Understanding Quasi-Static Unbalance

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Portable balancer & Vibration analyzer Balanset-1A

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Vibration sensor

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Dynamic balancer “Balanset-1A” OEM

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Quasi-static unbalance is a specific and relatively uncommon type of dynamic unbalance. It occurs when a rotor’s principal axis of inertia intersects the shaft’s rotational axis, but not at the rotor’s centre of gravity. In everyday terms it is a condition that contains both static unbalance and couple unbalance — with the special feature that the angular position of the static component sits exactly 90 degrees away from the plane of the couple. That precise alignment is what gives it its name and its distinctive behaviour.

1. Definition: What is Quasi-Static Unbalance?

To picture it, recall what defines a perfectly balanced rotor: its principal axis of inertia coincides with its axis of rotation. Different kinds of unbalance describe different ways those two axes can part company. In quasi-static unbalance the two axes cross — they intersect — but the crossing point is offset along the shaft from the centre of gravity rather than sitting on it. Geometrically this is a tilted-and-shifted axis whose static and couple ingredients are locked at a fixed 90-degree separation.

Like every form of dynamic unbalance, it can only be fully measured and corrected while the rotor is spinning, and it requires correction in at least two planes. A purely static check on knife-edges cannot reveal it, because the couple component only produces forces under rotation.

2. Relationship to Other Unbalance Types

It helps to place quasi-static unbalance alongside the three standard categories:

• Static unbalance: purely a displacement of the centre of gravity off the shaft axis. It generates centrifugal forces that are in phase at the two bearings.
• Couple unbalance: purely a “wobble”, with equal heavy spots on opposite ends and opposite sides. It generates forces that are 180 degrees out of phase at the bearings.
• Dynamic unbalance: the general case — a combination of static and couple unbalance at any arbitrary phase angle relative to one another.
• Quasi-static unbalance: a special case of dynamic unbalance in which the static and couple components are physically locked at exactly a 90-degree phase separation.

In other words, every quasi-static rotor is dynamically unbalanced, but only a particular geometric coincidence earns the “quasi-static” label.

3. Practical Example: The Overhung Rotor

The classic textbook example is an overhung rotor whose unbalance lies in a single plane far from the machine’s centre of gravity. Consider a large industrial fan with a heavy set of blades mounted on the end of a long shaft, beyond both bearings.

Suppose there is a single heavy spot on the fan disk — a pure static unbalance on the disk itself. The way that one force reaches the two bearings is not symmetrical:

• The bearing closer to the fan feels a large vibration force.
• The bearing further from the fan also feels a force, but because the mass is “overhung” beyond the supports, that force acts through a pivoting action about the near bearing.

The net result at the bearings is a complex motion that blends both a shaking (static) component and a rocking (couple) component. Because both originate from a single physical heavy spot, they share a fixed relationship — and it is exactly that fixed relationship which creates the quasi-static condition. This is also why overhung rotors are notoriously sensitive and almost always demand two-plane treatment.

4. Correction

Despite its precise definition, quasi-static unbalance is corrected just like any general dynamic unbalance — there is no special procedure. The balancing workflow is:

1. Measure the vibration amplitude and phase at 1× running speed at two bearing locations.
2. Compute the required correction weights and their angular placement for two chosen correction planes, typically using the influence-coefficient method with a trial weight.
3. Fit the weights so that they cancel both the static and the couple components simultaneously.

In the field this is a standard two-plane balancing job. A portable two-channel instrument such as the Balanset-1A measures amplitude and phase at both bearings, derives the influence coefficients of the rotor, and computes the mass and angle for each plane — then verifies that the residual unbalance meets the required ISO 21940-11 grade. An analyst may well identify the condition as quasi-static from the phase readings, but the practical correction is the same proven two-plane routine used for any dynamic unbalance.

5. Why the Distinction Matters

If the correction is identical, why name the condition at all? Because recognising a quasi-static pattern aids understanding, not procedure. The phase relationship tells the engineer that a single overhung heavy spot — rather than two independent ones — is the likely physical cause, which guides where to look for the source: a damaged blade, accumulated product, or an assembly fault on the overhung disk. That insight is part of the broader value of careful phase interpretation in rotor dynamics.

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