Understanding Quasi-Static Unbalance
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 static and couple unbalance vectors lie in one and the same axial plane. That coplanar 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 lie in the same axial plane — it is precisely that coplanar combination which makes the two axes intersect at all.
Like every form of dynamic unbalance, it can only be fully measured while the rotor is spinning. Because the whole condition is equivalent to a single resultant unbalance acting in one specific axial plane, a single correction of the right magnitude in that plane can remove it — provided that plane is accessible on the machine; otherwise it is treated as an ordinary two-plane balancing job. 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 unbalance vectors lie in the same axial plane, so the tilted principal axis still crosses the shaft axis (at a point other than the centre of gravity).
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
In principle, quasi-static unbalance can be removed by a single correction in the appropriate axial plane, because it is equivalent to one resultant unbalance acting in that plane. In practice that exact plane is often not accessible on the assembled machine, so in the field it is corrected just like any general dynamic unbalance. The balancing workflow is:
- Measure the vibration amplitude and phase at 1× running speed at two bearing locations.
- Compute the required correction weights and their angular placement for two chosen correction planes, typically using the influence-coefficient method with a trial weight.
- 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 field routine is usually the same two-plane job, why name the condition at all? Because recognising a quasi-static pattern aids understanding — and it can even simplify the procedure, since a single correction in the right axial plane is sufficient when that plane is accessible. 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.
