always a defect that has to be eliminated. Sometimes it's a normal property of the machine at its operating condition, and in that case the task isn't to remove the bow but to honestly balance the machine in the state it actually runs in.

Still, look for the cause first. Simple measures most often restore symmetrical heating: cleaning the cooling channels, fully opening the grille, eliminating recirculation of the hot exhaust back to the inlet, insulation or a shield against a directed flow of hot air, repairing the winding or the rotor bars. Every one of these reduces the bow itself, and no amount of weight will produce that effect.

If the cause has been eliminated but bow remains at the operating condition, balance the warmed-up machine. The point is to have every run happen in the same thermal state, so the condition that the system stays unchanged is satisfied, and the influence coefficients come out honest.

Keep a special case in mind separately: a rotor with residual bow from standing idle for a long time. A machine like this isn't balanced from its first minutes of running. Let it settle out at running speed, and take your data after that. If the bow doesn't straighten out after a full warm-up, the shaft has a permanent bend, and that's a question of straightening or replacement, not weights.

1. 01

   Reach a Steady Thermal State

   Warm up the machine until the bearing temperature and the 1x phase are both stable. Treat only this measurement as the baseline. Keep everything you recorded during warm-up for diagnostics only.

2. 02

   Shorten the Stops Between Runs

   Every stop to install a weight cools the machine down. Prepare the weights, fasteners, and tools in advance, mark out the correction planes before the run, and work in a pair. The shorter the downtime, the less the thermal states of the runs diverge.

3. 03

   Let the Machine Rewarm Before Every Measurement

   After installing a weight, don't measure right away. Give it the same number of warm-up minutes as the baseline run, and take the vector at the same point on the curve. It takes longer, but the data stays comparable.

4. 04

   Check Repeatability on Every Run

   Before accepting a measurement, check whether the phase has settled. If it's still drifting, the condition hasn't stabilized yet, or the thermal process isn't finished. Wait, don't calculate.

5. 05

   Save the Influence Coefficients

   Coefficients obtained on the warmed-up machine are good for repeat work on this same machine at this same operating condition. Next time you can skip the trial runs entirely, which means skipping the extra stops and cool-downs. For a machine that's hard to shut down, this is the main practical payoff.

6. 06

   Record the Conditions in the Report

   Record the speed, load, bearing temperature, warm-up time, and the measurement points and directions. Without these conditions, a figure like "came down to 1.6 mm/s" means nothing: the same machine will show a different number at a different thermal state.

ISO 20816 ties the assessment of overall condition by overall vibration in mm/s RMS over the 10–1000 Hz band to established operating conditions — that is, to the operating condition and load. For a machine with thermal bow, this isn't a formality: you can't compare a cold measurement against a hot one. The residual-imbalance tolerance by G class is set by ISO 21940-11. Check the applicable parts and editions for your machine, and for contractual acceptance, record them in the document together with the operating condition and measurement points.

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

The Practical Takeaway: If the Phase Is Drifting, Stop

Let's fold everything into one rule worth applying before you ever pick up a trial weight. Watch the 1x phase at constant speed. If it's holding steady, the system is fit for calculation. If it's drifting, no calculation has any validity, and continuing to balance just means shoving the vibration back and forth at random.

This rule saves more time than any other check you can run on site. Three extra runs with weights and re-installation take an hour and a half to two hours, while a warm-up test with phase logging runs alongside the machine's normal operation and requires zero shutdowns.

And don't lose sight of what all this is for. Balancing exists to remove the force from unbalanced mass. Rubbing and thermal bow aren't imbalance — they're other processes that show up at the same 1x frequency and so masquerade as imbalance. The only way to tell them apart is by their behaviour over time. The instrument shows you that behaviour right away, as long as you're looking at a curve instead of a single number.

• 1x phase holds within a few degrees over 10 minutes of running
• A repeat run gives the same vector: 10% in amplitude, a few degrees in phase
• 1x accounts for most of the overall vibration, harmonics and subharmonics are small
• The time waveform is symmetric, with no clipped peaks or once-per-revolution impacts
• Bearing temperatures are stable, no localized hot spots on the casing
• Clearances are normal, no contact marks on the metal
• Only now install the trial weight

If You'd Rather Not Sort This Out Yourself

We're engineers who design and manufacture Balanset instruments and use them to do field balancing ourselves. So the first thing we do on site is measure and watch how the machine behaves over time, not immediately start welding on weights. If the 1x phase drifts during warm-up, or the signal shows signs of rubbing, you'll hear about it before balancing ever starts, along with exactly what to check.

The technical side is simple. Balanset-1A records two channels at once and shows overall vibration, 1x amplitude and phase, speed, the FFT spectrum, and the time waveform — exactly the set you need to tell rubbing harmonics apart from the slow phase drift of thermal bow. The polar plot makes the spiral visible to the eye. The archive and reports let you compare the cold and hot measurements instead of arguing from memory.

When the cause genuinely turns out to be imbalance, the normal work follows from there: single- or two-plane balancing using the influence coefficient method, splitting the weight across fixed positions or calculating drilled-hole corrections if there's nowhere to weld, tolerance calculation by G class, adding weights as needed. Influence coefficients taken on the warmed-up machine get saved, and the next visit skips the trial runs entirely.

The instrument is also available for purchase, including the Balanset-1A OEM version without the case, for building into machine tools and test stands. Consulting support comes with it, including going through your spectra, time waveforms, and warm-up curves.

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

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