Worked example
Initial reading 4.0 mm/s ∠0°. A 10 g trial weight is fitted at 0° and the trial run at the same speed reads 6.0 mm/s ∠90°.
Trial effect T = (O+T) − O = 7.21 mm/s ∠123.7°; influence coefficient α = T / 10 g = 0.721 (mm/s)/g ∠123.7°. With the trial weight removed, the correction is W = −O / α = 5.55 g ∠56.3°.
If the trial weight stays on, the weight to add is W − Wt = 8.32 g ∠146.3°. Enter these values above to reproduce the result; angles follow the same direction convention as the phase readings.
Assumptions and limits
The method assumes vibration changes linearly with unbalance and that both runs are made at the same speed and operating condition.
If the trial effect is less than 20% of the initial vibration the result is unreliable; the calculator warns in that case. If the vibration comes from resonance, looseness or misalignment, balancing will not reduce it: diagnose first.
How to use it
Run the machine at operating speed and measure the 1X amplitude and phase (O).
Stop the machine and attach a trial weight of known mass at a known angle from the reference mark.
Measure again at the same speed (O+T).
Enter the values; make sure the angles use the same convention as the phase readings (e.g. against rotation).
Apply the calculated correction weight and take a verification reading.
Theory and formulas
Vibration vectors are treated as complex numbers: O = A₀∠φ₀, (O+T) = A₁∠φ₁. The effect of the trial weight alone is T = (O+T) − O.
The influence coefficient α = T / Wt gives the vibration produced per unit weight. The correction that cancels the initial vibration is Wc = −O / α.
If the trial weight stays in place, the weight to add is the vector Wc − Wt.
The suggested trial weight produces a centrifugal force of about 10% of the rotor weight: mt = 0.1·M·g / (r·ω²).
Frequently asked questions
Which angle direction should I use for single-plane balancing?
The trial weight angle and phase readings must follow the same convention. A common field convention measures angles from the reference mark against the direction of rotation. The calculated correction angle is applied using that same convention.
How large should the trial weight be?
Large enough to produce a clear change in amplitude or phase (typically 20–30% amplitude or 20–30° phase) but small enough not to endanger the machine. The calculator suggests the mass that creates a force of about 10% of the rotor weight.