ISO 21940-12: Procedures and Tolerances for Rotors with Flexible Behaviour
ISO 21940-12 is the international standard that addresses the harder problem of balancing flexible rotors — rotors whose shape and unbalance distribution change significantly with speed, particularly as they approach and pass through their bending critical speeds. Its full title is “Mechanical vibration — Rotor balancing — Part 12: Procedures and tolerances for rotors with flexible behaviour.” Unlike a rigid rotor, which can be balanced once at low speed and trusted to stay in balance, a flexible rotor balanced at rest may vibrate violently at its service speed. This standard supplies the specialised multi-speed, multi-plane procedures these rotors demand, and it is the natural companion to ISO 21940-11, which governs rigid rotors.
1. Scope and the Classification of Rotors
The standard applies to any rotor whose unbalance distribution and/or deflected shape changes with speed. ISO 21940-12 frames the work around typical rotor configurations with flexible behaviour and the balancing procedures suited to each, rather than a numbered class system. The widely cited five-category scheme below actually originates in the now-superseded ISO 11342:1998 and remains a useful guide to job complexity; rotors range from near-rigid to highly flexible:
- Class 1 — Rigid rotors: behave rigidly across the whole speed range and are handled under ISO 21940-11.
- Class 2 — Quasi-rigid rotors: can be balanced at low speed but may need a trim balance at service speed to clean up residual flexing.
- Class 3 — Rotors requiring balancing at several speeds: typically passing through one or more critical speeds, most often balanced with the ಪ್ರಭಾವ ಗುಣಾಂಕ method.
- Class 4 and 5 — Highly flexible rotors: such as large turbine-generator shafts, which excite multiple bending modes and need advanced modal balancing to correct each mode.
Placing a rotor in the correct class tells the analyst up front how complex the job will be and which procedure to reach for.
2. Balancing Procedures: Two Core Methods
This chapter is the technical core of the standard. Its central message is that a low-speed balance alone is insufficient for a flexible rotor and must be augmented by high-speed work that accounts for the shaft’s bending. ISO 21940-12 organises this work as a family of balancing procedures — low-speed procedures (designated A to F, such as single-plane, two-plane and balancing in stages during assembly) and high-speed procedures (G to I, carried out at one or more elevated speeds). The high-speed procedures rest on two principal techniques:
The Influence Coefficient Method
This versatile, widely used technique places a known trial weight in one correction plane at a time and records the resulting vibration response — both amplitude and phase — at multiple measurement points and across multiple speeds. Repeating this for every plane builds a matrix of influence coefficients that mathematically describes how unbalance in any plane affects vibration at any point and speed. A computer then inverts that matrix to solve for the set of correction-weight masses and angles that simultaneously minimise vibration across the whole operating range. The same mathematics underlies single-plane work; you can explore it interactively with the Influence Coefficient Calculator.
Modal Balancing
Modal balancing is the more physically intuitive approach: it treats each bending mode of the rotor as a separate unbalance problem. The rotor is run at or near a chosen critical speed to maximally excite the corresponding mode shape; vibration measurements then locate the effective “heavy spot” for that mode, and correction weights are placed at the points of maximum deflection — the anti-nodes — to counteract it. The process is repeated mode by mode for every significant bending mode within the operating range, balancing the rotor one mode at a time. The two methods are not rivals; large machines are often balanced with a hybrid that uses modal insight to choose planes and influence coefficients to refine the weights.
3. Specifying Balance Tolerances
The simple G-grade tolerance that works so well for rigid rotors is generally inadequate for flexible ones, because a single eccentricity figure cannot capture speed-dependent bending. ISO 21940-12 therefore introduces broader tolerance criteria, which may be based on:
- Limits on the residual modal unbalance for each significant bending mode.
- Limits on the absolute shaft vibration amplitudes at specified locations and speeds, especially at the service speed.
- Limits on the forces transmitted to the bearings.
These vibration- and force-based limits tie the acceptance criteria to in-service severity standards such as the ISO 20816 series, rather than to a single residual-unbalance number.
4. Verifying the Final Balance State
Acceptance of a flexible rotor is fundamentally different from a rigid one. A rigid rotor is verified at a single speed; a flexible rotor must be confirmed in balance throughout its entire operating range. After the final corrections, the rotor is taken through a run-up, with vibration continuously monitored at key locations such as the bearings and the points of maximum deflection. The rotor is accepted only if the measured vibration stays below the pre-defined limits at all speeds — particularly while passing through each critical speed and while dwelling at the maximum continuous operating speed. This comprehensive check confirms that the rotor’s full dynamic behaviour has been brought under control.
5. The Field Dimension and Practical Tools
While much flexible-rotor work happens on high-speed balancing rigs, the same amplitude-and-phase measurement skills apply to field balancing and trim balancing once a machine is installed. A portable two-channel analyser such as the ಬ್ಯಾಲೆನ್ಸೆಟ್-1ಎ captures 1× amplitude and phase in the machine’s own bearings, computes influence coefficients, and lets an engineer apply and verify a trim correction at operating speed without disassembly — a frequent need for Class 2 quasi-rigid rotors that pass their shop balance yet still flex slightly in service. For installed medium and large machines, the dedicated in-situ procedures and safeguards of ISO 21940-13 apply alongside this part.
6. Key Concepts to Carry Away
- Flexible vs rigid behaviour: a rotor is treated as flexible once its operating speed reaches a significant fraction — typically above 70% — of its first bending natural frequency. As it spins faster, centrifugal forces bend it and change its unbalance.
- Critical speeds and mode shapes: knowing the rotor’s critical speeds and the shapes it bends into at each is essential; every mode is a separate balancing problem.
- Multi-plane, multi-speed: corrections in several planes, informed by measurements at several speeds, are the rule rather than the exception.
- Modal balancing: a powerful strategy in which weights are added specifically to counteract the unbalance of each bending mode at its anti-nodes.
