Unbalance and Field Balancing

What Is Unbalance?

A perfectly balanced rotor has its mass distributed symmetrically around the rotation axis so the geometric center and mass center coincide. When that symmetry is broken, the offset mass center traces a circle with each revolution, generating a centrifugal force proportional to the product of the residual unbalance (mass times radius) and the square of the angular velocity. That rotating force transmits into the bearings and supporting structure as vibration, noise, and cyclically elevated bearing loads. Even small residual unbalance becomes significant at high speeds because the forcing grows with the square of RPM.

Types of Unbalance

Three geometric distributions of unbalance arise in practice, and identifying the correct type determines which balancing procedure to apply.

Static Unbalance

Static unbalance exists when the mass center is displaced from the rotation axis in a single radial plane, with no angular offset between planes. A disc-shaped rotor with a single heavy spot is the textbook case. The rotor rolls under gravity to the heavy side when placed on knife-edges, which is why it is detectable without rotation. In a vibration spectrum, static unbalance produces in-phase 1x signals at both bearing positions in the radial direction: the phase readings measured simultaneously at the drive end and non-drive end bearings differ by close to 0 degrees.

Couple Unbalance

Couple unbalance occurs when two equal heavy spots are located in different axial planes at 180 degrees to each other. The net static effect is zero (the rotor balances statically on knife-edges) but the two forces create a rotating couple that tilts the shaft during operation. The diagnostic signature is 1x radial vibration at both bearings with a phase difference of approximately 180 degrees between the two measurement planes. Couple unbalance cannot be corrected in a single plane; it requires weight corrections in at least two planes.

Dynamic Unbalance

Dynamic unbalance is the combination of static and couple components, which is the condition found on nearly all real rotors. The phase difference between radial vibration at the two bearing planes is between 0 and 180 degrees. Two-plane balancing resolves both components simultaneously by solving a set of simultaneous equations relating correction weights in each plane to the measured response.

Common Causes

Unbalance develops through several mechanisms during fabrication and service:

• Deposit buildup: Material accumulation on fan blades, impellers, and heat exchanger tubes shifts the mass center progressively. This is among the most frequent causes in process industries where airborne dust, scale, or slurry contacts rotating components.
• Erosion and corrosion: Material loss from one region of a rotor (blade tip erosion, pitting) removes mass asymmetrically and introduces or worsens imbalance over time.
• Lost or broken balance weights: Factory balance weights welded or bolted to fan wheels can detach in service, instantly shifting the balance state by the weight of the lost piece at its original radius.
• Manufacturing tolerances: Casting porosity, weld bead variation, and machining eccentricity leave rotors with residual unbalance from new. ISO balance grades account for this, specifying how much residual is permissible for a given rotor class.
• Thermal distortion: Rotors operating at elevated temperature can develop permanent bow if thermal gradients are uneven, displacing the mass center from the rotation axis. This is common in steam turbines and high-temperature blowers after a rapid cool-down.
• Shaft damage: A bent shaft or a shaft with a repaired weld shifts mass center offset and may also introduce coupling effects that complicate the balance state.

The 1x RPM Vibration Signature

Vibration Analysis of an unbalanced rotor produces a spectrum dominated by a peak at exactly one times the shaft running frequency (1x). The signal is predominantly radial (perpendicular to the shaft axis), because the centrifugal force acts outward from the shaft center. Axial vibration is generally low unless coupling or bearing geometry converts some radial force into an axial component.

The 1x peak grows with the square of speed: doubling RPM quadruples the centrifugal force and, for a linear system, doubles the vibration amplitude at the same unbalance magnitude. This speed-dependence is a useful diagnostic clue during coast-down tests.

Phase as a Diagnostic Tool

Amplitude alone does not confirm unbalance, because misalignment, looseness, and a bent shaft also produce 1x components. Phase measurement resolves the ambiguity:

• Unbalance: radial phase is stable (within a few degrees) across multiple readings; in-phase between the two bearing planes for static unbalance; 180-degree difference for couple unbalance.
• Angular misalignment: strong 1x axial component, often 180-degree phase opposition between the two sides of a coupling in the axial direction.
• Parallel misalignment: dominant 2x radial component alongside 1x; phase may be 180 degrees radially across the coupling.
• Bent shaft: 1x dominates and is stable, but phase measured at slow roll (a few RPM) is already elevated, distinguishing it from unbalance that grows with speed.

Industrial Vibration Analysis combines spectrum data with phase readings from a tachometer or optical trigger to produce a polar plot, giving a direct vector representation of the unbalance force and its angular position.

ISO Balance Grades (ISO 21940-11)

ISO 21940-11 (which replaced the older ISO 1940-1) codifies balance quality grades as G numbers. Each grade specifies a maximum permissible specific unbalance expressed as the product of eccentricity (e, in mm) and angular velocity (omega, in rad/s), giving units of mm/s. The grade number equals e x omega in mm/s at the rotor's maximum operating speed.

Grade Table

Worked Example: Permissible Residual Unbalance

Consider a centrifugal pump impeller with a rotor mass of 50 kg operating at 3,000 RPM, assigned balance grade G2.5.

