Static and Couple Unbalance Decomposition

Dynamic unbalance is the sum of a static unbalance at the centre of mass and an opposite pair (couple) in two planes. Splitting a two-plane result into these components helps to understand the source and the right balancing method.

Type of unbalance —

Static component S = W₁ + W₂: —
Couple component ±C = ±(W₁ − W₂)/2: —
Couple unbalance (C·r·L): —
Static / couple share: —
Static unbalance (S·r): —

Correction weights (W₁, W₂), static (S) and couple (±C) components

These tools are intended for preliminary assessment and training. Decisions on critical equipment should be based on on-site measurement and expert evaluation.

How to use

Enter the correction weights of both planes as mass and angle.
Enter the distance between the planes and the correction radius.
By the result: if static dominates, one plane may be enough; if couple or dynamic, correct in two planes.

Theory & formulas

W₁ = S/2 + C, W₂ = S/2 − C ⇒ S = W₁ + W₂, C = (W₁ − W₂)/2 (vector sums).

Static unbalance U_s = |S|·r (g·mm) turns the heavy spot down even at standstill. Couple unbalance U_c = |C|·r·L only shows when rotating, as out-of-phase vibration at the two bearings.

Out-of-phase (≈180°) vibration at the bearings suggests couple, in-phase vibration static unbalance. ISO 21940-11 tolerances can also be allocated through these two components.

Frequently asked questions

Why may one plane not be enough for static unbalance?

The static component should be corrected in the plane of the centre of mass. A correction placed in another plane creates a new couple, so wide rotors may need two planes even when static unbalance dominates.