What does a single-plane correction address?
One plane corrects the static unbalance of a narrow rotor from readings at 1× running speed. One plane cannot correct couple unbalance.
Single-plane field balancing
Rotor unbalance,
resolved as a vector.
One plane corrects the static unbalance of a narrow rotor from readings at 1× running speed. Use the original run, a run with a known trial mass, and that mass’s rotor position to resolve the correction by the influence-coefficient method.
Both runs need the same speed, sensor position and direction. The phase convention decides the sign of the angle: select whether measured phase and rotor mass angles increase in the same or opposite directions.
Run measurements
Enter both 1× readings and the fitted trial mass.
Correction vector
Trial removedInstall the correction
g
At the correction radius
°
Angle on the rotor
from the trial position, increasing in the rotor-angle direction.
Trial effect · E = T − O
mm/s
at
Influence coefficient · |α|
mm/s per g
Measured vector resolution
Original O
Trial T
Effect E
Angles are mapped into the rotor-angle direction, shown counterclockwise from 0°. The dashed connector shows T − O. All vectors share one amplitude scale.
Check passed
Amplitude
Phase
The trial response is not below both rule-of-thumb thresholds. This check does not establish the reliability of the balance.
Split across available positions
Enter a position count to resolve the mass onto two adjacent positions.
| Position | Rotor angle | Mass (g) |
|---|---|---|
| — | — | — |
| — | — | — |
The two position masses replace the unsplit correction; they are not additional masses.
How to use the result
- Record the original run.
Measure the amplitude and phase at 1× running speed. Keep the speed, sensor position and direction the same for the trial run.
- Fit and record the trial mass.
Stop the machine and secure the trial mass at its known angle and radius. Take the trial-run amplitude and phase with that mass fitted.
- Match the angle convention.
Select whether phase and mass angles increase in the same or opposite directions. Enter both runs in the same amplitude unit.
- Choose the final configuration.
Specify whether the trial mass will be removed or left in place. Enter the trial and correction radii if they differ. Add a position count if the correction must be split.
- Review before installing.
Check the trial effect, response warning and correction angle. Stop the machine and secure every mass before a run. Use a qualified balancing specialist to assess the preliminary result.
The vector calculation
Complex vectors use real and imaginary pairs. Trigonometric functions below use angles in degrees.
01 · Map phase into rotor coordinates
s = +1 (same), −1 (opposite)
O = A₀ (cos(sφ₀), sin(sφ₀))
T = A₁ (cos(sφ₁), sin(sφ₁))
Wₜ = mₜ (cos θₜ, sin θₜ)
O = A₀ (cos(sφ₀), sin(sφ₀))
T = A₁ (cos(sφ₁), sin(sφ₁))
Wₜ = mₜ (cos θₜ, sin θₜ)
02 · Resolve the trial effect
E = T − O
α = E / Wₜ
|α| = |E| / mₜ
α = E / Wₜ
|α| = |E| / mₜ
No correction can be resolved if |E| is zero.
03 · Resolve the required mass vector
W꜀ = −O Wₜ / E
W = W꜀ (trial removed)
W = W꜀ − Wₜ (trial left in place)
m = |W| × rₜ / r꜀
θ = atan2(Im W, Re W), wrapped to 0–360°
W = W꜀ (trial removed)
W = W꜀ − Wₜ (trial left in place)
m = |W| × rₜ / r꜀
θ = atan2(Im W, Re W), wrapped to 0–360°
The angle from the trial position is (θ − θₜ), wrapped to 0–360°.
04 · Split onto adjacent positions
Δ = 360° / Nₚ
θₖ = (k − 1) Δ
θᵦ = θₐ + Δ
mₐ = m sin(θᵦ − θ) / sin Δ
mᵦ = m sin(θ − θₐ) / sin Δ
θₖ = (k − 1) Δ
θᵦ = θₐ + Δ
mₐ = m sin(θᵦ − θ) / sin Δ
mᵦ = m sin(θ − θₐ) / sin Δ
Use the two positions bounding the correction angle. The final interval wraps back to position 1.
05 · Check the trial response
Amplitude change = 100 (A₁ − A₀) / A₀
Phase change = wrap(φ₁ − φ₀) to −180…180°
Phase change = wrap(φ₁ − φ₀) to −180…180°
Warn if the absolute amplitude change is less than 30% and the absolute phase change is less than 30°: the trial mass was too small for a reliable result. Phase change is a signed difference in the measured phase convention.
Common questions
Why must the two runs use the same setup?
The original run and the trial-mass run need the same speed, sensor position and direction.
How does the phase convention affect the result?
Choose whether measured phase and rotor mass angles increase in the same direction or in opposite directions. This convention decides the sign of the correction angle.
What changes if the trial mass stays on the rotor?
If the trial mass is removed, install the calculated correction. If it is left in place, subtract the trial-mass vector from the calculated correction vector, then adjust the added mass for the correction radius.