1. Convert speed to angular velocity: omega = 2 x pi x (3,000 / 60) = 314.2 rad/s
2. The grade specifies e x omega = 2.5 mm/s, so the permissible eccentricity is: e_per = 2.5 / 314.2 = 0.00796 mm (approximately 8 micrometers)
3. Permissible residual unbalance per plane: U_per = m x e_per = 50 x 0.00796 = 0.398 g·m
4. Expressed in the more common workshop unit: 0.398 g·m = 398 g·mm. For a single-plane rotor, the total permissible residual is 398 g·mm. For a two-plane rotor, this total is split between the two correction planes according to the rotor's mass distribution.

This calculated value is the acceptance criterion: after balancing, the residual unbalance in each plane must be at or below the calculated permissible value before the rotor passes inspection.

Field Balancing Procedure

Precision Maintenance programs often include field balancing as a standard competency, particularly for large or difficult-to-remove rotors.

When to Balance in the Field

Shop balancing on a dedicated balancing machine provides greater accuracy and should be the first choice when a rotor can be removed feasibly. Field balancing is preferred when the rotor is large (multi-meter fan wheels), when disassembly time and cost outweigh the achievable accuracy difference, when operational conditions (temperature, process load) affect the balance state at speed, or when the rotor was balanced at shop but in-situ installation conditions (pipe strain, soft foot, thermal growth) have introduced new forces. The practical accuracy limit of field balancing is typically G2.5 to G6.3 depending on instrument quality and rotor rigidity.

Single-Plane vs Two-Plane

Single-plane balancing places correction weights in one axial plane only. It is appropriate for disc-like rotors (width less than roughly half the diameter) where the unbalance is predominantly static. Two-plane balancing applies corrections in two separate axial planes and is required for rotors with a significant length-to-diameter ratio or when phase analysis confirms a couple component. Two-plane balancing requires simultaneous vibration measurements at two bearing positions.

The Influence Coefficient Method (Trial Weight Procedure)

The influence coefficient method is the dominant field balancing technique. It requires no prior knowledge of rotor mass distribution; the rotor itself reveals how it responds to a known perturbation.

Step 1: Initial run. Record vibration amplitude (mm/s or microns peak) and phase angle at the balancing measurement plane(s) with the rotor at operating speed and thermal equilibrium. This is the reference vector, often called the original run vector (O).

Step 2: Trial weight run. Shut down. Attach a trial weight of known mass at a known angular position and known radius on the rotor. The trial weight must be secured against centrifugal force at operating speed; a loose trial weight is a serious safety hazard. Restart and record the new amplitude and phase (T).

Step 3: Calculate the influence coefficient. The influence coefficient (IC) is the vibration change produced per unit of trial weight: IC = (T - O) / U_trial, where the subtraction is vector arithmetic (accounting for both magnitude and phase). Spreadsheet tools and dedicated balancing software handle this calculation directly.

Step 4: Calculate the correction weight. The required correction vector is: U_correction = -O / IC. The magnitude gives the correction weight (adjusted for the correction radius), and the phase angle gives its angular position on the rotor. Remove the trial weight and install the permanent correction weight, or remove material at the opposing position.

Step 5: Correction run verification. Restart and verify that residual vibration meets the acceptance criterion. If within specification, balancing is complete. If not, the influence coefficient from the previous run can be used to calculate a trim correction without a new trial weight run.

For two-plane balancing, the procedure extends to a 2x2 matrix of influence coefficients. Two trial weight runs (one weight in plane 1, one in plane 2) generate four influence coefficients that relate corrections in each plane to responses at each measurement location. The matrix inversion gives simultaneous correction weights for both planes.

Correction Methods

Once the correction weight magnitude and angular position are calculated, the physical correction takes one of three forms:

• Weight addition: The most common approach in the field. Bolted weights, weld-on weights, or adhesive balance weights are added at the calculated angular position on the rotor. Bolted weights should use thread-locking compound and be torqued to specification; weld-on weights require a qualified welder and subsequent verification.
• Material removal: Grinding, drilling, or milling removes material from the heavy side. This is irreversible, so it is applied conservatively and followed by a verification run. Common on pump impellers and motor rotors where adding weight is impractical.
• Balance correction rings and planes: Many rotors are designed with dedicated threaded correction planes or sliding balance rings that allow weight repositioning without welding or drilling. This is the preferred design for components requiring periodic rebalancing, such as cooling tower fans handling dirty air.

The Bottom Line

Rotor unbalance is one of the most prevalent fault conditions in rotating machinery, and it is among the most straightforward to detect and correct when a structured approach is followed. The 1x RPM vibration signature combined with phase measurement provides a reliable diagnostic path that distinguishes unbalance from superficially similar faults. ISO 21940-11 grades supply a quantitative acceptance criterion that removes ambiguity from the question of whether a rotor is balanced well enough for its service. Field balancing with the influence coefficient method makes correction feasible on large or hard-to-remove rotors without sacrificing the accuracy needed to protect bearings and extend machine life. Integrating balance monitoring into a broader predictive program, rather than responding only after symptoms become severe, is what separates reactive repair costs from controlled maintenance expenditure.

Frequently Asked Questions