Balance quality grade (ISO 21940) calculator
Enter the rotor speed, mass and the required balance quality grade (G); the tool gives the permissible specific residual unbalance e_per, the total permissible residual unbalance U_per, the split between two planes and the equivalent correction mass at a given radius.
Typical application example: Pump impellers, fans, flywheels, general machinery parts, electric motor rotors
An example; verify the suitability and the values of the grade for your application from the standard.
Correction mass (if a radius is entered)
The calculation runs in your browser; the values you enter are not sent anywhere.
- Permissible specific residual unbalance e_per (G6.3)
- 20.05 g·mm/kg
- = 20.05 µm
- Total permissible residual unbalance U_per
- 501.3 g·mm
- Angular velocity ω
- 314.16 rad/s
By plane
| Plane | Share | Permissible U (g·mm) | Correction mass (g) |
|---|---|---|---|
| Plane ARadius 80 mm | 50 % | 250.7 | 3.133 |
| Plane BRadius 80 mm | 50 % | 250.7 | 3.133 |
Sensitivity: permissible unbalance as speed changes
| Speed (rpm) | e_per (g·mm/kg) | U_per (g·mm) |
|---|---|---|
| 1,500 | 40.11 | 1,003 |
| 2,250 | 26.74 | 668.5 |
| 3,000 | 20.05 | 501.3 |
| 3,750 | 16.04 | 401.1 |
| 4,500 | 13.37 | 334.2 |
For the same grade G, e_per is inversely proportional to speed: if speed doubles, the permissible specific unbalance halves.
Assumptions
- The rotor is taken as rigid; for flexible rotors balancing is treated separately according to the mode shapes at running speed, and this calculation is not sufficient.
- The grade G rests on the product of permissible specific unbalance and angular velocity being constant (e_per · ω = G); which machines suit a grade is given in the standard.
- The two-plane split is a simplified rule; for a narrow plane spacing or high precision see the additional conditions of the standard.
- Residual unbalance is what remains in the rotor after balancing; effects of bearings, couplings and mounting must be considered separately.
ω = 2π n / 60 · e_per = 1000 · G / ω (g·mm/kg = µm) · U_per = e_per · m (g·mm) · U_A = U_per · l_B / (l_A + l_B) · correction mass = U / r
A helper calculation; verify against the standard and your catalogue before publishing. The grade list and the application examples are illustrative; determine the grade a rotor needs from ISO 21940-11 and the machine manufacturer's requirement. The tool is not a statement of conformity or a certificate.
Let's follow the change of residual unbalance over time with vibration monitoring after balancing.
Request a conversation01
How to use it
A
Enter the speed and rotor mass and choose the balance quality grade G, or enter your own G value.
B
Read e_per and U_per; choose a single or two planes to see the split between planes.
C
Optionally enter the correction radius to calculate the equivalent correction mass for each plane.
02
What is balance quality grade G?
Giving a rotor's residual unbalance only in gram-millimetres makes it hard to compare rotors of different size. The balance quality grade G keeps constant the product of the specific residual unbalance e_per (unbalance per unit mass, i.e. the offset of the centre of gravity from the axis) and the angular velocity, in mm/s: G = e_per · ω.
The grade number (for example G6.3) is the value of this product in mm/s. A smaller G means tighter balancing; the steps progress by a factor of about 2.5.
03
e_per, U_per and the split between planes
e_per = 1000 · G / ω, given in g·mm/kg (the same number as µm). The total permissible residual unbalance U_per = e_per × rotor mass is in g·mm. For a narrow rotor (such as a disc) this value is applied in one plane; for a long rotor it is divided between two planes.
If the centre of gravity is midway between the two planes, each plane gets U_per / 2. If not, the split follows the lever ratio: the plane nearer the centre takes the larger share. The U value in a plane is converted to an equivalent correction mass by dividing by the correction radius.
04
Balancing and vibration monitoring
Balance quality shows up in vibration data as the 1× component while the rotor runs. If the 1× amplitude of a freshly balanced rotor rises over time, residual unbalance may be growing: look for causes such as lost mass, deposit build-up, looseness or thermal bow.
Taking the first measurement after balancing as a reference and following the 1× amplitude and phase is therefore a simple way to catch an unbalance-related change early.
FAQ
- What is the difference between e_per and U_per?
- e_per is the permissible residual unbalance per unit mass (g·mm/kg); U_per is that value multiplied by the rotor mass (g·mm). Use e_per to compare rotors of different size and U_per to make a correction on a single rotor.
- Which G grade should I choose?
- The one the standard gives for the rotor type and the machine's requirement, or the value the machine manufacturer asks for. The application examples in the list are only examples; verify the exact choice from the standard.
- Which speed should I enter: the balancing speed or the service speed?
- The permissible unbalance is calculated for the service (maximum operating) speed. Even if you balance at a lower speed on the balancing machine, the criterion is the speed at which the rotor will run.
- Can it be used for flexible rotors?
- No. This calculation is for rigid rotors. For flexible rotors whose running speed is near or above a critical speed, balancing is treated separately according to the mode shapes.
- Is the correction mass always an added mass?
- The calculated value is the mass equivalent to the permissible unbalance at that radius. In an actual correction, mass is added opposite to the heavy spot or removed from the heavy spot; the measured residual unbalance must be below the calculated limit.
Monitor vibration after balancing
Let's set up a monitoring plan that catches an unbalance-related rise in vibration early.