Balancing rigid and flexible rotors

It is well known that a part "that doesn't turn round" generates rotating forces due to installed imbalances, which increase as the speed of rotation increases:

This causes the machine to vibrate, due to the forces developed by the bearings to counteract the forces of the unbalances. The best-known manifestation of this is the crossing of a "critical speed", the coincidence of a rotor natural frequency and the speed of rotation. In any case, there must be no contact between rotor and stator, and the fatigue integrity of the installation must be respected. The solution is balancing, which consists in minimizing rotor imbalance.

Punctually, the problem is very simple. It involves bringing the center of mass back onto the axis of rotation. In general, rotors feature several wheels, disks, masses or couplings... mounted on a shaft which is longer than the largest outside diameter. The difficulty is that the unbalance distribution along the entire length of the rotor is unknown and, consequently, the point unbalance cannot be corrected individually! A more rigorous definition is that balancing is the process of minimizing the effect of unbalance on rotor vibrations and on the forces transmitted to the bearings.

The procedures used consist in applying a finite set of corrective unbalances to this unknown unbalance distribution, so that the assembly behaves satisfactorily. It is therefore a question of finding a compromise, the result of which is linked to the conditions chosen to carry out the balancing operation.

Preventive maintenance of rotating machines requires constant monitoring of their vibrations. Healthy behavior is synonymous with low and constant vibration levels over time.

The residual unbalance that governs synchronous vibration is an intrinsic quality of the machine, just like its energy performance.

This article describes balancing procedures and criteria. The focus is on machines such as electric motors, rotary pumps, turbines, compressors, fans, gears, etc., which are in particularly common use for any form of energy transformation. The rotors under consideration have two main properties:

• they are axisymmetric (axis of symmetry of revolution);

• they are isotropic (same properties in all radial directions).

Balancing of rigid rotors (at low speed) and flexible rotors (at nominal speed or in situ) will be presented. On...