ISO 21940-11: Procedures and Tolerances for Rotors with Rigid Behaviour
ISO 21940-11 is the modern, authoritative international standard for the ಸಮತೋಲನ of rigid rotors — rotors whose unbalance distribution does not change significantly across their working speed range. It officially supersedes the long-established ISO 1940-1, carrying forward that document’s familiar machinery while refining the language, expanding the catalogue of rotor types, and giving far more explicit procedural guidance. Its full title is “Mechanical vibration — Rotor balancing — Part 11: Procedures and tolerances for rotors with rigid behaviour,” and it is the document an engineer turns to whenever a balance specification, tolerance, or acceptance test must be defended against a recognised reference.
1. Scope: What Counts as a Rigid Rotor
The standard applies exclusively to rotors that exhibit rigid behaviour. Formally, a rotor is treated as rigid when it can be corrected in any two arbitrary planes and, after that correction, its residual unbalance does not significantly exceed the specified tolerance at any speed up to the maximum service speed. In practice this means the shaft does not bend appreciably under the centrifugal forces it generates, so the mass distribution that you measure at low speed is effectively the same one the machine runs with at full speed.
This assumption is the dividing line of the entire ISO 21940 family. Where a rotor flexes — typically once its service speed climbs past roughly 70% of its first bending critical speed — the rigid model breaks down and the multi-speed procedures of ISO 21940-12 for flexible rotors must be used instead. The stated goal of rigid-rotor balancing is to reduce the mass eccentricity until the centrifugal forces and vibration from the surviving unbalance are acceptably low for the machine’s intended duty — never to chase a theoretical perfect balance, which is neither attainable nor economic.
2. Specifying the Balance Tolerance: G-Grades
This is the heart of the standard — the chapter that answers “how good does the balance need to be?” It carries forward the internationally recognised concept of Balance Quality Grades (G). A G-grade is a constant equal to the product of the rotor’s permissible specific eccentricity e and its maximum service angular velocity Ω:
G = e · Ω (numerically, the permissible orbital velocity of the centre of mass in mm/s)
The standard contains an extensive, updated table that lists hundreds of rotor types — from small electric armatures and grinding spindles through pumps, fans and machine-tool drives up to massive steam turbines and generators — and assigns each a recommended grade. An engineer reads off a grade such as G6.3 for a typical pump or fan, G2.5 for a turbine or rigid turbo-generator rotor, or tighter values for precision spindles. The standard then supplies the formula that converts that grade into a working number: the permissible residual specific unbalance eper, which multiplied by the rotor mass yields the total permissible residual unbalance in units such as gram-millimetres. Because eper = (G × 1000) / Ω, the permissible unbalance falls as service speed rises — a fast rotor must be balanced far more precisely than a slow one of the same mass. Our Residual Unbalance Calculator (ISO 21940-11) performs this conversion directly from a grade, mass and speed.
3. Allocating the Tolerance to Two Correction Planes
A single total tolerance is not enough to balance a real rotor, because correction is applied in two correction planes. Once the total permissible residual unbalance is known, it must be apportioned between those two planes, and ISO 21940-11 provides explicit formulas and vector diagrams to do so correctly. The split is not arbitrary: it depends on the rotor’s geometry — specifically the axial distance of each correction plane from the centre of gravity and from the bearing locations. Allocating the tolerance properly is what guarantees that both the static component and the couple unbalance are controlled, so the dynamic forces at both bearings are minimised along the full length of the rotor. For an inboard, symmetric rotor the division is close to even; for asymmetric or outboard geometries it can be markedly unequal. The companion guidance on how to split permissible residual unbalance between two correction planes walks through the same arithmetic step by step.
4. Verifying Residual Unbalance — The Acceptance Test
After the final correction weights are applied, a verification run confirms the result. On a dedicated balancing machine the remaining unbalance is measured in each correction plane and compared against the individual per-plane tolerances derived in the previous step. The rotor passes only when the measured residual unbalance is at or below tolerance in both planes — a pass in one plane and a near-miss in the other is a fail. The standard stresses that the verifying instrument must be properly calibrated and that any tooling errors (arbors, adapters, drive elements) be accounted for, since an uncorrected tooling eccentricity can mask or fake a passing result.
When the rotor is already installed, this same verification happens on-site rather than in a balancing pit. A portable two-channel analyser such as the ಬ್ಯಾಲೆನ್ಸೆಟ್-1ಎ measures the 1× amplitude and phase in the machine’s own bearings at operating speed, computes the rotor’s influence coefficients, and confirms that the residual vibration sits inside the chosen ISO 21940-11 grade — capturing the true installed state, including assembly and thermal effects a shop machine never sees.
5. Reporting and Traceability
The standard closes by specifying the minimum content of a formal balancing report, so results are traceable and unambiguous. A compliant report records the administrative details (date, operator), a full identification of the rotor (part and serial numbers), and the key balancing parameters: the specified balance quality grade, the maximum service speed, and the rotor mass. Crucially it documents both the initial unbalance and the final measured residual unbalance for each correction plane, demonstrating that each sits below its calculated tolerance. The result is a permanent, verifiable record that the rotor was balanced in accordance with the standard.
6. What Changed from ISO 1940-1
- Direct replacement: ISO 21940-11 is the official successor to ISO 1940-1. The fundamental principles and the core G = e·Ω relationship are unchanged, so legacy specifications calling out “G6.3 per ISO 1940-1” map cleanly onto the new document.
- More emphasis on the process: the new edition treats balancing as an end-to-end workflow — specify the tolerance, allocate it between planes, verify the result, and report it — rather than as a single tolerance value.
- Expanded tables and clearer guidance: the G-grade machinery tables now cover more rotor types, and the procedural and allocation instructions are more explicit.
- Better integration: the standard sits cleanly alongside the rest of the ISO 21940 series — Part 12 for flexible rotors and Part 13 for in-situ balancing — and references the modern ISO 20816 series for in-service vibration limits.
- Rigid-rotor assumption remains the gatekeeper: the whole document is valid only while the rotor behaves rigidly; the moment it bends at speed, the analyst must move to Part 12.
