Technology / Technical guide
Rotor Static Unbalance & Couple Unbalance: Force and Moment
A rotor’s mass distribution can create a rotating excitation even when its visible geometry looks symmetric. Static and couple unbalance describe different properties of that distribution. Their forces and moments are inputs to a structural response, not a direct measurement of vibration amplitude.
Keep the force sum and the axial moment sum separate.
Mass offset can be represented by vectors in planes normal to the axis. Adding those vectors and their axial moments explains why a rotor can have no resultant static unbalance while still producing an unbalance couple.
01 / Mass offset
An unbalance vector has mass–length units.
For rigid mass distribution relative to a nominated spin axis, a plane unbalance contribution can be written U = m r, with transverse offset vector r.
For rigid mass distribution relative to a nominated spin axis, a plane unbalance contribution can be written U = m r, with transverse offset vector r. U has units kg m. The vector sum describes the corresponding static-unbalance component.
A geometric centre is not automatically the mass centre, and the spin axis is part of the definition. Equal-looking blades do not prove equal mass distribution. These statements describe general rigid-rotor mechanics rather than a measured manufacturing condition of any actual turbine.
02 / Rotating force
The excitation magnitude scales with speed squared.
Under steady rigid rotation, a plane unbalance contribution produces a rotating force magnitude |U|ω² in the appropriate support-force balance.
Under steady rigid rotation, a plane unbalance contribution produces a rotating force magnitude |U|ω² in the appropriate support-force balance. The transverse direction changes with rotation. This is a force relationship, not a velocity or displacement amplitude.
With invented |U| = 0.02 kg m and ω = 10 rad/s, the magnitude is 2 N. Doubling ω gives 8 N under unchanged conditions. These are fictional inputs; actual movement also depends on mass, stiffness, damping, support and the excitation’s spatial distribution.
03 / Pure couple
Opposed offsets can cancel force but retain moment.
Consider equal and opposite plane unbalance vectors separated by axial distance ℓ.
Consider equal and opposite plane unbalance vectors separated by axial distance ℓ. Their resultant unbalance force cancels in the ideal rigid case, but the separated rotating forces create a couple. Its magnitude is |U|ℓω² for this simple pair.
Using the same fictional U and ω with ℓ = 0.10 m gives 0.20 N m. Static force cancellation therefore does not establish zero dynamic excitation at the supports. Schenck’s couple-unbalance explanation distinguishes these separated-plane effects.
04 / General distribution
Static and couple components can occur together.
A distribution can have both a nonzero transverse-vector sum and a nonzero axial moment contribution.
A distribution can have both a nonzero transverse-vector sum and a nonzero axial moment contribution. Dynamic unbalance is not merely another term for one heavy point. Schenck’s general description separates mass-centre offset and axis-orientation effects.
The chosen axial reference affects how the moment is stated when a resultant force also exists. Equivalent force and moment must remain together under a reference shift. A pure zero-resultant couple retains its moment independently of such an axial reference change.
05 / Observed motion
One excitation can create different support responses.
A rotating force can produce different measured amplitudes at different locations because the structure has its own dynamics.
A rotating force can produce different measured amplitudes at different locations because the structure has its own dynamics. A frequency near a responsive mode can alter amplitude and phase without changing the original U definition.
A once-per-revolution feature is consequently not a unique diagnosis of mass unbalance. Other periodic mechanisms can share an order. The order guide separates excitation timing from response, while the existing balance-evidence guide concerns records rather than corrective action.
06 / Scope
Rigid unbalance is only one rotor mechanism.
Flexible motion, aerodynamic differences and changing operating conditions can require a description beyond the rigid mass-distribution model.
Flexible motion, aerodynamic differences and changing operating conditions can require a description beyond the rigid mass-distribution model. An aerodynamic loading imbalance is not automatically the same physical quantity as a mass-offset vector.
No MARSTON unbalance value, balance grade, correction plane or vibration result is assigned here. The guide gives no added mass, removed material, balancing test or speed-change procedure. It explains the mechanical quantities without turning a hypothetical force into a product assessment.
Related technical guides: Campbell Diagrams: Modal Branches, Rotor Orders & Crossings · Bearing Stiffness and Damping Coefficients · Two-Inertia Torsional Vibration in Wind Generators.
General background: Schenck: separated-plane couple unbalance · Schenck: combined force and couple components. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Plane unbalance | U = m r in kg m | Defined transverse offset and spin axis. |
| Rotating force | |U|ω² in N | Rigid steady-rotation excitation. |
| Couple contribution | |U|ℓω² in N m | Equal opposed contributions separated axially. |
| General dynamic case | Force and moment together | Both components can coexist. |
| Vibration response | Motion of the supported structure | Not established by excitation magnitude alone. |
Engineering questions.
Does symmetric appearance prove mass balance?
No. Geometry and mass distribution are different facts.
Does |U|ω² directly give vibration displacement?
No. It gives an excitation force in the stated model.
Can zero static resultant coexist with couple unbalance?
Yes. Opposed contributions in separated planes can retain a moment.
Does doubling speed double the fictional force?
No. Fixed unbalance in the ideal model gives four times the force.
Does a 1x vibration uniquely prove mass unbalance?
No. Several periodic causes and response effects can share that order.
Does this prescribe a rotor correction?
No. No balancing or material-change procedure is supplied.
Technical enquiry
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