Free tool · ISO 21940-11
Work out the permissible residual unbalance for a rotor from its mass, service speed and balance quality grade, with every step of the working shown. Free, instant, no sign-up. The calculator follows ISO 21940-11, which replaced ISO 1940-1, for rotors with rigid behaviour, and splits the result between two symmetrical correction planes.
ISO 21940-11 · Rotors with rigid behaviour
Enter the rotor mass, the speed it runs at in service, and the balance quality grade you are working to. You get the permissible residual unbalance, with the working shown so you can check it. Free, instant, no sign-up.
A balance quality grade is a limit on the product of the rotor’s permissible mass-centre eccentricity and its angular velocity — eper × ω — expressed in mm/s. A grade is therefore not a single unbalance figure; it describes a family of rotors that behave alike. For the same grade, the faster a rotor turns the less eccentricity it is allowed. The grades run in a standard series in which each step is about 2.5 times the one below it. Choosing the right grade for a given type of machine is a judgement covered by ISO 21940-11 — consult the standard, or talk to us.
The per-plane figure this tool gives you is the total divided equally between two planes. That is only right when the correction planes sit symmetrically either side of the rotor’s centre of gravity. ISO 21940-11 sets out how to apportion the permissible unbalance when they do not, and puts limits on how much either plane may take. Check the split against your own rotor geometry before you work to it. For a rotor balanced in a single plane, use the total.
These results are indicative. They implement the method of ISO 21940-11 for rotors with rigid behaviour, and take no account of your rotor’s geometry, its bearing arrangement, flexible behaviour at or above its first critical speed, or any contractual or regulatory requirement placed on the machine. Verify the figures against the standard and have them checked by a qualified engineer for your specific application before you rely on them.
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The formula
Three steps.
ISO 21940-11 sets the balance tolerance for rotors with rigid behaviour through the balance quality grade G, in mm/s. The grade limits the product of the permissible eccentricity of the rotor's mass centre and its angular velocity. The calculator works it out in three steps:
1. Angular velocity: ω = 2π × n / 60, in rad/s, where n is the service speed in rpm.
2. Permissible specific unbalance: e = G × 1000 / ω, in g·mm/kg (numerically the same as µm of eccentricity).
3. Permissible residual unbalance: U = e × m, in g·mm, where m is the rotor mass in kg. For two correction planes placed symmetrically about the centre of gravity, each plane takes half.
ISO 21940-11 replaced ISO 1940-1, so an "ISO 1940 calculator" and this one give the same result. Choosing the right grade for a type of machine is covered by the standard; our guide to ISO 21940 balance grades explains what the grades mean.
Worked example
Check it by hand.
Angular velocity: ω = 2π × 3,000 / 60 = 314.16 rad/s.
Permissible specific unbalance: e = 6.3 × 1000 / 314.16 = 20.1 g·mm/kg.
Permissible residual unbalance: U = 20.1 × 250 = 5,010 g·mm in total, or about 2,510 g·mm in each of two symmetrical correction planes.
The results are indicative. They take no account of rotor geometry, bearing arrangement or flexible behaviour, and should be checked by a qualified engineer for your application.
FAQ
The most unbalance a rotor may have left after balancing and still meet its balance quality grade. It is given in g·mm, or per unit of rotor mass in g·mm/kg.
Yes. ISO 21940-11 replaced ISO 1940-1 and uses the same balance quality grades and method for rotors with rigid behaviour.
The grade limits eccentricity multiplied by angular velocity. For the same grade, the faster a rotor turns, the less eccentricity it is allowed.
Only when the correction planes sit symmetrically either side of the centre of gravity. ISO 21940-11 sets out how to apportion the tolerance when they do not. For a rotor balanced in a single plane, use the total.
No. It applies the ISO 21940-11 method for rotors with rigid behaviour only.
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