How this calculation works
Rotating masses do not combine by simply adding their weights. Their mass-radius vectors point in different directions around the rotor. This calculator sums those vectors in a single plane and finds an added correction mass at your chosen radius.
Ux = Σmr cosθ; Uy = Σmr sinθ; added mass = |U|/rc; correction angle opposes UA worked example
Two 10 g masses at 100 mm radius, located at zero and ninety degrees, sum to 1414.214 g mm. An added mass at 100 mm radius is 14.1421 g, positioned at 225 degrees. The equal orthogonal components explain why the result is not 20 g.
Good to know
All masses are assumed coplanar. A long rotor may have a couple unbalance even when its net mass-radius vector is zero. No vibration influence-coefficient test, balancing-machine calibration, two-plane solution or balance-quality certification is included.
Reference: Illinois mechanics reference — rotating-mass balancing (opens in a new tab) ↗
What this model answers
Rotating masses do not combine by simply adding their weights.
Their mass-radius vectors point in different directions around the rotor. This calculator sums those vectors in a single plane and finds an added correction mass at your chosen radius.
The Flywheel usable speed band energy and duration calculator accounts for a rotating body’s usable energy. Correcting a mass-radius imbalance does not verify that body’s stored-energy containment.
Keep the input conventions consistent
Use one angular datum and one positive rotation direction for every record.
Mass is in grams and radius in millimetres. The reported correction angle is for adding a mass, not drilling out the same mass; material removal would use the opposite location.
Read the result carefully
The resultant unbalance is a mass-distance quantity.
Rotational speed does not change the ideal correction vector, but it changes the resulting force amplitude with speed squared. This separates balance geometry from the force consequence at the entered speed.
A correction mass is defined together with its radius and angular direction. Moving it to a smaller permitted radius requires more mass for the same correction unbalance. Keep the angular reference and sign convention consistent when transferring a reported correction location to a drawing or measured rotor position.
Work through the numbers
Two 10 g masses at 100 mm radius, located at zero and ninety degrees, sum to 1414.214 g mm.
An added mass at 100 mm radius is 14.1421 g, positioned at 225 degrees. The equal orthogonal components explain why the result is not 20 g.
Where the calculation stops
All masses are assumed coplanar.
A long rotor may have a couple unbalance even when its net mass-radius vector is zero. No vibration influence-coefficient test, balancing-machine calibration, two-plane solution or balance-quality certification is included.
A few questions, answered
Will changing rpm change the correction mass?
No. It changes the estimated unbalanced force; the ideal geometric correction remains the same.
What should I change in the comparison?
Double speed and inspect the fourfold force change with unchanged correction mass.