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Balancing Without Phase: Four-Run Method

When no phase reference is available (no tachometer, or restricted access), balancing can be done from amplitude readings alone. After the initial reading the same trial weight is fitted at three positions in turn; the correction weight follows from the four amplitudes.

Amplitudes with the trial weight

Only one trial weight may be fitted in each run, always on the same radius. Angles are measured in the direction the trial weight positions advance; the result angle uses the same direction.

Correction weight —g at —°
Trial weight effect |T|
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Influence coefficient
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Measurement consistency error
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Assessment
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Circle method: the point where the three circles meet is the trial weight effect (T); W is the correction direction

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

  1. Run the machine at operating speed and measure the initial amplitude (V₀).

  2. Fit the trial weight at 0° and measure V₁; remove it, fit it at 120° for V₂ and at 240° for V₃.

  3. Remove the trial weight, fit the calculated correction at the angle shown and take a check reading.

Theory & formulas

In each trial run the measured amplitude is |Vi| = |V0 + T·ejθi| with θ = 0°, 120°, 240°. T is the effect of the trial weight on vibration.

With di = Vi² − V0², the mean gives |T|², and β = (1/3)·Σ(di − |T|²)·e−jθi = V0·T.

The correction weight is W = −mtrial·V0² / β; its magnitude is in grams, its angle relative to the 0° trial position.

For a linear, noise-free system |β| = V0·√(mean d); the difference shows how consistent the readings are. The three circles meeting in one point on the plot is the visual form of the same check.

Frequently asked questions

When is balancing without phase used?

When no tachometer or optical sensor can be fitted, no reflective tape can be applied, or only an amplitude meter is available. It needs more runs than phase-based balancing and is more sensitive to noise.

How large should the trial weight be?

Large enough to change the vibration by at least 20–30%, but not so large that the machine reaches a dangerous level. A trial weight with a weak effect carries measurement error straight into the result.