Dynamic balancing corrects a rotor’s imbalance while it spins, by running it at a fixed low speed, adding a known trial weight at three marked positions 120° apart and recording the vibration each time. The four vibration readings give the size and position of the imbalance by simple arithmetic, so no instrument other than a pointer and a ruler is needed: for example 1.00, 1.42, 1.19 and 0.56 mm with a 2 g trial weight call for a 4 g correction at 220° from the first trial position.
Part of Centrifuge Building
Dynamic balancing is the correction of imbalance in a rotor at running speed, by comparing the vibration with and without trial weights, which catches faults that static balancing at rest cannot.
Some Imbalance Shows Only When The Rotor Spins
Static balancing at rest puts the center of mass on the axis, but if the rotor has unequal masses at different places along its length it still rocks; the carrier says dynamic imbalance shows up as vibration only when spinning. The carrier’s procedure is: run at 10-20% of target speed, feel for vibration, add a trial weight at a marked position, run again, and adjust amount and angle until vibration is minimal, then increase the speed in steps and recheck. This article turns “feel” into a measurement that gives the answer in one set of runs.
What You Need
- The rotor mounted in its own bearings and frame, with a shield
- A fixed pointer or a gauge that shows the vibration amplitude at the frame, read the same way every run (a ruler against a fixed edge, or the width of a chalk mark)
- A set of trial weights, a scale and a way to clamp them at a marked angle; mark the rim in 10° steps from a zero mark
- The same running speed for every measurement, 10-20% of target to begin with
Method: The Three-Trial-Weight Calculation
This is the amplitude-only method for a single plane. The vibration amplitude is proportional to the imbalance at a fixed speed, so you can use the readings as relative sizes.
Run 0: no trial weight. Read the amplitude A₀.
Runs 1, 2, 3: clamp a trial weight T at 0°, then 120°, then 240° (measured from the zero mark), one at a time. Read A₁, A₂, A₃.
Calculate.
- The effect of the trial weight alone, in amplitude units, is t, where t² = (A₁² + A₂² + A₃²) ÷ 3 − A₀².
- The cosine of the heavy-spot angle φ from the 0° mark is b₀ = (A₁² − A₀² − t²) ÷ (2 × t × A₀), and b₁ = (A₂² − A₀² − t²) ÷ (2 × t × A₀) is cos(120° − φ).
- sin φ = (b₁ + 0.5 × b₀) ÷ 0.866. Then φ = the angle whose cosine is b₀ and sine is that value.
- The weight needed is W = T × A₀ ÷ t, placed at φ + 180°. (Or remove the same mass at φ.)
Worked Example
A rotor at 20% of target speed gives A₀ = 1.00 mm. A 2 g trial weight gives A₁ = 1.42, A₂ = 1.19 and A₃ = 0.56 mm at 0°, 120° and 240°.
- Squares: A₁² = 2.016, A₂² = 1.416 (1.19² = 1.4161), A₃² = 0.314. Sum = 3.746; ÷ 3 = 1.249. t² = 1.249 − 1.000 = 0.249, so t = 0.50 mm.
- b₀ = (2.016 − 1.000 − 0.249) ÷ (2 × 0.50 × 1.00) = 0.767 ÷ 1.0 = 0.767.
- b₁ = (1.416 − 1.000 − 0.249) ÷ 1.0 = 0.167.
- sin φ = (0.167 + 0.5 × 0.767) ÷ 0.866 = 0.551 ÷ 0.866 = 0.636. cos φ = 0.767, so φ = 39.7°, about 40°.
- W = 2 g × 1.00 ÷ 0.50 = 4 g, placed at 40° + 180° = 220° (or remove 4 g at 40°).
Check by arithmetic: a 2 g weight at 220° gives an amplitude of 1.00 − 0.50 = 0.50 mm (the weight alone is worth 0.50 mm, and 220° is opposite the heavy spot), half the original, and 4 g gives zero. Take off the trial weight, fit a 4 g clamp-on weight at 220°, run again and the reading should fall to a small residue.
Real rotors do not behave perfectly (vibration is not exactly proportional to imbalance), so after the correction repeat the procedure once with a smaller trial weight to trim the remainder.
Two-Plane Rotors
A long rotor needs the procedure repeated for each end, because a weight at one end affects the vibration at both. Correct one plane, then the other, and repeat the pair until both are small. A short bowl or tube rotor is mostly single-plane.
A Rotor Balanced Slow Can Still Shake Fast
After balancing at low speed, step up the speed (the carrier says increase incrementally and recheck) and balance again at each step; a rotor can be balanced at 1,600 RPM and shake at 6,000 RPM because the machine’s own resonances and the rotor’s bending appear at different speeds.
Common Mistakes
- Changing the speed between runs. The amplitudes are no longer comparable.
- Measuring on a loose frame. Bolt the machine down so the reading is the rotor’s.
- Trial weight too small or too large. A weight that changes the amplitude by under 20% is lost in the noise, and one that more than doubles it risks a bad run.
- Correcting at an angle measured from the wrong mark. All angles come from one zero mark, in the direction of rotation.
Safety
The trial weight is the part most likely to leave the rotor
A 2 g weight at 100 mm radius at 1,600 RPM (ω = 167.6 rad/s) pulls with 0.002 × 0.100 × 167.6² = 5.6 N, small for a good clamp but not for tape or putty. Use a clamp or screw, fit it before spinning, and stand away from the plane of the rotor. Stop at the first rise in vibration.
What’s Next
- Learn next: Vibration Isolation — dealing with the remainder
- Combine with: Safe Operating Procedures — the run-up checks