Understanding Eccentricity in Rotating Machinery

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In rotor dynamics, eccentricity is the radial offset between a rotor’s centre of mass (its centre of gravity) and its geometric centre — the true centre of its shaft. In a perfectly balanced rotor those two centres would coincide, but manufacturing imperfections and non-uniform material density guarantee that some eccentricity almost always remains. When an eccentric rotor spins, the off-centre mass generates a centrifugal force, and that force is the root cause of unbalance vibration. Eccentricity, in other words, is the geometry behind the most common machinery fault there is.

1. Definition: What is Eccentricity?

Eccentricity is a distance — usually a handful of micrometres — measured perpendicular to the axis of rotation, separating where the mass actually centres from where the shaft turns. Because it is a property of how mass is distributed rather than of how the surface looks, true mass eccentricity cannot be seen, and it cannot be read with a dial indicator on a stationary rotor. It reveals itself only when the rotor turns and the offset mass begins to throw a centrifugal force outward once per revolution.

2. The Direct Relationship Between Eccentricity and Unbalance

Eccentricity and unbalance are two sides of the same coin. Unbalance is the measure of the effect of eccentricity at a given speed; eccentricity is the physical cause. The amount of unbalance is directly proportional to the rotor’s mass and to its eccentricity:

Unbalance (U) = Mass (M) × Eccentricity (e)

This simple product explains why eccentricity is so critical. The centrifugal force it produces grows with the square of rotational speed, so even a few micrometres of eccentricity on a heavy, high-speed rotor can create an enormous force, driving severe vibration and rapid bearing wear. You can see how steeply that force climbs with mass, eccentricity, and speed using a centrifugal force from unbalance calculator.

3. Types of Eccentricity

It is important to distinguish true eccentricity from related geometric imperfections that are often confused with it.

Mass Eccentricity

The true eccentricity defined above — the offset between the mass centre and the geometric centre. This is what causes unbalance and is the target of every balancing procedure. It cannot be measured directly with a dial indicator on a stationary rotor; it only shows up dynamically, as a once-per-revolution force whose direction (its heavy-spot angle) is found from the phase of the 1× vibration.

Geometric Eccentricity (Runout)

A deviation of the rotor’s surface from a perfect circle — a measure of how “out-of-round” a shaft or rotor is, also called mechanical runout. A journal may be slightly oval, or a pulley machined off-centre on its shaft. Unlike mass eccentricity, this can be measured with a dial indicator during a slow roll. It does not represent mass unbalance directly, but an eccentric geometric form very often contributes to it. The distinct but closely related concept of rotor eccentricity describes this geometric offset in the context of motors and air-gap clearance.

Electrical Runout

Not a physical imperfection at all, but a measurement artefact peculiar to non-contact proximity probes. Where the shaft surface varies in magnetic permeability or electrical conductivity, the probe returns a false signal that mimics geometric runout. This noise must be characterised and subtracted — typically through cable compensation and slow-roll runout subtraction — during rotor-dynamic testing, or it will masquerade as real shaft motion.

4. Causes of Eccentricity

Mass eccentricity enters a rotor through several routes:

• Manufacturing tolerances: no machining, casting, or assembly process is perfect, so small errors are inevitable.
• Non-uniform material density: inclusions, voids, or porosity in a casting or forging make the material inhomogeneous and shift the mass centre.
• Asymmetric design: some components, such as crankshafts, are inherently asymmetric.
• Assembly errors: a pulley or bearing that is not perfectly centred on the shaft creates an eccentric mass.
• Thermal distortion: uneven heating or cooling can bow a rotor, temporarily shifting its mass centre — a thermal bow, often described as a thermal vector because both its size and direction matter.

5. How Eccentricity is Addressed

Because mass eccentricity is the cause of unbalance, it is corrected through balancing. By adding or removing small amounts of mass, a technician creates an opposing centrifugal force that effectively draws the rotor’s mass centreline back toward its geometric centreline, minimising the net force and the resulting vibration. On an assembled machine this is done in place: a portable two-channel analyser such as the Balanset-1A measures the 1× amplitude and phase in the machine’s own bearings, computes how much correction weight to add and where, and verifies the residual unbalance afterwards. Note that balancing cancels the effect of eccentricity; it does not move the geometric surface, so a rotor with large geometric runout may balance well yet still rub or read high on a proximity probe.

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