Every rotating part carries some unbalance. The question is never whether it exists, but whether it is small enough to live with at the speed the part actually runs. This page covers the fundamentals: what unbalance is, the three forms it takes, how it is expressed, and why speed matters more than anything else.
It is drawn from The Basics of Balancing 101, written by Gary K. Grim, Joel M. Book PhD and Jake Schlaegel of Balance Technology Inc. The original paper is available as a PDF.
Four Terms You Need First
| Term | What it means |
|---|---|
| Centre of gravity | The point at which the resultant gravitational force on a body acts. For practical purposes on a balancing machine it coincides with the centre of mass. |
| Centre of mass | The point at which the body’s mass could be concentrated and produce the same motion under linear acceleration. It is the point that obeys F = ma. |
| Geometric axis | The axis the part is engineered to rotate about, established by its bearing journals or mounting surfaces. This is the axis the machine holds. |
| Principal inertia axis | The axis a part would naturally spin about if released in free space. Balancing is the work of bringing this axis into line with the geometric axis. |
That last pair is the whole problem in one sentence. A part is balanced when its principal inertia axis and its geometric axis are the same line. Unbalance is the distance and angle between them.
The Three Types of Unbalance
Static unbalance
Also called force unbalance. It exists when the centre of mass sits off the axis of rotation, but the principal inertia axis remains parallel to the geometric axis. The part is heavy on one side, and that is all.
U = w × e or U = w × r
where U is unbalance, w is the correction weight and e or r is its distance from the axis. Static unbalance needs a single correction weight in one plane, and because it acts under gravity alone it can be measured without spinning the part.
Disc-shaped parts — wide relative to their length — typically carry only this kind. Brake rotors, flywheels, fan wheels and grinding wheels are the common examples.
Couple unbalance
Couple unbalance exists when the principal inertia axis is no longer parallel to the geometric axis, but still intersects it at the centre of mass. The part is not heavy on one side; it is heavy at one end on one side, and at the other end on the opposite side. The centre of mass may sit perfectly on the axis, so the part can appear balanced at rest and be badly unbalanced turning.
U = w × r × d
where d is the couple arm, the axial distance between the two planes. Units are therefore squared — g·mm² or oz·in². Correction requires two equal weights, 180 degrees apart, in two separate planes.
Couple unbalance cannot be found on a static balancer. It only reveals itself when the part spins.
Two-plane, or dynamic, unbalance
Real parts rarely carry one form cleanly. Dynamic unbalance is the vector sum of static and couple unbalance, and it is what nearly every shaft-type component actually has. The principal inertia axis neither meets nor parallels the geometric axis.
Correction requires two weights that are unrelated to each other — different magnitudes, different angles, in two different planes. It can only be measured on a spinning balancer.
As a working rule: if a part is longer along its axis than it is wide, assume it needs two-plane correction.
How Unbalance Is Expressed
Unbalance is a weight multiplied by a distance, so its units are always a weight unit and a length unit paired together.
| Component | Units in use |
|---|---|
| Weight | grams (g), ounces (oz), kilograms (kg) |
| Length | inches (in), millimetres (mm), centimetres (cm), metres (m) |
| Common pairings | oz·in, g·in, g·mm, g·cm, kg·m |
Couple unbalance, carrying the extra couple-arm term, is expressed in squared units such as oz·in². Mixing unit systems between a drawing, a specification and a machine readout is one of the more common sources of confusion on a shop floor, and it is worth settling explicitly before a machine is specified.
Why Speed Matters More Than Mass
The force produced by a given unbalance rises with the square of rotational speed. Double the speed and the force quadruples. A useful working form:
F = 1.77 × U × (rpm ÷ 1000)²
with U in oz·in and F in pounds of force. The practical consequence is that a residual unbalance entirely acceptable at 900 rev/min can be destructive at 9,000, and it is why tolerance is always specified against a service speed rather than as an absolute figure.
This is the reasoning behind ISO 21940-11, which assigns a balance quality grade G by component type and derives permissible residual unbalance from that grade and the service speed. The ISO balance tolerance calculator works it out for a specific part.
Resonance, and Why Suspension Design Matters
Every balancing machine suspension has a resonant frequency. Where the machine runs relative to that frequency determines what it actually measures.
Well below resonance, displacement is small and largely independent of speed — the machine is effectively measuring force. Well above resonance, the part rotates about its own principal inertia axis and displacement approaches a limit set by the ratio of unbalance to part weight:
Xp = U ÷ part weight
Near resonance, with little mechanical damping present, vibration amplitude can reach many times its off-resonance value. That amplification is why balancing machines are deliberately designed to operate well away from their own resonant frequency in one direction or the other — and it is the origin of the hard-suspension and soft-suspension distinction.
How Unbalance Gets Measured
Static balancers do not rotate the part. They measure the effect of gravity on a centre of mass that sits off-axis, typically with the part on a vertical shaft over a pivot, and displacement read by a pair of sensors set 90 degrees apart. They find static unbalance only.
Dynamic balancers spin the part and measure the resulting centrifugal force or displacement at the supports, which is the only way to resolve couple and two-plane unbalance.
Hard-suspension machines run below resonance and measure force, which means a single factory calibration holds across different parts. Soft-suspension machines run above resonance and measure displacement, which requires calibration for each part setup using a known trial weight, but can resolve smaller residual unbalance.
For how those choices translate into machine selection, see BTI industrial balancing machines.
Frequently Asked Questions
What is the difference between static and dynamic unbalance?
Static unbalance is a single heavy spot — the centre of mass sits off the axis of rotation — and it can be corrected in one plane without spinning the part. Dynamic unbalance is the vector sum of static and couple unbalance, requires correction in two planes with unrelated weights, and can only be measured while the part rotates.
Can a part be balanced at rest but unbalanced when spinning?
Yes, and this is exactly what couple unbalance is. The centre of mass can sit perfectly on the axis while the principal inertia axis is tilted relative to it. On a static balancer such a part reads as balanced. Spin it and the couple appears.
How do I know whether my part needs one-plane or two-plane balancing?
Geometry decides. Disc-shaped parts that are wide relative to their length generally need only single-plane correction. Anything longer along its axis than it is wide should be treated as two-plane.
Why does a small unbalance cause problems at high speed?
Because force rises with the square of speed. The same residual unbalance produces four times the force at double the rev/min, which is why tolerances are always tied to a service speed.
What units is unbalance measured in?
A weight unit paired with a length unit — oz·in, g·mm, g·cm and kg·m are all in common use. Couple unbalance carries a squared length term, for example oz·in².
Source
Adapted from The Basics of Balancing 101 by Gary K. Grim, Joel M. Book PhD and Jake Schlaegel, Balance Technology Inc. Download the original paper (PDF).
Browse all BTI technical resources or talk to an application engineer.
